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deduced

deduced Sentence Examples

  • Elisabeth immediately deduced what was going on.

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  • I cleverly deduced the location, checked birth dates and newly arrived individuals.

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  • The Mayas have left no r cord of their institutions or of the causes of their decline, beyond what may be deduced from their ruined structures.

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  • Sir John Murray deduced the mean height of the land of the globe as about 2250 ft.

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  • It is even somewhat precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions.

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  • - The leading features of Aegean civilization, as deduced from the evidence, must be stated very briefly.

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  • The mean height deduced for the land was 2300 ft.

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  • To clear up this last point for himself, Prince Andrew, utilizing his position and acquaintances, tried to fathom the character of the control of the army and of the men and parties engaged in it, and he deduced for himself the following of the state of affairs.

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  • And she deduced the essentials of his wishes quite correctly, and having once arrived at them clung to them tenaciously.

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  • Physical science, if there was anything deserving that name, was cultivated, not by experiment in the Aristotelian way, but by arguments deduced from premises resting on authority or custom.

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  • It can be deduced from (17), (12) and (13) that the couple on S'N' due to SN, and tending to increase 4), is MM' (sin 0 cos 4-2 sin 4) cos 0)/r'.

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  • For a long time the final result deduced by Joule by these varied and careful investigations was accepted as the standard value of the mechanical equivalent of heat.

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  • Utilizing the best of his detective training, he deduced she was as deaf as a turnip.

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  • In a particular case where the boiler pressure was maintained constant at 130 lb per square inch, and the cut-off was approximately 20% of the stroke, the values c =55 and b=o 031 were deduced, from which it will be found that the value of the piston speed corresponding to the maximum horsepower is 887 ft.

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  • In a refined form this method is often employed for measuring the intensity of a magnetic field at a given place, just as the intensity of gravity at different parts of the earth is deduced from observations of the rate at which a pendulum of known length vibrates.

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  • Utilizing the best of his detective training, he deduced she was as deaf as a turnip.

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  • I needed time to formulate a response to Detective Jackson's questions but I wished I had some idea of the extent of what he knew or had deduced.

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  • If AP =p, the element of volume is dx2xpdp, and the number A of particles to be found in it is deduced by the introduction of the factor n.

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  • This car is equipped with apparatus by means of which a continuous record of the draw-bar pull is obtained on a distance base; time indications are also made on the diagram from which the speed at any instant can be deduced.

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  • He ceased to attend the society in 1829, but he carried away from it the strengthening memory of failure overcome by persevering effort, and the important doctrinal conviction that a true system of political philosophy was "something much more complex and many-sided than he had previously had any idea of, and that its office was to supply, not a set of model institutions but principles from which the institutions suitable to any given circumstances might be deduced."

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  • The moment of a magnet may also be deduced from a measurement of the couple exerted on the magnet by a uniform field H.

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  • The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency ioo may be deduced from that at any other frequency n by simply multiplying by too n.

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  • The third column shows the relative amount of hysteresis deduced by Ewing as a general mean from actual tests of many samples (Journ.

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  • The following approximate figures for small magnetizing forces are deduced from Hopkinson's curves: 9 Proc. Roy.

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  • Hence may be deduced an explanation of the fact that, while the susceptibility of all known diamagnetics (except bismuth and antimony) is independent of the temperature, that of paramagnetics varies inversely as the absolute temperature, in accordance with the law of Curie.

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  • 2 From the fundamental principle of virtual velocities, which thus acquired a new significance, Lagrange deduced, with the aid of the calculus of variations, the whole system of mechanical truths, by processes so elegant, lucid and harmonious as to constitute, in Sir William Hamilton's words, "a kind of scientific poem."

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  • Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

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  • From a measurement of the maximum distance the least angle between consecutive lines consistent with resolution may be deduced, and a comparison made with the rule stated above.

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  • Following, unknown to himself, in the footsteps of Young, he deduced the principle of interference from the circumstance that the darkness of the interior bands requires the co-operation of light from both sides of the obstacle.

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  • It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.

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  • He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections.

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  • Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

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  • The configurations of the pentaand tetra-aldoses have been determined by similar arguments; and those of the ketoses can be deduced from the aldoses.

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  • They have been identified with the AKarcpoc (perhaps AkKhazari, or White Khazars) who appear upon the lower Volga in the Byzantine annals, and thence they have been deduced, though with less convincing proof, either from the AyetOvpvoc (Agathyrsi) or the Kariapoc of Herodotus, iv.

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  • historically deduced (London, 1703).

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  • And as these truths were self-evident, so the religion he deduced from them was sufficient, not only for his own moral and intellectual nature, but also for man as he conceived him, for history as he knew it, and for society as he saw it.

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  • This is at once connected with the nebular hypothesis, and subsequently deduced "from the ultimate law of the" persistence of force,"and finally supplemented by a counter-process of dissolution, all of which appears to Spencer only as" the addition of Von Baer's law to a number of ideas that were in harmony with it."It is clear, however, that Spencer's ideas as to the nature of evolution were already pretty definite when Darwin's Origin of Species (1859) revolutionized the subject of organic evolution by adding natural selection to the direct adaptation by use and disuse, and so suggesting an intelligible method of producing modifications in the forms of life.

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  • § 99a (3rd ed., 1892), where the expression in question is deduced as a corollary of Green's theorem.

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  • Applying the above equation to a gas obeying the law pv=RT, for which the work done in isothermal expansion from a volume i to a volume r is W=RT loger, whence dW=R log e rdt, he deduced the expression for the heat absorbed by a gas in isothermal expansion H=R log er/F'(t).

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  • Holtzmann (1845) by the same assumption deduced the value J/T for the function F'(t), but obtained erroneous results by combining this assumption with the caloric theory.

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  • Clausius (1850), applying the same assumption, deduced the same value of F'(t), and showed that it was consistent with the mechanical theory and Joule's experiments, but required that a vapour like steam should deviate more considerably from the gaseous laws than was at that time generally admitted.

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  • - The most important and most useful of the relations between the thermodynamical properties of a substance may be very simply deduced from a consideration of the indicator diagram by a geometrical method, which is in many respects more instructive than the analytical method generally employed.

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  • It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÆC) XEC. The ratio BEÆC of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.

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  • The final state of the substance, when equilibrium has been restored, may be deduced from this condition, if the energy can be expressed in terms of the co-ordinates.

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  • The atomic weight of gold was first determined with accuracy by Berzelius, who deduced the value 195.7 (H= i) from the amount of mercury necessary to precipitate it from the chloride, and 195.2 from the ratio between gold and potassium chloride in potassium aurichloride, KAuC1 4.

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  • The important part played by the residual air in the globe had also been deduced by Osborne Reynolds from observing that on turning off the light, the vanes came to rest very much sooner than the friction of the pivot alone would account for; in fact, the rapid subsidence is an illustration of Maxwell's great theoretical discovery that viscosity in a gas (as also diffusion both of heat and of the gas itself) is sensibly independent of the density.

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  • From this evidence it has been deduced that a king called Kozulokadphises, Kujulakasa or Kieu-tsieu-k'io (?

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  • The result was a treatise in which he deduced practical conclusions from the past history and present temper of the city, blending these with his favourite principles of government in general.

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  • By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured.

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  • Instead of the expensive mile-long stout hemp lines used and since 1887 those of the prince of Monaco in his yachts, as by Ross, Maury introduced a ball of strong twine attached to a well as numerous Danish vessels in the sea between Iceland and cannon shot, which ran it out rapidly; when the bottom was Greenland, conspicuous amongst which were the expeditions reached the twine was cut and the depth deduced from the length in1896-1898on board the " Ingolf."

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  • Aime showed that on a calm bright day in the Mediterranean the temperature rose o 1° C. between the early morning and noon at a depth of about 12 fathoms. Luksch deduced a much greater penetration of solar warmth from the comparison of observations at different hours at neighbouring stations in the eastern Mediterranean, but his methods were not exact enough to give confidence in the result.

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  • From this meaning is deduced that of the person in whom lies the right of presenting to public offices, privileges, &c., still surviving in the title of the Patronage Secretary of the Treasury in Great Britain.

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  • From the hypothesis of an external world a series of contradictions are deduced, such as that the world is both finite and infinite, is movable and immovable, &c.; and finally, Aristotle and various other philosophers are quoted, to show that the external matter they dealt with, as mere potentiality, is just nothing at all.

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  • Of these, evidently the first must be the fundamental; to some extent it conditions the other two, though these cannot be deduced from it or proved by it.

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  • Thus in the Rechtslehre and Sittenlehre, the multiplicity of egos is deduced, and with this deduction the first form of the Wissenschaftslehre appeared to end.

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  • This opinion is deduced from our experience of the behaviour of bodies of sensible size, but we have no experimental evidence that two atoms may not sometimes coincide.

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  • In like manner, after the French mathematicians had attempted, with more or less ingenuity, to construct a theory of elastic solids from the hypothesis that they consist of atoms in equilibrium under the action of their mutual forces, Stokes and others showed that all the results of this hypothesis, so far at least as they agreed with facts, might be deduced from the postulate that elastic bodies exist, and from the hypothesis that the smallest portions into which we can divide them are sensibly homogeneous.

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  • Soc., 1890, 46, p. 74) deduced the value 89.95.

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  • The expression 27ra for the length of the circumference can be deduced by considering the limit of the area cut off from a circle of radius a by a concentric circle of radius a - a, when a becomes indefinitely small; this is an elementary case of differentiation.

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  • It may be deduced from the formula given above.

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  • This might have been deduced directly from Simpson's first formula, by a series of eliminations.

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  • The general principle is that the numerical data from which a particular result is to be deduced are in general not exact, but are given only to a certain degree of accuracy.

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  • The velocity deduced at 8.1° C. was U=1435 met./sec., agreeing very closely with the value calculated from the formula U 2 = E/p.

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  • The amount radiated out in the form of sound waves is deduced, and hence the energy of the stream at any distance is known.

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  • In the other, the waves produce a measurable effect on a vibrating system of the same frequency, and the amplitude in the waves can be deduced.

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  • The relative antiquity of the earlier settlements of the Stone and Bronze ages is not capable of being deduced from existing evidence.

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  • Hence the formula is more useful in the form w = (w i +w2)1 2 / (Kd -1 2) = (wl +w 2)lr/ (K -lr) where k= (wl+w2-1-w3)lr/w3 is to be deduced from the data of some bridge previously designed with the same working stresses.

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  • - f min ., from which the working stress is deduced, is not the ordinary range of stress which is repeated a practically infinite number of times, but is a range of stress to which the bridge is subjected only at comparatively long intervals.

