Formula Sentence Examples

formula
  • Every morning before I went to school I had chores to do, which began with mixing up the formula and feeding the calves.

    162
    79
  • The students could not figure out the math problem until their teacher provided them with a helpful formula.

    122
    50
  • The baby was unable to breastfeed, so her mother had to use formula instead.

    92
    47
  • The chemical formula shows all the elements and compounds involved in the reaction.

    60
    22
  • In point of fact, bourgeois democracy is the political formula for free trade, nothing more.

    77
    44
  • Aiden's mother sent a big tub of formula to daycare so he would not get hungry.

    63
    33
  • I bought some lamb milk formula.

    22
    9
  • Bredig point to the salt possessing the double formula.

    14
    3
  • Cane-sugar has the formula C12H22011.

    12
    1
  • This formula, notwithstanding many attempts at both disproving and modifying it, has well stood the test of time; the subject has been the basis of constant discussion, many variations have been proposed, but the original conception of Kekule remains quite as convenient as any of the newer forms, especially when considering the syntheses and decompositions of the benzene complex.

    5
    2
    Advertisement
  • By fusing two nuclei we obtain the formula of naphthalene, C 1 oH 8; by fusing three, the hydrocarbons anthracene and phenanthrene, C14H10; by fusing four, chrysene, C18H12, and possibly pyrene, C16H1n; by fusing five, picene, C22 H 14.

    3
    1
  • This formula is valid between speeds of 37 and 77 m.

    4
    3
  • This implied that in the benzene complex there was at least one carbon atom linked to three others, thus rendering Kekule's formula impossible and Ladenburg's and Claus' possible.

    1
    0
  • Van 't Hoff's formula is equivalent to taking the frequency of dissociation as proportional to the square of the concentration of the molecules, and the frequency of recombination as proportional to the cube of the concentration of the ions.

    1
    0
  • The forces between the ions of a strongly dissociated solution will thus be considerable at a dilution which makes forces between undissociated molecules quite insensible, and at the concentrations necessary to test Ostwald's formula an electrolyte will be far from dilute in the thermodynamic sense of the term, which implies no appreciable intermolecular or interionic forces.

    1
    0
    Advertisement
  • The properties of caoutchouc clearly show, however, that its actual molecular structure is considerably more complex than is represented by the empirical formula, and that it is to be regarded as the polymer of a terpene or similar hydrocarbon and composed of a cluster of at least ten or twenty molecules of the formula C5H8.

    1
    0
  • The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric function of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!

    1
    0
  • The analogous formula appertaining to n systems of quantities which Vienna Transactions, t.

    1
    0
  • The partitions being taken as denoting symmetric functions we have complete correspondence between the algebras of quantity and operation, and from any algebraic formula we can at once write down an operation formula.

    1
    0
  • It dissolves in an excess of alkali to form plumbites of the general formula Pb(OM) 2.

    1
    0
    Advertisement
  • Steinmetz's formula may be tested by taking a series of hysteresis curves between different limits of B,' measuring their areas by a pianimeter, and plotting the logarithms of these divided by 47r as ordinates against logarithms of the corresponding maximum values of B as abscissae.

    1
    0
  • But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to r t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.

    1
    0
  • Shimizu 3 indicate that Steinmetz's formula holds for nickel and annealed cobalt up to B =3000, for cast cobalt and tungsten steel up to B =8000, and for Swedish iron up to B =18,000, the range being in all cases extended at the temperature of liquid air.

    1
    0
  • He showed that there was, on the whole, a fair agreement between the values determined ballistic ally and those given by the formula B = 871-F.

    1
    0
  • If the pull is measured in pounds and the area in square inches, the formula may be written B =1317 X iI P/S +H.

    1
    0
    Advertisement
  • The range of + B within which Steinmetz's formula is applicable becomes notably increased at low temperature.

    1
    0
  • Steinmetz's formula applies only for very weak inductions when the alloys are at the ordinary temperature, but at the temperature of liquid air it becomes applicable through a wide range of inductions.

    1
    0
  • Owing to the difficulty of determining the magnetization I and the susceptibility K with accuracy, it has not yet been possible to submit this formula to a quantitative test, but it is said to afford an indication of the results given by actual experiment.

    1
    0
  • It is pointed out that this formula may be used as a temperature correction in magnetic determinations carried out in air.