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  • The evidence for the existence of the luminiferous aether has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium, as deduced from the phenomena of light, have been found to be precisely those required to explain electromagnetic phenomena."

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  • Philosophical truth, as deduced from the teaching of Aristotle, it was said, directly contradicts the teaching of the church, which determines truth in theology; but the contradiction leaves the authority of the latter unimpaired in its own sphere.

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  • From Maskelyne's observations Charles Hutton deduced a density for the earth 4.5 times that of water (ib.

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  • 184, 254) also deserve mention, as well as his discussions of the rotation of Mars, by which he deduced its period with a probable error of 0 9.005.

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  • He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.

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  • 2 4 2m +2 2m+4; the function of zero order C is deduced by making m= o, and is equivalent to the series I -22 -}- 2-.4-, , &c. O.

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  • iv.), His choice of Israel, and the love and faithfulness which He had shown towards it, by redeeming it from slavery in Egypt, and planting it in a free and fertile land; from which are deduced the great practical duties of loyal and loving devotion to Him, an uncompromising repudiation of all false gods, the rejection of all heathen practices, a cheerful and ready obedience to His will, and a warm-hearted and generous attitude towards man.

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  • For the weight of the cubic decimetre of water, as deduced from the experiments made in London in 1896 as to the weight of the cubic inch of water, D.

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  • 3: Objects which have been made by measure or weight, and from which the unit of construction can be deduced.

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  • For the length of the building cubit Sir C. Warren has deduced a length equivalent to 20.6169 English inches, which compares with a mean Pyramid cubit of 20.6015 in.

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  • As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit.

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  • If this unit haS any connexion with the kat, it is that a kat of gold is worth 15 shekels or 1/4 mina of silver; this agrees well with the range of both units, only it must be remembered that 129 was used as gold unit, and another silver unit deduced from it.

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  • m r = r logo m, logo m= (I /r) logo m, which may be readily deduced from the definition of a logarithm.

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  • The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.

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  • The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

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  • From (i.) and (ii.) it may be deduced that exp x= (I !

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  • He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.

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  • Briggs calculated in a similar manner log 6, and thence deduced log 3.

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  • the former of these equations gives a convergent series for logep, and the latter a very convergent series by means of which the logarithm of any number may be deduced from the logarithm of the preceding number.

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  • to 276 places of decimals, and deduced the value of log e lo and its reciprocal M, the modulus of the Briggian system of logarithms. The value of the modulus found by Adams is Mo = 0-43429 44 81 9 03251 82765 11289 18916 60508 22 943 97 00 5 80366 65661 14453 78316 58646 4920-8870 77 47292 2 4949 33 8 43 17483 18706 106 74 47 6630-3733 64167 92871 58963 90656 92210 64662 81226 58521 27086 56867 03295 9337 0 86965 88266 88331 16360 773849 0514 28443 48666 76864 65860 85135 56148 212 34 87653 43543 43573 25 which is true certainly to 272, and probably to 273, places (Proc. Roy.

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  • The fundamental features of knowledge, whether as activity or as sum of apprehended fact, and of conduct had been deduced as elements necessary in the attainment of self-consciousness.

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  • Properties of the limagon may be deduced from its mechanical construction; thus the length of a focal chord is constant and the normals at the extremities of a focal chord intersect on a fixed circle.

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  • Matter is deduced by the "original synthesis."

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  • as usual, over the east walk; but, as a general rule, the arrangements deduced from the examples described may be regarded as invariable.

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  • The general equation to the circle in trilinear co-ordinates is readily deduced from the fact that the circle is the only curve which intersects the line infinity in the circular points.

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  • The general equation to a circle in this system of co-ordinates is deduced as follows: If p be the radius and 1p+mg+nr=o the centre, we have p= (lpl+mgi+nri)/(l+m+n), in which i, q i, r i is a line distant p from the point 1p+mq+nr= o.

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  • The readings of X which can be deduced from considering the agreements in B, C, D will be of higher antiquity and of greater external aut l ority than any of the readings in B, C, D taken singly.

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  • The Value Of L Is Always Given By The Formula For The Dominical Letter, And P And 1 Are Easily Deduced From The Epact, As Will Appear From The Following Considerations.

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  • The Times Of All Future New Moons May Consequently Be Deduced By Successively Adding 29 Days 12 Hours 44 Min.

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  • To Compute The Times Of The New Moons Which Determine The Commencement Of Successive Years, It Must Be Observed That In Passing From An Ordinary Year The New Moon Of The Following Year Is Deduced By Subtracting The Interval That Twelve Lunations Fall Short Of The Corresponding Gregorian Year Of 365 Or 366 Days; And That, In Passing From An Embolismic Year, It Is To Be Found By Adding The Excess Of Thirteen Lunations Over The Gregorian Year.

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  • The Gregorian epact being the age of the moon of Tebet at the beginning of the Gregorian year, it represents the day of Tebet which corresponds to January I; and thus the approximate date of Tisri I, the commencement of the Hebrew year, may be otherwise deduced by subtracting the epact from Sept.

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  • From the measured distances of the diffraction bands the width of the slit may be easily deduced.

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  • Taking the Trunk and Main Branch Series, we find they depend altogether on the four constants: al, b, a', b', while N is a universal constant identical with that deduced from the hydrogen series.

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  • Riecke, 3 who deduced a differential equation of the 10th order.

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  • Kant first deduced that from the experience of mental phenomena all logical use of reason is limited to mental phenomena, and then maintained that to explain moral responsibility practical reason postulates the existence of real noumena.

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  • Applying this " synechological view " to the supposed inclusion of soul in soul, he deduced the conclusion that, as here the nature of one's soul is to unite one's little body, so hereafter its essence will be to unite a greater body, while God's spirit unites the whole world by His omnipresence; and he pertinently asked, in opposition to the " punctual " view, whether God's soul is centred in a point.

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  • But his substitute was his own hypothesis of panpsychism, from which he deduced a "cosmorganic " evolution from a " cosmorganic " or original condition of the world as a living organism into the inorganic, by the principle of tendency to stability.

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  • Hence he deduced that whatever we know from sensations arranged in such a priori forms are objects of our own experience and mental phenomena.

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  • Its consistency, as deduced by Lange, was to reduce all use of reason, speculative and practical, to its logical use of proceeding from the assumed mental data of outer and inner sense, arranged a priori, to mental phenomena of experience, beyond which we can conceive ideas but postulate nothing.

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  • Hence, from the two observations the value of the earth's total force can be deduced.

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  • Trans., 1839) deduced his method of correcting the compass by permanent magnets and soft iron, giving practical rules for the same in 1840.

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  • But this proof was rather insufficient, as indeed it was felt to be, and, in any case, nothing could be deduced from it save a kind of precedence in honour, which was never contested even by the Greeks.

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  • Thus F = r(n - I) + 2 - n(r - t) = n - r + 2, a result which was deduced by J.

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  • But at intermediate compositions we can only guess at the form of the energy-composition curve, and the freezing point composition curve, deduced from it, will vary according to the supposition which we make.

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  • But the elucidation of the complicated phenomena of solid solutions would have been impossible without the theoretical knowledge deduced from the principle of available energy.

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  • The experiments of Raoult on solutions of organic bodies in water and on solutions of many substances in some dozen organic solvents have confirmed this result, and therefore the theoretical value of the osmotic pressure from which it was deduced.

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  • All the thermodynamic relations we have deduced hold on any theory of solution and favour no one theory rather than another.

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  • In the limit of dilution when n is very small compared with N this gives Raoult's experimental law that the relative lowering is n/N, which we deduced from the osmotic law, and conversely from which the osmotic law follows, while for more concentrated solutions agreement is obtained by assigning arbitrary values to a, which, as we have seen, is 5 in the case of cane-sugar.

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  • It pointed out distinctly and temperately the grounds of the right of punishment, and from these principles deduced certain propositions as to the nature and amount of punishment which should be inflicted for any crime.

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  • He himself tells us that when, after the publication of the original essay, the main argument of which he had deduced from David Hume, Robert Wallace, Adam Smith and Richard Price, he began to inquire more closely into the subject, he found that "much more had been done" upon it "than he had been aware of."

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  • It is, in fact, the confluence of the Malthusian ideas with the theories of Ricardo, especially with the corollaries which the latter deduced from the doctrine of rent (though these were not accepted by Malthus), that has led to the introduction of population as an element in the discussion of so many economic questions in modern times.

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  • The method of Forbes (in which the conductivity is deduced from the steady distribution of temperature on the assumption that the rate of loss of heat at each point of the bar is the same as that observed in an auxiliary experiment in which a short bar of the same kind is set to cool under conditions which are supposed to be identical) is well known, but a consideration of its weak points is very instructive, and the results have been most remarkably misunderstood and misquoted.

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  • The heat Q transmitted in a given time T may be deduced from an observation of the rise of temperature of the water, and the amount which passes in the interval.

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  • The gradient near the entrance to the calorimeter was deduced from observations with five thermometers at suitable intervals along the bar.

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  • Ire these methods the flow of heat is deduced from observations of the rate of change of temperature with time in a body exposed to known external or boundary conditions.

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  • The diffusivity can be deduced from observations at different depths x' and x", by observing the ratio of the amplitudes, which is (x '- x ") for a simple-harmonic wave.

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  • In any case results deduced from the annual wave must be expected to vary in different years according to the distribution of the rainfall, as the values represent averages depending chiefly on the diffusion of heat by percolating water.

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  • The following are a few typical values for sand or gravel deduced from the annual wave in different localities: - [[Table Ii]].

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  • It is probable for this reason that the average conductivity of the earth's crust, as deduced from surface observations, is too large; and that estimates of the age of the earth based on such measurements are too low, and require to be raised; they would thereby be brought into better agreement with the conclusions of geologists derived from other lines of argument.

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  • He deduced the variations of the mean temperature of a section of a bar from the sum S of the E.M.F.'s of a number of couples, inserted at suitable equal intervals 1 and connected in series.

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  • In this case the curve representing the distribution of temperature is a parabola, and the conductivity k is deduced from the mean rise of temperature (R-R°)/aR° by observing the increase of resistance R-R° of the bar, and the current C. It is also necessary to measure the cross-section g, the length 1, and the temperature-coefficient a for the range of the experiment.

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  • This proposition, which he called the mystic hexagram, he made the keystone of his theory; from it alone he deduced more than 400 corollaries, embracing, according to his own account, the conics of Apollonius, and other results innumerable.

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  • Also, whilst the mean azimuths deduced from the observations between 6 A.M.

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  • The assumption may be a reasonable one, and if the results agree with probabilities as deduced from the rest of the evidence it is wise to adopt it; if on the other hand the other evidence seems in any serious degree contrary to those results it may be surmised that the assumption is faulty in some particular.

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  • They had learned to read God's will in the events of history, and deduced (for example) the doctrine of the resurrection of the dead from the death of the martyrs under Antiochus Epiphanes and Alcimus.

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  • From a discussion of the observations of Mars made in 1860 and 1862 at Greenwich and Williamstown (near Melbourne), Stone deduced for it a value of 8.932" (Mon.

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  • It is considered to be an extinct volcano because it makes the plumb-line deviate only 7" to 8", from which it is deduced that the mountain is hollow.

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  • The simplest equation to the parabola is that which is referred to its axis and the tangent at the vertex as the axes of co-ordinates, when it assumes the form y 2 = 4ax where as = semilatus rectum; this may be deduced directly from the definition.

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  • Other forms which correspond to other relations between the roots can be readily deduced from the most general form.

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  • Fawsitt (The Education of the Examiner, Royal Philosophical Society of Glasgow, 1905) shows that frequency-curves deduced from actual investigation of class-marks are not symmetrical, but have two maxima corresponding to the performance of " non-workers " and of " workers."

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  • Reason contains principles which we cannot demonstrate, but which can be deduced, and are the proper objects of belief.

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  • In 1754 Euler communicated to the Berlin Academy a further memoir, in - which, starting from the hypothesis that light consists of vibrations excited in an elastic fluid by luminous bodies, and that the difference of colour of light is due to the greater or less frequency of these vibrations in a given time, he deduced his previous results.

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  • experiments quoted by Dollond, because he asserted that the difference between the law deduced by Newton and that which he assumed would not be rendered sensible by such an experiment.

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  • 4 Dollond did not reply to this memoir, but soon afterwards he received an abstract of a memoir by Samuel Klingenstierna, the Swedish mathematician and astronomer, which led him to doubt the accuracy of the results deduced by Newton on the dispersion of refracted light.

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  • The following are some of the values deduced by well-known experimentalists for the latent heat of fusion: - Regnault, 79.06 to 79.24 calories, corrected by Person to 79.43; Person, 79.99 calories; Hess, 80.34 calories; Bunsen, 80.025 calories.

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  • The Values Deduced In This Manner For The Equivalent Agreed As Closely As Could Be Expected Considering The Impossibility Of Regulating The External Condition Of Temperature And Moisture With Any Certainty In An Engine Room.

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  • The Resistance R Could Be Deduced From A Knowledge Of The Temperature Of The Calorimeter And The Coefficient Of The Wire.

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  • In Spite Of The Large Corrections The Results Were Extremely Consistent, And The Value Of The Temperature Coefficient Of The Diminution Of The Specific Heat Of Water, Deduced From The Observed Variation In The Rate Of Rise At Different Points Of The Range 15° To 25°, Agreed With The Value Subsequently Deduced From Rowland'S Experiments Over The Same Range, When His Thermometers Were Reduced To The Same Scale.

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  • The Absolute Value Of The Specific Heat Deduced Necessarily Depends On The Absolute Values Of The Electrical Standards Employed In The Investigation.

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  • The Specific Heat Itself Can Be Deduced Only By Differentiating The Curve Of Observation, Which Greatly Increases The Uncertainty.

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  • The Value 4.180 Joules At 20° C. Is The Mean Between Rowland'S Corrected Result 4.181 And The Value 4.179, Deduced From The Experiments Of Reynolds And Moorby On The Assumption That The Ratio Of The Mean Specific Heat O° To 100° To That At 20° Is 1.043'6, As Given By The Formulae Representing The Results Of Callendar And Barnes.

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  • No Doubt There Must Be Approximate Relations Between The Atomic And Molecular Heats Of Similar Elements And Compounds, But Considering The Great Variations Of Specific Heat With Temperature And Physical State, In Alloys, Mixtures Or Solutions, And In Allotropic Or Other Modifications, It Would Be Idle To Expect That The Specific Heat Of A Compound Could Be Accurately Deduced By Any Simple Additive Process From That Of Its Constituents.

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  • and its companion a diameter of 830,000 m.; the distance between their centres cannot be deduced without making certain doubtful assumptions, but may be about 3,000,000 m.

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  • Frost have deduced that the average speed is only 8 m.

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  • Halm deduced a velocity of 20.8 km.

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  • Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

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  • Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.

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  • Hitherto the assumption of the probable as true rather than as what will be conceded in debate ° has been the main distinction of the standpoint of analytic from that of dialectic. But the true is true only in reference to a coherent system in which it is an immediate ascertainment of van, or to be deduced from a ground which is such.

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  • A principle is transcendentally " deduced " when it and only it can explain the validity of some phase of experience, some order Limitation of truths.

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  • Nature, e.g., is not deduced as real because rational, but being real its rationality is presumed and, very imperfectly, exhibited in a way to make it possible to conceive it as in its essence the reflex of Reason.

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  • Arrhenius, by reasoning similar to that of section 5, applied to an osmotic cell supporting a column of solution by osmotic pressure, deduced the relation between the osmotic pressure P at the bottom of the column and the vapour-pressure p" of the solution at the top, viz.

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  • The rate of change of the latent heat is easily deduced from that of the total heat by subtracting the specific heat of the liquid.

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  • The deviations from the ideal volume may also be deduced by the method of Joule and Thomson.

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  • Formula (23) for the vapour-pressure was subsequently deduced by Rankine (Phil.

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  • The form (I) is deduced from it by putting itt, and taking t to be infinitely small.

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  • It may also be deduced from the principles of linear and angular momentum as embodied in the equations (9).

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  • By its aid, for example, the whole of the properties a elliptical arches, whether square or skew, whether level or sloping in their span, are at once deduced by projection from those of symmetrical circular arches, and the properties of ellipsoidal and ellipticconoidal domes from those of hemispherical and circular-conoidal domes; and the figures of arches fitted to resist the thrust of earth, which is less horizontally than vertically in a certain given ratio, can be deduced by a projection from those of arches fitted to resist the thrust of a liquid, which is of equal intensity, horizontally and vertically.

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  • The following empirical formulae for the stiffness of hempen ropes have been deduced by Mono from the experiments of Coulomb: Let F be the stiffness in pounds avoirdupois; d the diameter of the rope In inches, fl = 48d2 for white ropes and 35d2 for tarred ropes; r the effectire radius of the pulley in inches; T the tension in pounds.

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  • At intermediate instants, however, other principles have also to be taken into account, which are deduced from the second law of motion, as applied to direct deviation, or acceleration and retardation.

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  • The standard mortality of each community is deduced from a life-table, representing a "generation" of people assumed to be born at the same moment and followed throughout their hypothetical life, in the light of the distribution by age ascertained.

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  • 800 and 1004, extracted from Caussin's translation of Ibn Junis, the eclipses and occultations of Bullialdus, Gassendi, and Hevelius, of the French astronomers at Paris and St Petersburg, and of Flamsteed at Greenwich, and deduced a secular acceleration of 8.8", agreeing well with the theoretical value.

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  • He discovered a function, which has been called the potential of one circuit on another, from which he deduced a theory of induction, completely in accordance with experiment.

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  • Weber at the same time deduced the mathematical laws of induction from his elementary law of electrical action, and with his improved instruments arrived at accurate verifications of the law of induction which by this time had been developed mathematically by Neumann and himself.

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  • For the hydrogen atom the ratio of charge to mass as deduced from electrolysis is about Io 1.

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  • von Rohr, Die Bilderzeugung in optischen Instrumenten, pp. 3 1 7-3 2 3) have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically (pp. 212-316).

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  • This he is supposed + to have deduced, no one knows how, from Wallis' formula for ??r, v 3.3.5.5.7.7 4 ...

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  • A more definite date cannot be deduced from the evidence at our disposal, but his era may safely be placed as far back as 1000 B.C.

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  • When turbines, as often happens in land practice, are directly coupled to electrical generators, their horse-power can be deduced from the electrical output.

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  • In the Supplement to the Theory of Capillary Action, Laplace deduced the equation of the surface of the fluid from the condition that the resultant force on a particle at the surface must be normal to the surface.

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  • The early writers on capillary action supposed that the diminution of capillary action was due simply to the change of density corresponding to the rise of temperature, and, therefore, assuming the surface-tension to vary as the square of the (37)?(f) =eP f (38) density, they deduced its variations from the observed dilatation of the liquid by heat.

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  • The tension of the surface separating two liquids which do not mix cannot be deduced by any known method from the tensions of the surfaces of the liquids when separately in contact with air.

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  • p. 463) deduced relative to the interfacial tensions of three bodies.

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  • The fact that a pair of plates which repel one another at a certain distance may attract one another at a smaller distance was deduced by Laplace from theory, and verified by the observations of the abbe Haiiy.

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  • From the pitch of the note due to a jet of given diameter, and issuing under a given head, the wave-length of the nascent divisions can be at once deduced.

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  • The diameter of the orifice was 3 millims., from which that of the jet is deduced by the introduction of the coefficient 8.

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  • The theological calmness of the West, amid the violent theological disputes which troubled the Eastern patriarchates, and the statesmanlike wisdom of Rome's greater bishops, combined to give a unique position to the pope, which councils in vain strove to shake, and which in time of difficulty the Eastern patriarchs were fain to acknowledge and make use of, however they might protest against it and the conclusions deduced from it.

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  • While Aquinas affirmed the positions of Augustine, he deduced them from his Aristotelian conception of God as "first mover, itself unmoved."

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  • The inference to be deduced from the foregoing is plainly this, that even in large-bodied, small-winged insects and birds the wing-surface is greatly in excess, the surplus wing area supplying Not, FIG.

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  • The history of the origin of the land-forms of England, as far as they have been deduced from geological studies, is exceedingly complicated.

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  • In 1377 the levying of a polltax provides partial figures from which a total of two to twoand-a-half millions has been deduced, but again divergent views have been expressed as to how far the number was still affected by the Black Death of 1348-1349.

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  • Torricelli, by employing the "method of indivisibles," deduced that the area was exactly three times that of the generating circle; this result had been previously established in 1640 in France by G.

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  • Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.

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  • The radius of curvature at any point is readily deduced from the intrinsic equation and has the value p=4 cos 40, and is equal to twice the normal which is 2a cos 2B.

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  • Bruns in 1889; measured an arc of the meridian in East Prussia in 1831-1832; and deduced for the earth in 1841 an ellipticity of 2 4 9.