    1
    0
  • His treatise was remarkable, not only as offering a satisfactory explanation of the coincidence between the lunar periods of rotation and revolution, but as containing the first employment of his radical formula of mechanics, obtained by combining with the principle of d'Alembert that of virtual velocities.

    1
    0
  • To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems. To the calculus of finite differences he contributed the beautiful formula of interpolation which bears his name; although substantially the same result seems to have been previously obtained by Euler.

    1
    0
  • A formula was found by Bynkershoek in his De dominio maxis (1702) for the restriction of dominion over the sea to the actual distance to which cannon range could protect it.

    1
    0
  • The inherent difficulties of Realism led to a J variety of attempts to reach a more satisfactory formula.

    1
    0
  • Biot, who assisted in the correction of its proof sheets, remarked that it would have extended, had the demonstrations been fully developed, to eight or ten instead of five volumes; and he saw at times the author himself obliged to devote an hour's labour to recovering the dropped links in the chain of reasoning covered by the recurring formula.

    1
    0
  • In the case of division we get two kinds of arithmetical formula, which, however, may be regarded as requiring a single kind of numerical process in order to determine the final result.

    1
    0
  • In the second place, particular cases lay the foundation for the general formula.

    1
    0
  • In this, as in almost all other cases, particular examples should be worked before obtaining a general formula.

    1
    0
  • The binomial theorem gives a formula for writing down the coefficient of any stated term in the expansion of any stated power of a given binomial.

    1
    0
  • Assuming the above formula to represent guncotton, there is sufficient oxygen for internal combustion without any carbon being left.

    1
    0
  • He found out the formula for deriving the sine of a multiple angle, knowing that of the simple angle with due regard to the periodicity of sines.

    1
    0
  • There may be an advantage to the divorce action being filed in a certain jurisdiction; for example a couple may not want to file in a community property state if they have agreed on a different formula for dividing their marital property.

    33
    32
  • Strecker to be trichloracetoacrylic acid, was more favourably explained by his formula than by Ladenburg's.

    0
    0
  • From these results Baeyer concluded that Claus' formula with three para-linkings cannot possibly be correct, for the Q2.5 dihydroterephthalic acid undoubtedly has two ethylene linkages, since it readily takes up two or four atoms of bromine, and is oxidized in warm aqueous solution by alkaline potassium permanganate.

    0
    0
  • The stronger argument against the ethylenoid linkages demanded by Kekule's formula is provided by the remarkable stability towards oxidizing and reducing agents which characterizes all benzenoid compounds.

    0
    0
  • In this formula, the so-called " centric formula," the assumption made is that the fourth valencies are simply directed towards the centre of the ring; nothing further is said about the fourth valencies except that they exert a pressure towards the centre.

    0
    0
  • Claus maintained that Baeyer's view was identical with his own, for as in Baeyer's formula, the fourth valencies have a different function from the peripheral valencies, being united at the centre in a form of potential union.

    0
    0
  • Marckwald (Ann., 93, 74, 331; 1894, 79, 14) has supported this formula from considerations based on the syntheses of the quinoline ring.

    0
    0
  • Bamberger (a strong supporter of the centric formula), have shown that the nature of the substituent groups influences the distribution of the fourth valencies; therefore it may be con-?

    0
    0
  • A similar contradiction apparently exists with regard to the specific volume, for while benzene has a specific volume correspinding to Claus' formula, toluene, or methylbenzene, rather points to Kekule's.

    0
    0
  • Stohmann of Leipzig; and the new data and the conclusions to be drawn from them formed the subject of much discussion, Briihl endeavouring to show how they supported Kekule's formula, while Thomsen maintained that they demanded the benzene union to have a different heat of combustion from the acetylene union.

    0
    0
  • It was found that the results were capable of expression by the empirical relation CaH2b= 104.3b+49'09m+105.47n, where C a H 2b denotes the formula of the hydrocarbon, m the number of single carbon linkings and n the number of double linkings, m and n being calculated on the Kekule formulae.

    0
    0
  • Experiments showed that the second acid was much more difficult to esterify than the first, pointing to the conclusion that Claus' formula for benzene was more probable than Kekule's.

    0
    0
  • Ladenburg's prism formula would give two enantiomorphic ortho-di-substitution derivatives; while forms in which the hydrogen atoms are placed at the corners of a regular octahedron would yield enantiomorphic tri-substitution derivatives.

    0
    0
  • The octahedral formula discussed by Julius Thomsen (Ber., 1886, 19, p. 2 944) consists of the six carbon atoms placed at the corners of a regular octahedron, and connected together by the full lines as shown in (I); a plane projection gives a hexagon with diagonals (II).

    0
    0
  • Therefore formula (2), being unsymmetrical, is impossible.

    0
    0
  • It remains, therefore, to consider Erlenmeyer's formula and those derived from the centric hypothesis.

    0
    0
  • The centric formula proposed by Bamberger represents naphthalene as formed by the fusion of two benzene rings, this indicates that it is a monocyclic composed of ten atoms of carbon.

    0
    0
  • The formula has the advantage that it may be constructed from tetrahedral models of the carbon atom; but it involves the assumption that the molecule has within it a mechanism, equivalent in a measure to a system of railway points, which can readily close up and pass into that characteristic of benzene.

    0
    0
  • These isomeric hydrocarbons, of the formula C14H10, are to be regarded as formed by the fusion of three.

    0
    0
  • Thus a comparison of numbers occurring in a table of squares 1 2 =1 112=121 2 2= 4 122=144 3 2 =9 132=169 suggests the formula (A+a)2=A2+2Aa+a2.

    0
    0
  • Now suppose that the formula (2) has been established for every power of A+a up to the (n-i)th inclusive, so that (ii_ I) = (n- I) (r), (y I) = (n -1) (r _ l).

    0
    0
  • Hence the formula (2) is also true for the nth power of A-I-a.

    0
    0
  • Thus we get a formula for the sum of n terms of a series such as 2.4.6+4.6.8+..., or 6.8.10.12+8.10.12.14+...

    0
    0
  • The general formula (which is established by more advanced methods) is 4.

    0
    0
  • Whatever value is to be attached to Mendel's observation of the breaking up of self-fertilized hybrids of cultivated varieties into the two original parent forms according to the formula " 'PP, 2PN, INN," it cannot be considered as more than a contribution to the extensive investigation of heredity which still remains to be carried out.

    0
    0
  • From the general formula (2), if A be the area of aperture, 102 = A2 / x2 f (7) The formation of a sharp image of the radiant point requires that the illumination become insignificant when, n attain small values, and this insignificance can only arise as a consequence of discrepancies of phase among the secondary waves from various parts of the aperture.

    0
    0
  • The formula expressing the optical power of prismatic spectroscopes may readily be investigated upon the principles of the wave theory.

    0
    0
  • Fresnel (1815), who gave a formula equivalent to (5) below.

    0
    0
  • If 8 and 4' denote the angles with the normal made by the incident and diffracted rays, the formula (5) still holds, and, if the deviation be reckoned from the direction of the regularly reflected rays, it is expressed as before by (0+0), and is a minimum when 8 = 0, that is, when the diffracted rays return upon the course of the incident rays.

    0
    0
  • This is the ordinary formula for a reflecting plane grating, and it shows that the spectra are formed in the usual directions.

    0
    0
  • The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...

    0
    0
  • Peligot's results, though called in question by Berzelius, have been amply confirmed by all subsequent investigators; only now, on theoretical grounds, first set forth by Mendeleeff, we double Peligot's atomic weight, so that U now signifies 240 parts of uranium, while UO 3 stands as the formula of the yellow oxide, and UO 2 as that of Berzelius's metal.

    0
    0
  • Stannic sulphide, SnS 2, is obtained by heating a mixture of tin (or, better, tin amalgam), sulphur and sal-ammoniac in proper proportions in the beautiful form of aurum musivum (mosaic gold) - a solid consisting of golden yellow, metallic lustrous scales, and used chiefly as a yellow "bronze" for plaster-of-Paris statuettes, &c. The yellow precipitate of stannic sulphide obtained by adding sulphuretted hydrogen to a stannic solution readily dissolves in solutions of the alkaline sulphides to form thiostannates of the formula M 2 SnS 31 the free acid, H2SnS3, may be obtained as an almost black powder by drying the yellow precipitate formed when hydrochloric acid is added to a solution of a thiostannate.

    0
    0
  • This colouring power is due to the presence of polychlorite, a substance whose chemical formula appears to be C4 8 1-160018, and which may be obtained by treating saffron with ether, and afterwards exhausting with water.

    0
    0
  • The smallest empirical formula for cellulose (q.v.) may certainly be written C6H1005.