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  • Airy deduced a parallax of 8.76" and E.

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  • Stone 8.88"; from the French observations of the same date Stone deduced 8.88" and V.

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  • Trans., 1813 and 181 4) he deduced that the illuminating power of the former exceeded that of the latter in the proportion of 5: 2.

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  • Connected with these doctrines was their famous theory of the "rehabilitation of the flesh," deduced from the philosophic theory of the school, which was a species of Pantheism, though they repudiated the name.

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  • Conservtiv~ politicians deduced from these circumstances the necessity of applying firm government to Ireland.

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  • His cardinal position, from which he deduced so many important conclusions, namely, that the parts and organs of the old constitution of France were sound, and only needed moderate invigoration, is absolutely mistaken and untenable.

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  • It serves as a means of research, more particularly in mathematical investigations, the simple laws thus deduced being subsequently modified by introducing assumptions in order to co-ordinate actual experiences.

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  • The fact that men give different answers to moral problems which seem similar in character, or even the mere fact that men disregard, when they act immorally, the dictates and implicit principles of the moral consciousness is certain sooner or later to produce the desire either, on the one hand, to justify immoral action by casting doubt upon the authority of the moral consciousness and the validity of its principles, or, on the other hand, to justify particular moral judgments either by (the only valid method) an analysis of the moral principle involved in the judgment and a demonstration of its universal acceptation, or by some attempted proof that the particular moral judgment is arrived at by a process of inference from some universal conception of the Supreme Good or the Final End from which all particular duties or virtues may be deduced.

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  • It will be seen that neither Reid nor Stewart offers more than a very meagre and tentative contribution to that ethical science by which, as they maintain, the received rules of morality may be rationally deduced from self-evident first principles.

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  • For the belief that moral obligation is absolute in character, that it is alike impossible to explain its origin and transcend its laws, would make the search for a scientific criterion of conduct to be deduced from the laws of life and conditions of existence meaningless, if not absurd.

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  • In the case of the greater number of the fixed stars this is so slow that centuries may have to elapse before motion can be deduced.

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  • In China, Egypt and Babylonia, strength and continuity were lent to this native tendency by the influence of a centralized authority; considerable proficiency was attained in the arts of observation; and from millennial stores of accumulated data, empirical rules were deduced by which the scope of prediction was widened and its accuracy enhanced.

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  • Tobias Mayer of Göttingen (1723-1762) originated the mode of adjusting transit-instruments still in vogue; drew up a catalogue of nearly a thousand zodiacal stars (published posthumously in 1775); and deduced the proper motions of eighty stars from a comparison of their places as given by Olaus Romer in 1706 with those obtained by himself in 1756.

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  • The agreement thus brought about between the results deduced from the law of radiation and the most delicate observa tions of the quantity of heat radiated is of great interest, as showing that the theory of cosmicai temperature now rests upon a sound basis.

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  • The verb "to dress" has various applications which can be deduced from its original meaning.

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  • Creation, itself a free and non-temporal act of God's love and will, cannot be speculatively deduced, but must be accepted as an historic fact.

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  • From a series of elaborate experiments, Person deduced o 505 as the specific heat of ice, or about half that of water.

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  • From this or otherwise it is readily deduced that the ordinates of an ellipse and of the circle described on the major axis are in the ratio of the minor to the major axis.

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  • The area of the ellipse is 7rab, where a, b are the semi-axes; this result may be deduced by regarding the ellipse as the orthogonal projection of a circle, or by means of the calculus.

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  • That this is actually the case is proved by experiments on the interference of polarized light, from which it may be deduced that the polarization-vector of a train of plane waves of plane polarized light executes rectilinear vibrations in the plane of the waves.

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  • 149) has shown that the results deduced from Airy's waves of permanent type may be obtained by regarding the action of the medium as the superposition of the effects of ordinary double refraction and of an independent rotary power.

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  • Conceiving that the simplest principle is the most likely to be true, he assumed as a postulate that bodies falling freely towards the earth descend with a uniformly accelerated motion, and deduced thence that the velocities acquired are in the direct, and the spaces traversed in the duplicate ratio of the times, counted from the beginning of motion; finally, he proved, by observing the times of descent of bodies falling down inclined planes, that the postulated law was the true law.

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  • of any couple can be at once deduced by addition from the values given by its components with a single standard metal.

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  • are easily deduced from the tabulated values of dE/dt and d2E/dt2 respectively.

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  • The value found at a temperature of 150° C. was +2.5 microjoules per ampere-second per degree, or +2.5 microvolts per degree in the case of copper, which agrees very fairly with the value deduced from thermoelectric tests.

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  • But, again, in what particular respects he wishes it to be reformed can be best deduced from Aim of the certain preponderant ideas which make themselves felt in the apocryphal documents.

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  • a map of the heavens at the hour of birth, showing, according to the Ephemeris, the position of the heavenly bodies, from which their influence may be deduced.

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  • From this conception all the properties of conics can be deduced.

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  • Desargues has a special claim to fame on account of his beautiful theorem on the involution of a quadrangle inscribed in a conic. Pascal discovered a striking property of a hexagon inscribed in a conic (the hexagrammum mysticum); from this theorem Pascal is said to have deduced over 400 corollaries, including most of the results obtained by earlier geometers.

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  • He has not in any way "deduced" space and time, but, proceeding from the ordinary current view of sense-experience, has found these remaining as residuum after analysis.

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  • The system of principles which may be deduced from the consideration of the mode in which understanding and sense are united by productive imagination is the positive result of the critical theory of knowledge, and some of its features are remarkable enough to deserve attention.

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  • The method for superposing the two spaces on one another was deduced by Sir David Brewster in 1856, but he does not appear to have dealt with the problem of range-finding.

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  • I needed time to formulate a response to Detective Jackson's questions but I wished I had some idea of the extent of what he knew or had deduced.

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  • I cleverly deduced the location, checked birth dates and newly arrived individuals.

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  • Elisabeth immediately deduced what was going on.

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  • Of what nature were the conclusions deduced from this scrutiny?

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  • deduced very easily from another.

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  • I quickly deduced that I wouldn't be finding the pack where I left it.

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  • deduced from the variational principle.

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  • deduced from the context.

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  • deduced from histochemical analysis using cryosections.

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  • All this may be deduced from reading the first epistle.

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  • Of the building situated against the river frontage little can be deduced.

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  • Thus, he strived to advance the principle of materialism and deduced a property of ideality from certain aspects of material praxis.

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  • protrudewas a mysterious little device protruding from the side of the box which I quickly deduced was a stage movement.

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  • Surface winds over the ocean will be deduced from scatterometer data and sea surface temperature (SST) from satellite radiometers.

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  • But Russell skilfully reminds the reader that if causes are deduced from wrong effects then the causes themselves will be wrong.

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  • Moreover, she deduced that the Union Jack's chief sub-editor must of course be Tinker.

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  • The above gives some idea of the evidence that has been accumulated in favour of the laws of chemical combination, laws which can be deduced from the atomic theory.

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  • In the former the author sets forth the analytical process by which the laws he discovered were deduced from facts.

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  • P. Baxter and others deduced the value 58.995 (0 =16).

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  • If AP =p, the element of volume is dx2xpdp, and the number A of particles to be found in it is deduced by the introduction of the factor n.

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  • With a view to this, it has become increasingly common of late years to publish not the voltages actually observed, but values deduced from them for the potential gradient in the open in volts per metre.

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  • It is even somewhat precipitate to assume that a mean value deduced from a single year is fairly representative of average conditions.

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  • Mazelle (47) deduced an increase of about 3% in a + for a rise of I km.

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  • He inserted a slip of metal, of variable breadth, at the focus of the telescope, and observed at what part it exactly covered the object under examination; knowing the focal length of the telescope and the width of the slip at the point observed, he thence deduced the apparent angular breadth of the object.

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  • " Scarcely any supposition," 2 he says, " can be made from which the same result, though possibly with greater difficulty, might not be deduced by the same laws of nature; for since, in virtue of these laws, matter successively assumes all the forms of which it is capable, if we consider these forms in order, we shall at one point or other reach the existing form of the world, so that no error need here be feared from a false supposition."

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  • From a fresh discussion of the transits of Venus in 1761 and 1769 he deduced (1822-1824) a solar parallax of 8" 57, long accepted as authoritative.

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  • He showed that the heat motion of particles, which is too small to be perceptible when these particles are large, and which cannot be observed in molecules since these themselves are too small, must be perceptible when the particles are just large enough to be visible and gave complete equations which enable the masses themselves to be deduced from the motions of these particles.

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  • For a long time the final result deduced by Joule by these varied and careful investigations was accepted as the standard value of the mechanical equivalent of heat.

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  • It is interesting to observe that though deduced exclusively from the study of flowering plants, they are in substantial agreement with those now generally adopted by zoologists, and may therefore be presumed to be on the whole natural.

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  • Applying this principle to the art of poetry, and analysing, line by line and even word by word, the works of great poets, he deduced the law that the beauty of poetry consists in the accuracy, beauty and harmony of individual expression.

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  • This was no new idea; it had been fami:iar for centuries in a less definite form, deduced from a priori considerations, and so far as regards the influence of surrounding circumstances upon man, Kant had already given it full expression.

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  • Sir John Murray deduced the mean height of the land of the globe as about 2250 ft.

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  • He showed that an imaginary spheroidal shell, concentric with the earth and cutting the slope between the elevated and depressed areas at the contour-line of 1700 fathoms, would not only leave above it a volume of the crust equal to the volume of the hollow left below it, but would also divide the surface of the earth so that the area of the elevated region was equal to that of the depressed region.6 A similar observation was made almost simultaneously by Romieux, 7 who further speculated on the equilibrium between the weight of the elevated land mass and that of the total Areas of waters of the ocean, and deduced some interesting relathe cru st tions between them.

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  • The mean height deduced for the land was 2300 ft.

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  • It must be noted, however, that since 1895 the soundings of Nansen in the north polar area, of the " Valdivia," " Belgica," " Gauss " and " Scotia " in the Southern Ocean, and of various surveying ships in the North and South Pacific, have proved that the mean depth of the ocean is considerably greater than had been supposed, and mean-sphere level must therefore lie deeper than the calculations of 1895 show; possibly not far from the position deduced from the freer estimate of 1888.

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  • The atomic weight of the element was determined by C. Winkler by analysis of the pure chloride GeCl4, the value obtained being 72.32, whilst Lecoq de Boisbaudran (Comptes rend us, 1886, 103, 45 2), by a comparison of the lines in the spark spectrum of the element, deduced the value 72.3.