    0
    0
  • If guncotton be correctly represented by the formula C 6 H 7 0 2 (NO 3) 3, it should contain a little more than 14% of nitrogen.

    0
    0
  • Busch (Ber., 1905, 38, pp. 856, 4049) has isolated a series of bridged ring compounds which he describes as endo-iminodihydrotriazoles, the triphenyl derivative (annexed formula) being prepared by condensing triphenylaminoguanidine with formic acid.

    0
    0
  • In reply to Rudolf Hospinian's Concordia discors (1607), he wrote a work, rich in historical material but one-sided in its apologetics, Concordia concors (1614), defending the formula of Concord, which he regarded as inspired.

    0
    0
  • Another work, based on the formula of Concord, was entitled Loci communes theologici.

    0
    0
  • His formula was "to royalize France and to nationalize the monarchy."

    0
    0
  • I +W a W a), ' (k) 4 (I I) I+ w- R For a shot in air the ratio W'/W is so small that the square may be neglected, and formula (II) can be replaced for practical purpose in artillery by tan26= n2 = W i (0 - a) (k ð)7()4, (12) if then we can calculate /3, a, or (3-a for the external shape of the shot, this equation will give the value of 6 and n required for stability of flight in the air.

    0
    0
  • Its dental formula (as that of Tragulus) is i., c. m.1 =34.

    0
    0
  • The first term includes simple sugars containing two to nine atoms of carbon, which are known severally as bioses, trioses, tetroses, pentoses, hexoses, &c.; whilst those of the second group have the formula C12H22011 and are characterized by yielding two monosaccharose molecules on hydrolysis.

    0
    0
  • In addition trisaccharoses are known of the formula C13H32016; these on hydrolysis yield one molecule of a monosaccharose and one of a disaccharose, or three of a monosaccharose.

    0
    0
  • According to Mayer, the formula of convolvulin is C34HSO016, and that of jalapin C31HS0016.

    0
    0
  • To the bishop's formula, "I separate thee from the church militant and the church triumphant," Savonarola replied in firm tones, "Not from the church triumphant; that is beyond thy power."

    0
    0
  • C. von Hahn as the Aryan Expulsion and Return formula, which counts among its representatives such heroes as Perseus, Cyrus, Romulus and Remus, Siegfried, and, as Alfred Nutt has pointed out, Arthur himself.

    0
    0
  • Spencer tries to express in a sweeping general formula the belief in progress which pervaded his age, and to erect it into the supreme law of the universe as a whole.

    0
    0
  • The Formula of Concord (1577),which gave to the whole Lutheran Church of Germany a common doctrinal system, declined to accept the Calvinistic position that man's condemnation as well as his salvation is an object of divine predestination.

    0
    0
  • Methane and its homologues give origin to the " paraffin " or " fatty series " of the general formula C,H 2, ,+ 1 000H, ethylene gives origin to the acrylic acid series, C n H 27, - 1 000H, and so on.

    0
    0
  • Dibasic acids of the paraffin series of hydrocarbons have the general formula C n H 2 (000H) 2 "; malonic and succinic acids are important members.

    0
    0
  • By uttering a sacred formula the good spirit throws the evil one into a state of confusion for a second 3000 years, while he produces the archangels and the material creation, including the sun, moon and stars.

    0
    0
  • The summit C of the branch BCD occurs at a percentage exactly corresponding to the formula Hg 2 T1.

    0
    0
  • Potassium and sodium readily dissolve in ethyl alcohol with the production of alcoholates of the formula C2 H5 OK(Na).

    0
    0
  • In the extreme case when e=1, the prolate ellipsoid becomes a long thin rod, and then the capacity is given by C 1 = a/log e 2a/b (io), which is identical with the formula (2) already obtained.

    0
    0
  • This formula is important in connexion with the capacity of electric cables, which consist of a cylindrical conductor (a wire) enclosed in a conducting sheath.

    0
    0
  • Many complicated expressions have been suggested by subsequent writers in the attempt to represent the continuity of the gaseous and liquid states in a single formula, but these are of a highly empirical nature, and beyond the scope of the present inquiry.

    0
    0
  • This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a function of the temperature only.

    0
    0
  • They are not conceived of in any anthropomorphic form, their sex even may often be indeterminate ("sive mas, sive femina" is the constantly recurring formula of prayer), but the sphere of action of each is clearly marked and an appeal to a spirit outside his own special sphere would never even be thought of.

    0
    0
  • In conjunc tion with Andrea and Selnecker he induced the Lutherans of Saxony and Swabia to adopt the Formula Concordiae and so become one body.

    0
    0
  • Schmalkalden, drawn up by Luther in 1536, Luther's catechisms, and the Formula of Concord which was an attempt to settle doctrinal divisions promulgated in 1580, sum up what is called " the confessional theology of Lutheranism."

    0
    0
  • It shows the influence of Arminian theology against Calvinism, which was vigorously upheld in the Quin-particular formula, put forward by the synod of Dort in 1619 to uphold the five points of Calvinism, after heated discussion, in which English delegates took part, of the problems of divine omniscience and human free-will.

    0
    0
  • True, the impression conveyed by the attitude of the Catholic party at the second Diet of Spires had served to awaken the feeling for solidarity among the Evangelicals there assembled; and on the 22nd of April they had even secured the basis for a provisional alliance in the shape of a formula drawn up by Bucer and dealing with the Lord's Supper.

    0
    0
  • The dental formula is i.

    0
    0
  • This formula must have been known to Vieta in 1593.

    0
    0
  • There are several corrections of the formula O =W/(W - W1) necessary to the accurate expression of the density.

    0
    0
  • The pipette having been carefully dried, the process is repeated with pure alcohol or with proof spirits, and the strength of any admixture of water and spirits is determined from the corresponding number of drops, but the formula generally given is not based upon sound data.

    0
    0
  • The "service of God and his majesty" was the formula which expressed the belief of the sovereign and his subjects.

    0
    0
  • He has been classed with Arians, but he endorses in his own way the homoousian formula, and denounces Arius as " Christi gloriae incapacissimus."

    0
    0
  • Such a simple formula is only possible because the salts of sea-water are of such uniform composition throughout the whole ocean that the chlorine bears a constant ratio to the total salinity as newly defined whatever the degree of concentration.

    0
    0
  • The temperature of maximum density of sea-water of any specific gravity was found by Knudsen to be given with sufficient accuracy for all practical purposes by the formula 0 = 3.950.2660 -0, where 0 is the temperature of maximum density in degrees centigrade.

    0
    0
  • The number of molecules of the first kind of gas, whose components of velocity lie within the ranges between u and u+du, v and v+dv, w and w+dw, will, by formula (5), be v?l (h 3 m 3 /7 3)e hm (u2+v2+w2)dudvdw (9) per unit volume.

    0
    0
  • To examine what is meant by a zero value of n we refer to formula (15).

    0
    0
  • If a solid body is regarded as an aggregation of similar atoms each of mass m, its specific heat C is given, as in formula (19) by C = i (n+3) R/Jm.

    0
    0
  • In the formula used by Synesius (4,0) which is to be found in Bingham's Antiquities, we already find the attention of magistrates specially called to the censured person.

    0
    0
  • In conditional baptism the Latins, since about the year 1227, use the formula, " If thou art not baptized, then do I baptize thee," &c. The Latins further insist on a strict observance of the traditional matter and form.

    0
    0
  • Its compound with calcium chloride has the formula CaC1 2.4CH 3.

    0
    0
  • It passes over equal spaces in equal times, but falls with an accelerating velocity according to the formula h = zgt 2, where h is the height fallen through, g the force of gravity, and t the time of flight.

    0
    0
  • The formula for length of scale is, length = sighting radius X tangent of the angle of elevation.

    0
    0
  • None are to partake of it save those who have been "baptized in the name of the Lord" (an expression which is of interest in a document which prescribes the threefold formula).

    0
    0
  • On the Protestant side the identity is still clear in the Lutheran Formula of Concord (1577).

    0
    0
  • It has the exact vapour-density corresponding to the formula.

    0
    0
  • But an area or a volume cannot generally be measured by successive applications of the unit of area or volume; intermediate processes are necessary, the result of which is expressed by a formula.

    0
    0
  • Mensuration, then, is mainly concerned with quadratureformulae and cubature formulae, and, to a not very clearly defined extent, with the methods of obtaining such formulae; a quadrature-formula being a formula for calculating the numerical representation of an area, and a cubature-formula being a formula for calculating the numerical representation of a volume, in terms, in each case, of the numerical representations of particular data which determine the area or the volume.