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  • At 524° Dumas deduced the structure S6 from vapour-density determinations, whilst for the range 860 0 to 1040 0, Sainte-Claire Deville and Troost deduced the formula S2.

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  • This car is equipped with apparatus by means of which a continuous record of the draw-bar pull is obtained on a distance base; time indications are also made on the diagram from which the speed at any instant can be deduced.

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  • in the second column, the first column being added to give some idea of the rate at which the engine was working when the data from which the efficiency has been deduced were observed.

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  • In a particular case where the boiler pressure was maintained constant at 130 lb per square inch, and the cut-off was approximately 20% of the stroke, the values c =55 and b=o 031 were deduced, from which it will be found that the value of the piston speed corresponding to the maximum horsepower is 887 ft.

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  • The data from which this result is deduced will be found in Professor Goss's paper quoted above in Table XXI.

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  • The Mayas have left no r cord of their institutions or of the causes of their decline, beyond what may be deduced from their ruined structures.

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  • He ceased to attend the society in 1829, but he carried away from it the strengthening memory of failure overcome by persevering effort, and the important doctrinal conviction that a true system of political philosophy was "something much more complex and many-sided than he had previously had any idea of, and that its office was to supply, not a set of model institutions but principles from which the institutions suitable to any given circumstances might be deduced."

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  • The pre-existence of souls is another inference from the immutability of God, although Origen also deduced it from the nature of the soul, which as a spiritual potency must be eternal.

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  • - The leading features of Aegean civilization, as deduced from the evidence, must be stated very briefly.

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  • Physical science, if there was anything deserving that name, was cultivated, not by experiment in the Aristotelian way, but by arguments deduced from premises resting on authority or custom.

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  • The city is supposed to have been surrounded by a wall before the time of Solon, the existence of which may be deduced from Thucydides' account of the assassination of Hipparchus (vi.

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  • In his classical thesis Berthollet vigorously attacked the results deduced by Bergman, who had followed in his table of elective attractions the path traversed by Stahl and S.

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  • deduced the relative weight of the oxygen atom to be 6.5; from marsh gas and olefiant gas he deduced carbon = 5, there being one atom of carbon and two of hydrogen in the former and one atom of hydrogen to one of carbon in the latter; nitrogen had an equivalent of 5, and so on.'

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  • equal changes in temperature and pressure occasion equal changes in equal volumes of all gases and vapours - Avogadro deduced the law: Under the same conditions of temperature and pressure, equal volumes of gases contain equal numbers of molecules; and he showed that the relative weights of the molecules are determined as the ratios of the weights of equal volumes, or densities.

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  • This attitude was due to his adherence to the " dualistic theory" of the structure of substances, which he deduced from electrochemical researches.

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  • His terminology was vague and provoked caustic criticism from Berzelius; he assumed that all molecules contained two atoms, and consequently the atomic weights deduced from vapour density determinations of sulphur, mercury, arsenic, and phosphorus were quite different from those established by gravimetric and other methods.

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  • The solution came abOut by arranging the elements in the order of their atomic weights, tempering the arrangement with the results deduced from the theory of valencies and experimental observations.

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  • In this compound only two of the oxygen atoms are wholly associated with the sulphur atom, each of the remaining oxygen atoms being united by one of its affinities to the sulphur atoms, and by the remaining affinity to an atom of hydrogen; thus H O S ?O H O> The graphic formula of a sulphate is readily deduced by remembering that the hydrogen atoms are partially or entirely replaced.

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  • Baeyer supposes that in the formation of carbon, rings " the valencies become deflected from their positions, and that the tension thus introduced may be deduced from a comparison of this angle with the angles at which the strained valencies would meet.

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  • But, at the same time, the constants in the above relation are not identical with those in the corresponding relation empirically deduced from observations on fatty hydrocarbons; and we are therefore led to conclude that a benzene union is considerably more stable than an ethylene union.

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  • The critical volume of oxygen can be deduced from the data of the above table, and is found to be 29, whereas the experimental value is 25.

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  • Thus the actually observed densities of liquid chlorine and bromine at the boilingpoints are 1 56 and 2-96, leading to atomic volumes 22.7 and 26.9, which closely correspond to Kopp's values deduced from organic compounds.

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  • Neumann, who, in 1831, deduced from observations on many carbonates (calcium, magnesium, ferrous, zinc, barium and lead) that stoichiometric quantities (equimolecular weights) of compounds possess the same heat capacity.

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  • the heat evolved when an organic compound is completely burned in oxygen; the heat of formation is deduced from the fact that it is equal to the heats of formation of the products of combustion less the observed heat of combustion.

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  • The thermal effects increase as one passes from primary to tertiary alcohols, the values deduced from propyl and isopropyl alcohols and trimethyl carbinol being: - primary =45 08, secondary = 50.39, tertiary = 60.98.

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  • Thomsen deduced that a single bond between a carbon and a nitrogen gramme-atom corresponds to a thermal effect of 2.77 calories, a double bond to 5.44, and a treble bond to 8.31.

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  • - Formerly map makers contented themselves with placing upon their maps a linear scale of miles, deduced from the central meridian or the equator.

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  • He moreover accuses Eratosthenes, (whose determination of a degree he accepts without hesitation) with trusting too much to hypothesis in compiling his map instead of having recourse to latitudes and longitudes deduced by astronomical observations.

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  • We have no evidence as to the method by which he deduced this theory (cf.

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  • It had been the dream of this man's whole life to supersede both forms of Christianity by a semi-pagan theosophy deduced from the writings of the later Pythagoreans and Platonists.

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  • The boundaries of Bashan may to some extent be deduced from the indications afforded in the earlier historical books.

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  • With these definitions it is now possible to prove the following six premisses applying to finite cardinal numbers, from which Peano 2 has shown that all arithmetic can be deduced i.

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  • The proof of the six premisses requires an elaborate investigation into the general properties of classes and relations which can be deduced by the strictest reasoning from our ultimate logical principles.

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  • In "applied mathematics" the "deductions" are given in the shape of the experimental evidence of natural science, and the hypotheses from which the "deductions" can be deduced are sought.

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  • Given that such observations at the surface of the sea, at intermediate levels and at the bottom are sufficiently numerous and are of a high degree of precision, general conclusions as to the movements of the ocean may be deduced from established theorems in hydrodynamics.

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  • The season was soon after Easter; the year may be safely deduced from the fact that the first nine canons are intended to repair havoc wrought in the church by persecution, which ceased after the overthrow of Maximinus in 313.

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  • In the case of nonelectrolytes and of all non-ionized molecules this analogy completely represents the facts, and the phenomena of diffusion can be deduced from it alone.

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  • The great object of 17th-century moralists had been to find some general principle from which the whole of ethics could be deduced; common-sense, by turning its back on abstract principles of every kind, forced the philosophers to come down to the solid earth, and start by inquiring how the world does make up its mind in fact.

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  • In a refined form this method is often employed for measuring the intensity of a magnetic field at a given place, just as the intensity of gravity at different parts of the earth is deduced from observations of the rate at which a pendulum of known length vibrates.

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  • It can be deduced from (17), (12) and (13) that the couple on S'N' due to SN, and tending to increase 4), is MM' (sin 0 cos 4-2 sin 4) cos 0)/r'.

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  • du Bois has deduced the corresponding mean demagnetizing factors.

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  • The moment of a magnet may also be deduced from a measurement of the couple exerted on the magnet by a uniform field H.

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  • The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency ioo may be deduced from that at any other frequency n by simply multiplying by too n.

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  • The third column shows the relative amount of hysteresis deduced by Ewing as a general mean from actual tests of many samples (Journ.

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  • Soc., 1886, 40, 486), who in 1886 published an account of some experiments in which the relation of magnetization to magnetic field was deduced from observations of the force in grammes weight which just sufficed to tear asunder the two halves of a divided ring electro-magnet when known currents were passing through the coils.

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  • The force required to detach it is measured by a registering spring balance, which is clamped to the upper end of the rod, and thence the induction or the magnetization is deduced by applying the formula (B-H)2/81r = 27r1 2 = Pg/S, where P is the pull in grammes weight, S the sectional area of the rod in square cm., and g=981.

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  • The following approximate figures for small magnetizing forces are deduced from Hopkinson's curves: 9 Proc. Roy.

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  • Hence may be deduced an explanation of the fact that, while the susceptibility of all known diamagnetics (except bismuth and antimony) is independent of the temperature, that of paramagnetics varies inversely as the absolute temperature, in accordance with the law of Curie.

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  • 2 From the fundamental principle of virtual velocities, which thus acquired a new significance, Lagrange deduced, with the aid of the calculus of variations, the whole system of mechanical truths, by processes so elegant, lucid and harmonious as to constitute, in Sir William Hamilton's words, "a kind of scientific poem."

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  • Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

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  • From every proposition in this algebra a reciprocal one may be deduced by interchanging + and X, and also the symbols o and i.

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  • From a measurement of the maximum distance the least angle between consecutive lines consistent with resolution may be deduced, and a comparison made with the rule stated above.

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  • Following, unknown to himself, in the footsteps of Young, he deduced the principle of interference from the circumstance that the darkness of the interior bands requires the co-operation of light from both sides of the obstacle.

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  • It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.

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  • Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity, and hence he deduced the proposition that the velocities of liquids are as the square root of the head, apart from the resistance of the air and the friction of the orifice.

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  • He regarded, therefore, the section of the contracted vein as the true orifice from which the discharge of water ought to be deduced, and the velocity of the effluent water as due to the whole height of water in the reservoir; and by this means his theory became more conformable to the results of experience, though still open to serious objections.

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  • Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

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  • The configurations of the pentaand tetra-aldoses have been determined by similar arguments; and those of the ketoses can be deduced from the aldoses.

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  • They have been identified with the AKarcpoc (perhaps AkKhazari, or White Khazars) who appear upon the lower Volga in the Byzantine annals, and thence they have been deduced, though with less convincing proof, either from the AyetOvpvoc (Agathyrsi) or the Kariapoc of Herodotus, iv.

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  • historically deduced (London, 1703).

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  • And as these truths were self-evident, so the religion he deduced from them was sufficient, not only for his own moral and intellectual nature, but also for man as he conceived him, for history as he knew it, and for society as he saw it.