    0
    0
  • The deduction of the formula tab, where a and b are numbers, should be regarded as a later step.

    0
    0
  • This involves the use of Cartesian co-ordinates, and leads to important general formulae, such as Simpson's formula.

    0
    0
  • The numerical result obtained by applying a formula to particular data will generally not be exact.

    0
    0
  • The length of the arc of a circle, for instance, is known if the length of the chord and its distance from the middle point of the arc are known; but it may be more convenient in such a case to use a formula such as Huygens's rule than to obtain a more accurate result by means of trigonometrical tables.

    0
    0
  • Such a formula is approximative, in that it is known that the result of its application will only be approximately correct; it differs from an approximative formula of the kind mentioned in (i) (b) above, in that it is adopted of necessity, not by choice.

    0
    0
  • The formula is a deduction from a general formula, considered later (§ 58), and may be verified in various ways.

    0
    0
  • Hence, by (i) and (ii), the formula holds for this figure.

    0
    0
  • By (i) and (iii), the formula holds for each of these figures; and therefore it holds for the prismoid as a whole.

    0
    0
  • The first of these is a particular case of the prismoidal formula (§ 58).

    0
    0
  • The area is then given by the formula of § 25 (ii).

    0
    0
  • This is Simpson's formula.

    0
    0
  • This is Simpson's second formula.

    0
    0
  • It may be deduced from the formula given above.

    0
    0
  • Simpson's (first) formula, for instance, holds for f = I, and is obtained by taking p = i and ignoring differences after 52up.

    0
    0
  • Thus we find from (i) that Simpson's second formula, for the case where the top is a parabola (with axis, as before, at right angles to the base) and there are three strips of breadth h, may be replaced by area = 8h(3u i + 2U 1 + 3us).

    0
    0
  • This might have been deduced directly from Simpson's first formula, by a series of eliminations.

    0
    0
  • The same formula will also hold (§ 52) for any cubic trapezette through the points.

    0
    0
  • It follows from §§ 48 and 51 that, if V is a solid figure extending from a plane K to a parallel plane L, and if the area of every cross-section parallel to these planes is a quadratic function of the distance of the section from a fixed plane parallel to them, Simpson's formula may be applied to find the volume of the solid.

    0
    0
  • This formula applies to such figures as the cone, the sphere, the ellipsoid and the prismoid.

    0
    0
  • The formula is known as the prismoidal formula.

    0
    0
  • If u is an algebraical function of x of degree not exceeding p, and if the area of a trapezette, for which the ordinate v is of degree not exceeding p+q, may be expressed by a formula Aovo-1--yivi+..

    0
    0
  • This ordinate will be an algebraical function of x, and we can again apply a suitable formula.

    0
    0
  • The areas of the sides for which 0 and x=xo+2h, and of the section by the plane x=xo+h, may be found by Simpson's second formula; call these Ao and A2, and Al.

    0
    0
  • Hence Simpson's formula applies, and the volume is lh(A0-I-4A1+ A2).

    0
    0
  • The process is simplified by writing down the general formula first and then substituting the values of u.

    0
    0
  • The volume of a frustum of a cone, for instance, can be expressed in terms of certain magnitudes by a certain formula; but not only will there be some error in the measurement of these magnitudes, but there is not any material figure which is an exact cone.

    0
    0
  • The formula may, however, be used if the deviation from conical form is relatively less than the errors of measurement.

    0
    0
  • In the case of mathematical functions certain conditions of continuity are satisfied, and the extent to which the value given by any particular formula differs from the true value may be estimated within certain limits; the main inaccuracy, in favourable cases, being due to the fact that the numerical data are not absolutely exact.

    0
    0
  • Applying Simpson's formula to each of these, we have A -__9= *h(uo + 4 14 1 + u2) + 3 h (14 2 + 4u3 + u4) + ..

    0
    0
  • The legitimacy of this assumption, and of the further assumption which enables the area of the new figure to be expressed by an approximate formula instead of by an exact formula, must be verified in every case by reference to the actual differences.

    0
    0
  • The alternative method, therefore, consists in taking a simple formula, such as the trapezoidal rule, and correcting it to suit the mutual relations of the differences.

    0
    0
  • Their generalization is given by the Euler-Maclaurin formula = I, = 0, = 0, = 0 .

    0
    0
  • Either or both of the expressions K and L will have to be calculated by means of the formula of § 84; if this is applied to both expressions, we have a formula which may be written in a more general form f f 4 u4(x, y) dx dy = u dx dy.