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  • This is at once connected with the nebular hypothesis, and subsequently deduced "from the ultimate law of the" persistence of force,"and finally supplemented by a counter-process of dissolution, all of which appears to Spencer only as" the addition of Von Baer's law to a number of ideas that were in harmony with it."It is clear, however, that Spencer's ideas as to the nature of evolution were already pretty definite when Darwin's Origin of Species (1859) revolutionized the subject of organic evolution by adding natural selection to the direct adaptation by use and disuse, and so suggesting an intelligible method of producing modifications in the forms of life.

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  • § 99a (3rd ed., 1892), where the expression in question is deduced as a corollary of Green's theorem.

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  • Applying the above equation to a gas obeying the law pv=RT, for which the work done in isothermal expansion from a volume i to a volume r is W=RT loger, whence dW=R log e rdt, he deduced the expression for the heat absorbed by a gas in isothermal expansion H=R log er/F'(t).

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  • Holtzmann (1845) by the same assumption deduced the value J/T for the function F'(t), but obtained erroneous results by combining this assumption with the caloric theory.

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  • Clausius (1850), applying the same assumption, deduced the same value of F'(t), and showed that it was consistent with the mechanical theory and Joule's experiments, but required that a vapour like steam should deviate more considerably from the gaseous laws than was at that time generally admitted.

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  • - The most important and most useful of the relations between the thermodynamical properties of a substance may be very simply deduced from a consideration of the indicator diagram by a geometrical method, which is in many respects more instructive than the analytical method generally employed.

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  • It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÆC) XEC. The ratio BEÆC of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.

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  • The final state of the substance, when equilibrium has been restored, may be deduced from this condition, if the energy can be expressed in terms of the co-ordinates.

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  • The atomic weight of gold was first determined with accuracy by Berzelius, who deduced the value 195.7 (H= i) from the amount of mercury necessary to precipitate it from the chloride, and 195.2 from the ratio between gold and potassium chloride in potassium aurichloride, KAuC1 4.

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  • The important part played by the residual air in the globe had also been deduced by Osborne Reynolds from observing that on turning off the light, the vanes came to rest very much sooner than the friction of the pivot alone would account for; in fact, the rapid subsidence is an illustration of Maxwell's great theoretical discovery that viscosity in a gas (as also diffusion both of heat and of the gas itself) is sensibly independent of the density.

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  • From this evidence it has been deduced that a king called Kozulokadphises, Kujulakasa or Kieu-tsieu-k'io (?

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  • The result was a treatise in which he deduced practical conclusions from the past history and present temper of the city, blending these with his favourite principles of government in general.

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  • By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured.

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  • Instead of the expensive mile-long stout hemp lines used and since 1887 those of the prince of Monaco in his yachts, as by Ross, Maury introduced a ball of strong twine attached to a well as numerous Danish vessels in the sea between Iceland and cannon shot, which ran it out rapidly; when the bottom was Greenland, conspicuous amongst which were the expeditions reached the twine was cut and the depth deduced from the length in1896-1898on board the " Ingolf."

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  • Aime showed that on a calm bright day in the Mediterranean the temperature rose o 1° C. between the early morning and noon at a depth of about 12 fathoms. Luksch deduced a much greater penetration of solar warmth from the comparison of observations at different hours at neighbouring stations in the eastern Mediterranean, but his methods were not exact enough to give confidence in the result.

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  • From this meaning is deduced that of the person in whom lies the right of presenting to public offices, privileges, &c., still surviving in the title of the Patronage Secretary of the Treasury in Great Britain.

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  • From the hypothesis of an external world a series of contradictions are deduced, such as that the world is both finite and infinite, is movable and immovable, &c.; and finally, Aristotle and various other philosophers are quoted, to show that the external matter they dealt with, as mere potentiality, is just nothing at all.

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  • To complete Kant's work, to demonstrate that all the necessary conditions of knowledge can be deduced from a single principle, and consequently to expound the complete system of reason, that is the business of the Wissenschaftslehre.

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  • Of these, evidently the first must be the fundamental; to some extent it conditions the other two, though these cannot be deduced from it or proved by it.

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  • Thus in the Rechtslehre and Sittenlehre, the multiplicity of egos is deduced, and with this deduction the first form of the Wissenschaftslehre appeared to end.

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  • This opinion is deduced from our experience of the behaviour of bodies of sensible size, but we have no experimental evidence that two atoms may not sometimes coincide.

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  • In like manner, after the French mathematicians had attempted, with more or less ingenuity, to construct a theory of elastic solids from the hypothesis that they consist of atoms in equilibrium under the action of their mutual forces, Stokes and others showed that all the results of this hypothesis, so far at least as they agreed with facts, might be deduced from the postulate that elastic bodies exist, and from the hypothesis that the smallest portions into which we can divide them are sensibly homogeneous.

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  • Soc., 1890, 46, p. 74) deduced the value 89.95.

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  • The expression 27ra for the length of the circumference can be deduced by considering the limit of the area cut off from a circle of radius a by a concentric circle of radius a - a, when a becomes indefinitely small; this is an elementary case of differentiation.

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  • It may be deduced from the formula given above.

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  • This might have been deduced directly from Simpson's first formula, by a series of eliminations.

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  • The general principle is that the numerical data from which a particular result is to be deduced are in general not exact, but are given only to a certain degree of accuracy.

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  • The velocity deduced at 8.1° C. was U=1435 met./sec., agreeing very closely with the value calculated from the formula U 2 = E/p.

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  • It is shown below how the vibrations of a string may be deduced from stationary waves.

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  • The amount radiated out in the form of sound waves is deduced, and hence the energy of the stream at any distance is known.

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  • In the other, the waves produce a measurable effect on a vibrating system of the same frequency, and the amplitude in the waves can be deduced.

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  • The relative antiquity of the earlier settlements of the Stone and Bronze ages is not capable of being deduced from existing evidence.

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  • Hence the formula is more useful in the form w = (w i +w2)1 2 / (Kd -1 2) = (wl +w 2)lr/ (K -lr) where k= (wl+w2-1-w3)lr/w3 is to be deduced from the data of some bridge previously designed with the same working stresses.

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  • - f min ., from which the working stress is deduced, is not the ordinary range of stress which is repeated a practically infinite number of times, but is a range of stress to which the bridge is subjected only at comparatively long intervals.

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  • The evidence for the existence of the luminiferous aether has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium, as deduced from the phenomena of light, have been found to be precisely those required to explain electromagnetic phenomena."

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  • Philosophical truth, as deduced from the teaching of Aristotle, it was said, directly contradicts the teaching of the church, which determines truth in theology; but the contradiction leaves the authority of the latter unimpaired in its own sphere.

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  • From Maskelyne's observations Charles Hutton deduced a density for the earth 4.5 times that of water (ib.

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  • 184, 254) also deserve mention, as well as his discussions of the rotation of Mars, by which he deduced its period with a probable error of 0 9.005.

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  • He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.

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  • 2 4 2m +2 2m+4; the function of zero order C is deduced by making m= o, and is equivalent to the series I -22 -}- 2-.4-, , &c. O.

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  • iv.), His choice of Israel, and the love and faithfulness which He had shown towards it, by redeeming it from slavery in Egypt, and planting it in a free and fertile land; from which are deduced the great practical duties of loyal and loving devotion to Him, an uncompromising repudiation of all false gods, the rejection of all heathen practices, a cheerful and ready obedience to His will, and a warm-hearted and generous attitude towards man.

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  • In his optical researches, Optiska Undersiikningar, presented to the Stockholm Academy in 1853, he not only pointed out that the electric spark yields two superposed spectra, one from the metal of the electrode and the other from the gas in which it passes, but deduced from Euler's theory of resonance that an incandescent gas emits luminous rays of the same refrangibility as those which it can absorb.

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  • For the weight of the cubic decimetre of water, as deduced from the experiments made in London in 1896 as to the weight of the cubic inch of water, D.

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  • 3: Objects which have been made by measure or weight, and from which the unit of construction can be deduced.

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  • For the length of the building cubit Sir C. Warren has deduced a length equivalent to 20.6169 English inches, which compares with a mean Pyramid cubit of 20.6015 in.

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  • As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit.

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  • If this unit haS any connexion with the kat, it is that a kat of gold is worth 15 shekels or 1/4 mina of silver; this agrees well with the range of both units, only it must be remembered that 129 was used as gold unit, and another silver unit deduced from it.

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  • m r = r logo m, logo m= (I /r) logo m, which may be readily deduced from the definition of a logarithm.

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  • The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.

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  • The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.

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  • From (i.) and (ii.) it may be deduced that exp x= (I !

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  • He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.

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  • Briggs calculated in a similar manner log 6, and thence deduced log 3.

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  • the former of these equations gives a convergent series for logep, and the latter a very convergent series by means of which the logarithm of any number may be deduced from the logarithm of the preceding number.

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  • to 276 places of decimals, and deduced the value of log e lo and its reciprocal M, the modulus of the Briggian system of logarithms. The value of the modulus found by Adams is Mo = 0-43429 44 81 9 03251 82765 11289 18916 60508 22 943 97 00 5 80366 65661 14453 78316 58646 4920-8870 77 47292 2 4949 33 8 43 17483 18706 106 74 47 6630-3733 64167 92871 58963 90656 92210 64662 81226 58521 27086 56867 03295 9337 0 86965 88266 88331 16360 773849 0514 28443 48666 76864 65860 85135 56148 212 34 87653 43543 43573 25 which is true certainly to 272, and probably to 273, places (Proc. Roy.

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  • Waagen's law of mutation, or the appearance of new parts or organs so gradually that they can be perceived only by following them through successive geologic time stages, appears to be directly contradictory to the saltation principle; it is certainly one of the most firmly established principles of palaeontology, and it constitutes the contribution par excellence of this branch of zoology to the law of evolution, since it is obvious that it could not possibly have been deduced from comparison of living animals but only through the long perspective gained by comparison of animals succeeding each other in time.

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  • The fundamental features of knowledge, whether as activity or as sum of apprehended fact, and of conduct had been deduced as elements necessary in the attainment of self-consciousness.

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  • Properties of the limagon may be deduced from its mechanical construction; thus the length of a focal chord is constant and the normals at the extremities of a focal chord intersect on a fixed circle.

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  • Matter is deduced by the "original synthesis."

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  • as usual, over the east walk; but, as a general rule, the arrangements deduced from the examples described may be regarded as invariable.

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  • The general equation to the circle in trilinear co-ordinates is readily deduced from the fact that the circle is the only curve which intersects the line infinity in the circular points.

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  • The general equation to a circle in this system of co-ordinates is deduced as follows: If p be the radius and 1p+mg+nr=o the centre, we have p= (lpl+mgi+nri)/(l+m+n), in which i, q i, r i is a line distant p from the point 1p+mq+nr= o.

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  • The readings of X which can be deduced from considering the agreements in B, C, D will be of higher antiquity and of greater external aut l ority than any of the readings in B, C, D taken singly.

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  • The Value Of L Is Always Given By The Formula For The Dominical Letter, And P And 1 Are Easily Deduced From The Epact, As Will Appear From The Following Considerations.

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  • The Times Of All Future New Moons May Consequently Be Deduced By Successively Adding 29 Days 12 Hours 44 Min.

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  • To Compute The Times Of The New Moons Which Determine The Commencement Of Successive Years, It Must Be Observed That In Passing From An Ordinary Year The New Moon Of The Following Year Is Deduced By Subtracting The Interval That Twelve Lunations Fall Short Of The Corresponding Gregorian Year Of 365 Or 366 Days; And That, In Passing From An Embolismic Year, It Is To Be Found By Adding The Excess Of Thirteen Lunations Over The Gregorian Year.

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  • The Gregorian epact being the age of the moon of Tebet at the beginning of the Gregorian year, it represents the day of Tebet which corresponds to January I; and thus the approximate date of Tisri I, the commencement of the Hebrew year, may be otherwise deduced by subtracting the epact from Sept.

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  • Daub had become so hopelessly addicted to this perverse principle that he deduced not only Jesus as the embodiment of the philosophical idea of the union of God and man, but also Judas Iscariot as the embodiment of the idea of a rival god, or Satan."

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  • From the measured distances of the diffraction bands the width of the slit may be easily deduced.

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  • Taking the Trunk and Main Branch Series, we find they depend altogether on the four constants: al, b, a', b', while N is a universal constant identical with that deduced from the hydrogen series.

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  • Riecke, 3 who deduced a differential equation of the 10th order.

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  • Kant first deduced that from the experience of mental phenomena all logical use of reason is limited to mental phenomena, and then maintained that to explain moral responsibility practical reason postulates the existence of real noumena.

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  • Applying this " synechological view " to the supposed inclusion of soul in soul, he deduced the conclusion that, as here the nature of one's soul is to unite one's little body, so hereafter its essence will be to unite a greater body, while God's spirit unites the whole world by His omnipresence; and he pertinently asked, in opposition to the " punctual " view, whether God's soul is centred in a point.

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  • But his substitute was his own hypothesis of panpsychism, from which he deduced a "cosmorganic " evolution from a " cosmorganic " or original condition of the world as a living organism into the inorganic, by the principle of tendency to stability.

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  • Hence he deduced that whatever we know from sensations arranged in such a priori forms are objects of our own experience and mental phenomena.

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  • Its consistency, as deduced by Lange, was to reduce all use of reason, speculative and practical, to its logical use of proceeding from the assumed mental data of outer and inner sense, arranged a priori, to mental phenomena of experience, beyond which we can conceive ideas but postulate nothing.

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  • Hence, from the two observations the value of the earth's total force can be deduced.

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  • Trans., 1839) deduced his method of correcting the compass by permanent magnets and soft iron, giving practical rules for the same in 1840.

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  • From Poisson's equations Archibald Smith deduced the formulae given in the Admiralty Manual for Deviations of the Compass (1st ed., 1862), a work which has formed the basis of numerous other manuals since published in Great Britain and other countries.

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  • But this proof was rather insufficient, as indeed it was felt to be, and, in any case, nothing could be deduced from it save a kind of precedence in honour, which was never contested even by the Greeks.

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  • The phenomena of solution and of vapour pressure constitute cases of equilibrium, and conform to the laws deduced by Gibbs, which thus yield a valuable method of investigating and classifying the equilibria of solutions.

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  • Thus F = r(n - I) + 2 - n(r - t) = n - r + 2, a result which was deduced by J.

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  • But at intermediate compositions we can only guess at the form of the energy-composition curve, and the freezing point composition curve, deduced from it, will vary according to the supposition which we make.

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  • But the elucidation of the complicated phenomena of solid solutions would have been impossible without the theoretical knowledge deduced from the principle of available energy.

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  • The experiments of Raoult on solutions of organic bodies in water and on solutions of many substances in some dozen organic solvents have confirmed this result, and therefore the theoretical value of the osmotic pressure from which it was deduced.

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  • All the thermodynamic relations we have deduced hold on any theory of solution and favour no one theory rather than another.

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  • In the limit of dilution when n is very small compared with N this gives Raoult's experimental law that the relative lowering is n/N, which we deduced from the osmotic law, and conversely from which the osmotic law follows, while for more concentrated solutions agreement is obtained by assigning arbitrary values to a, which, as we have seen, is 5 in the case of cane-sugar.

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  • It pointed out distinctly and temperately the grounds of the right of punishment, and from these principles deduced certain propositions as to the nature and amount of punishment which should be inflicted for any crime.

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  • He himself tells us that when, after the publication of the original essay, the main argument of which he had deduced from David Hume, Robert Wallace, Adam Smith and Richard Price, he began to inquire more closely into the subject, he found that "much more had been done" upon it "than he had been aware of."

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  • It is, in fact, the confluence of the Malthusian ideas with the theories of Ricardo, especially with the corollaries which the latter deduced from the doctrine of rent (though these were not accepted by Malthus), that has led to the introduction of population as an element in the discussion of so many economic questions in modern times.

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  • The method of Forbes (in which the conductivity is deduced from the steady distribution of temperature on the assumption that the rate of loss of heat at each point of the bar is the same as that observed in an auxiliary experiment in which a short bar of the same kind is set to cool under conditions which are supposed to be identical) is well known, but a consideration of its weak points is very instructive, and the results have been most remarkably misunderstood and misquoted.

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  • The heat Q transmitted in a given time T may be deduced from an observation of the rise of temperature of the water, and the amount which passes in the interval.

    0
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  • The gradient near the entrance to the calorimeter was deduced from observations with five thermometers at suitable intervals along the bar.

    0
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  • Ire these methods the flow of heat is deduced from observations of the rate of change of temperature with time in a body exposed to known external or boundary conditions.

    0
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  • The diffusivity can be deduced from observations at different depths x' and x", by observing the ratio of the amplitudes, which is (x '- x ") for a simple-harmonic wave.

    0
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  • In any case results deduced from the annual wave must be expected to vary in different years according to the distribution of the rainfall, as the values represent averages depending chiefly on the diffusion of heat by percolating water.

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  • The following are a few typical values for sand or gravel deduced from the annual wave in different localities: - [[Table Ii]].

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  • It is probable for this reason that the average conductivity of the earth's crust, as deduced from surface observations, is too large; and that estimates of the age of the earth based on such measurements are too low, and require to be raised; they would thereby be brought into better agreement with the conclusions of geologists derived from other lines of argument.

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  • He deduced the variations of the mean temperature of a section of a bar from the sum S of the E.M.F.'s of a number of couples, inserted at suitable equal intervals 1 and connected in series.

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  • In this case the curve representing the distribution of temperature is a parabola, and the conductivity k is deduced from the mean rise of temperature (R-R°)/aR° by observing the increase of resistance R-R° of the bar, and the current C. It is also necessary to measure the cross-section g, the length 1, and the temperature-coefficient a for the range of the experiment.

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  • This proposition, which he called the mystic hexagram, he made the keystone of his theory; from it alone he deduced more than 400 corollaries, embracing, according to his own account, the conics of Apollonius, and other results innumerable.

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  • Also, whilst the mean azimuths deduced from the observations between 6 A.M.

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  • The assumption may be a reasonable one, and if the results agree with probabilities as deduced from the rest of the evidence it is wise to adopt it; if on the other hand the other evidence seems in any serious degree contrary to those results it may be surmised that the assumption is faulty in some particular.

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  • They had learned to read God's will in the events of history, and deduced (for example) the doctrine of the resurrection of the dead from the death of the martyrs under Antiochus Epiphanes and Alcimus.

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  • From a discussion of the observations of Mars made in 1860 and 1862 at Greenwich and Williamstown (near Melbourne), Stone deduced for it a value of 8.932" (Mon.

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  • It is considered to be an extinct volcano because it makes the plumb-line deviate only 7" to 8", from which it is deduced that the mountain is hollow.

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  • The simplest equation to the parabola is that which is referred to its axis and the tangent at the vertex as the axes of co-ordinates, when it assumes the form y 2 = 4ax where as = semilatus rectum; this may be deduced directly from the definition.

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  • More convenient forms in terms of a single parameter are deduced by substituting x' =am t, y' = aam (for on eliminating in between these relations the equation to the parabola is obtained).

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  • Other forms which correspond to other relations between the roots can be readily deduced from the most general form.

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  • Fawsitt (The Education of the Examiner, Royal Philosophical Society of Glasgow, 1905) shows that frequency-curves deduced from actual investigation of class-marks are not symmetrical, but have two maxima corresponding to the performance of " non-workers " and of " workers."

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  • Reason contains principles which we cannot demonstrate, but which can be deduced, and are the proper objects of belief.

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  • In 1754 Euler communicated to the Berlin Academy a further memoir, in - which, starting from the hypothesis that light consists of vibrations excited in an elastic fluid by luminous bodies, and that the difference of colour of light is due to the greater or less frequency of these vibrations in a given time, he deduced his previous results.

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  • experiments quoted by Dollond, because he asserted that the difference between the law deduced by Newton and that which he assumed would not be rendered sensible by such an experiment.

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  • 4 Dollond did not reply to this memoir, but soon afterwards he received an abstract of a memoir by Samuel Klingenstierna, the Swedish mathematician and astronomer, which led him to doubt the accuracy of the results deduced by Newton on the dispersion of refracted light.

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  • The following are some of the values deduced by well-known experimentalists for the latent heat of fusion: - Regnault, 79.06 to 79.24 calories, corrected by Person to 79.43; Person, 79.99 calories; Hess, 80.34 calories; Bunsen, 80.025 calories.

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  • The Values Deduced In This Manner For The Equivalent Agreed As Closely As Could Be Expected Considering The Impossibility Of Regulating The External Condition Of Temperature And Moisture With Any Certainty In An Engine Room.

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  • The Resistance R Could Be Deduced From A Knowledge Of The Temperature Of The Calorimeter And The Coefficient Of The Wire.

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  • In Spite Of The Large Corrections The Results Were Extremely Consistent, And The Value Of The Temperature Coefficient Of The Diminution Of The Specific Heat Of Water, Deduced From The Observed Variation In The Rate Of Rise At Different Points Of The Range 15° To 25°, Agreed With The Value Subsequently Deduced From Rowland'S Experiments Over The Same Range, When His Thermometers Were Reduced To The Same Scale.

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  • The Absolute Value Of The Specific Heat Deduced Necessarily Depends On The Absolute Values Of The Electrical Standards Employed In The Investigation.

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  • The Specific Heat Itself Can Be Deduced Only By Differentiating The Curve Of Observation, Which Greatly Increases The Uncertainty.

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  • The Value 4.180 Joules At 20° C. Is The Mean Between Rowland'S Corrected Result 4.181 And The Value 4.179, Deduced From The Experiments Of Reynolds And Moorby On The Assumption That The Ratio Of The Mean Specific Heat O° To 100° To That At 20° Is 1.043'6, As Given By The Formulae Representing The Results Of Callendar And Barnes.

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  • No Doubt There Must Be Approximate Relations Between The Atomic And Molecular Heats Of Similar Elements And Compounds, But Considering The Great Variations Of Specific Heat With Temperature And Physical State, In Alloys, Mixtures Or Solutions, And In Allotropic Or Other Modifications, It Would Be Idle To Expect That The Specific Heat Of A Compound Could Be Accurately Deduced By Any Simple Additive Process From That Of Its Constituents.

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  • and its companion a diameter of 830,000 m.; the distance between their centres cannot be deduced without making certain doubtful assumptions, but may be about 3,000,000 m.

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  • Frost have deduced that the average speed is only 8 m.

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  • Halm deduced a velocity of 20.8 km.

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  • Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

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  • Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.

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  • Hitherto the assumption of the probable as true rather than as what will be conceded in debate ° has been the main distinction of the standpoint of analytic from that of dialectic. But the true is true only in reference to a coherent system in which it is an immediate ascertainment of van, or to be deduced from a ground which is such.

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  • A principle is transcendentally " deduced " when it and only it can explain the validity of some phase of experience, some order Limitation of truths.

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  • Nature, e.g., is not deduced as real because rational, but being real its rationality is presumed and, very imperfectly, exhibited in a way to make it possible to conceive it as in its essence the reflex of Reason.

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  • Arrhenius, by reasoning similar to that of section 5, applied to an osmotic cell supporting a column of solution by osmotic pressure, deduced the relation between the osmotic pressure P at the bottom of the column and the vapour-pressure p" of the solution at the top, viz.

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  • 40 deduced from the velocity of sound, Rankine found for air S = 240, which was much smaller than the best previous determinations (e.g.

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  • The rate of change of the latent heat is easily deduced from that of the total heat by subtracting the specific heat of the liquid.

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  • The deviations from the ideal volume may also be deduced by the method of Joule and Thomson.

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  • Formula (23) for the vapour-pressure was subsequently deduced by Rankine (Phil.

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  • The form (I) is deduced from it by putting itt, and taking t to be infinitely small.

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  • It may also be deduced from the principles of linear and angular momentum as embodied in the equations (9).

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  • By its aid, for example, the whole of the properties a elliptical arches, whether square or skew, whether level or sloping in their span, are at once deduced by projection from those of symmetrical circular arches, and the properties of ellipsoidal and ellipticconoidal domes from those of hemispherical and circular-conoidal domes; and the figures of arches fitted to resist the thrust of earth, which is less horizontally than vertically in a certain given ratio, can be deduced by a projection from those of arches fitted to resist the thrust of a liquid, which is of equal intensity, horizontally and vertically.

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  • The following empirical formulae for the stiffness of hempen ropes have been deduced by Mono from the experiments of Coulomb: Let F be the stiffness in pounds avoirdupois; d the diameter of the rope In inches, fl = 48d2 for white ropes and 35d2 for tarred ropes; r the effectire radius of the pulley in inches; T the tension in pounds.

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  • At intermediate instants, however, other principles have also to be taken into account, which are deduced from the second law of motion, as applied to direct deviation, or acceleration and retardation.

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  • The standard mortality of each community is deduced from a life-table, representing a "generation" of people assumed to be born at the same moment and followed throughout their hypothetical life, in the light of the distribution by age ascertained.

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  • 800 and 1004, extracted from Caussin's translation of Ibn Junis, the eclipses and occultations of Bullialdus, Gassendi, and Hevelius, of the French astronomers at Paris and St Petersburg, and of Flamsteed at Greenwich, and deduced a secular acceleration of 8.8", agreeing well with the theoretical value.

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  • He discovered a function, which has been called the potential of one circuit on another, from which he deduced a theory of induction, completely in accordance with experiment.

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  • Weber at the same time deduced the mathematical laws of induction from his elementary law of electrical action, and with his improved instruments arrived at accurate verifications of the law of induction which by this time had been developed mathematically by Neumann and himself.

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  • For the hydrogen atom the ratio of charge to mass as deduced from electrolysis is about Io 1.

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  • von Rohr, Die Bilderzeugung in optischen Instrumenten, pp. 3 1 7-3 2 3) have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically (pp. 212-316).

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  • This he is supposed + to have deduced, no one knows how, from Wallis' formula for ??r, v 3.3.5.5.7.7 4 ...

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  • A more definite date cannot be deduced from the evidence at our disposal, but his era may safely be placed as far back as 1000 B.C.

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  • When turbines, as often happens in land practice, are directly coupled to electrical generators, their horse-power can be deduced from the electrical output.

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  • In the Supplement to the Theory of Capillary Action, Laplace deduced the equation of the surface of the fluid from the condition that the resultant force on a particle at the surface must be normal to the surface.

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  • The early writers on capillary action supposed that the diminution of capillary action was due simply to the change of density corresponding to the rise of temperature, and, therefore, assuming the surface-tension to vary as the square of the (37)?(f) =eP f (38) density, they deduced its variations from the observed dilatation of the liquid by heat.

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  • The tension of the surface separating two liquids which do not mix cannot be deduced by any known method from the tensions of the surfaces of the liquids when separately in contact with air.

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  • p. 463) deduced relative to the interfacial tensions of three bodies.

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  • The fact that a pair of plates which repel one another at a certain distance may attract one another at a smaller distance was deduced by Laplace from theory, and verified by the observations of the abbe Haiiy.

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  • From the pitch of the note due to a jet of given diameter, and issuing under a given head, the wave-length of the nascent divisions can be at once deduced.

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  • The diameter of the orifice was 3 millims., from which that of the jet is deduced by the introduction of the coefficient 8.

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  • The theological calmness of the West, amid the violent theological disputes which troubled the Eastern patriarchates, and the statesmanlike wisdom of Rome's greater bishops, combined to give a unique position to the pope, which councils in vain strove to shake, and which in time of difficulty the Eastern patriarchs were fain to acknowledge and make use of, however they might protest against it and the conclusions deduced from it.

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  • While Aquinas affirmed the positions of Augustine, he deduced them from his Aristotelian conception of God as "first mover, itself unmoved."

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  • The inference to be deduced from the foregoing is plainly this, that even in large-bodied, small-winged insects and birds the wing-surface is greatly in excess, the surplus wing area supplying Not, FIG.

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  • The history of the origin of the land-forms of England, as far as they have been deduced from geological studies, is exceedingly complicated.

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  • In 1377 the levying of a polltax provides partial figures from which a total of two to twoand-a-half millions has been deduced, but again divergent views have been expressed as to how far the number was still affected by the Black Death of 1348-1349.

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  • Torricelli, by employing the "method of indivisibles," deduced that the area was exactly three times that of the generating circle; this result had been previously established in 1640 in France by G.

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  • Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.

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  • The radius of curvature at any point is readily deduced from the intrinsic equation and has the value p=4 cos 40, and is equal to twice the normal which is 2a cos 2B.

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  • Bruns in 1889; measured an arc of the meridian in East Prussia in 1831-1832; and deduced for the earth in 1841 an ellipticity of 2 4 9.

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  • Airy deduced a parallax of 8.76" and E.

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  • Stone 8.88"; from the French observations of the same date Stone deduced 8.88" and V.

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  • Trans., 1813 and 181 4) he deduced that the illuminating power of the former exceeded that of the latter in the proportion of 5: 2.

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  • Connected with these doctrines was their famous theory of the "rehabilitation of the flesh," deduced from the philosophic theory of the school, which was a species of Pantheism, though they repudiated the name.

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  • Conservtiv~ politicians deduced from these circumstances the necessity of applying firm government to Ireland.

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  • His cardinal position, from which he deduced so many important conclusions, namely, that the parts and organs of the old constitution of France were sound, and only needed moderate invigoration, is absolutely mistaken and untenable.

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  • It serves as a means of research, more particularly in mathematical investigations, the simple laws thus deduced being subsequently modified by introducing assumptions in order to co-ordinate actual experiences.

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  • The fact that men give different answers to moral problems which seem similar in character, or even the mere fact that men disregard, when they act immorally, the dictates and implicit principles of the moral consciousness is certain sooner or later to produce the desire either, on the one hand, to justify immoral action by casting doubt upon the authority of the moral consciousness and the validity of its principles, or, on the other hand, to justify particular moral judgments either by (the only valid method) an analysis of the moral principle involved in the judgment and a demonstration of its universal acceptation, or by some attempted proof that the particular moral judgment is arrived at by a process of inference from some universal conception of the Supreme Good or the Final End from which all particular duties or virtues may be deduced.

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  • It will be seen that neither Reid nor Stewart offers more than a very meagre and tentative contribution to that ethical science by which, as they maintain, the received rules of morality may be rationally deduced from self-evident first principles.

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  • For the belief that moral obligation is absolute in character, that it is alike impossible to explain its origin and transcend its laws, would make the search for a scientific criterion of conduct to be deduced from the laws of life and conditions of existence meaningless, if not absurd.

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  • Finally, the conceptions of strength, power and masterfulness by which Nietzsche attempts to determine his own moral ideal, become, when examined, as relative and unsatisfactory as other criteria of moral action said to be deduced from evolutionary principles.

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  • In the case of the greater number of the fixed stars this is so slow that centuries may have to elapse before motion can be deduced.

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  • In China, Egypt and Babylonia, strength and continuity were lent to this native tendency by the influence of a centralized authority; considerable proficiency was attained in the arts of observation; and from millennial stores of accumulated data, empirical rules were deduced by which the scope of prediction was widened and its accuracy enhanced.

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  • Professor Newcomb, who has compiled an instructive table of the equinoxes severally observed by Hipparchus and Ptolemy, with their errors deduced from Leverrier's solar tables, finds palpable evidence that the discrepancies between the two series were artificially reconciled on the basis of a year 6 m too long, adopted by Ptolemy on trust from his predecessor.

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