    0
    0
  • The Euler-Maclaurin formula (§ 75) assumes that the bounding values of u', u"',..

    0
    0
  • To find the quantity of timber in a trunk with parallel ends, the areas of a few sections must be calculated as accurately as possible, and a formula applied.

    0
    0
  • The formula applied can then be either Simpson's rule or a rule based on Gauss's theorem for two ordinates (§ 56).

    0
    0
  • He supposed that in air Boyle's law holds in the extensions and compressions, or that p = kp, whence dp/dp = k = p/p. His value of the velocity in air is therefore U = iJ (p ip.) (Newton's formula).

    0
    0
  • That is to say, instead of using Boyle's law, which supposes that the pressure changes so exceedingly slowly that conduction keeps the temperature constant, we must use the adiabatic relation p = kpy, whence d p /d p = y k p Y 1= yp/p, and U = (yp/p) [Laplace's formula].

    0
    0
  • This formula was very nearly confirmed for hydrogen, carbon dioxide and nitrous oxide.

    0
    0
  • Its introduction into the baptismal formula (in the Greek Church it is pronounced after the name of each person of the Trinity) is probably later.

    0
    0
  • 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.

    0
    0
  • The reciprocal figure for any loaded frame is a complete formula for the stress on every member of a frame of that particular class with loads on given joints.

    0
    0
  • About 15% of a volatile oil is obtained by distilling cubebs with water; after rectification with water, or on keeping, this deposits rhombic crystals of camphor of cubebs, C 15 H 26 O; cubebene, the liquid portion, has the formula C15HV4.

    0
    0
  • It is evident, therefore, that the request for a definition of Ultramontanism cannot be answered with a concise formula, but that the varied character of its manifestations necessitates a more detailed examination of its peculiar objects.

    0
    0
  • But about the r3th century the Roman formula was altered, and the council of Trent (1551) declared that the "form" and power of the sacrament of penance lay in the words Ego to absolvo, &c., and that the accompanying prayers are not essential to it.

    0
    0
  • On hearing from Rome, Cyril at once held a synod and drew up a doctrinal formula for Nestorius to sign, and also twelve anathemas covering the various points of the Nestorian dogmatic. Nestorius, instead of yielding to the combined pressure of his two great rivals, merely replied by a counter excommunication.

    0
    0
  • The commotion which had been thus raised did not so easily subside in the more eastern section of the church; the Antiochenes continued to maintain for a considerable time an attitude of antagonism towards Cyril and his creed, and were not pacified until an understanding was reached in 433 on the basis of a new formula involving some material conce9sions by him.

    0
    0
  • His seeming inconsistencies are reconciled to apprehension, not by a formula of the intellect, but by the many-sidedness of a highly impressible nature.

    0
    0
  • MacCullagh's hands the correct equations were derived from a single energy formula by the principle of least action; and while the validity of this dynamical method was maintained, it was frankly admitted that no mechanical analogy was forthcoming.

    0
    0
  • The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.

    0
    0
  • In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation.

    0
    0
  • Integrating (27) again, (31) y =g(zTt2t 2) = zgt(T -t); and denoting T-t by t', and taking g= 32f/s2,) y =16tt', (32 which is Colonel Sladen's formula, employed in plotting ordinates.

    0
    0
  • The last column in the Range Table giving the inches of penetration into wrought iron is calculated from the remaining velocity by an empirical formula, as explained in the article Armour Plates.

    0
    0
  • But no formula has yet been invented, derived on theoretical principles from the physical data, which will assign by calculation a definite magnitude to 3.

    0
    0
  • The formula shows that except for numbers of the form (3n 2 n) the number of partitions without repetitions into an odd number of parts is equal to the number of partitions without repetitions into an even number of parts, whereas for the excepted numbers these numbers differ by unity.

    0
    0
  • We have such analytical formulae as that is, any number from I to 15 can be made with the parts I, 2, 4, 8; and similarly any can be made up, and in one way only, with A like formula is I - x 3 I - x9 I - x27 I x.

    0
    0
  • The olefines may be synthetically prepared by eliminating water from the alcohols of the general formula CnH2n+1 OH, using sulphuric acid or zinc chloride generally as the dehydrating agent, although phosphorus pentoxide, syrupy phosphoric acid and anhydrous oxalic acid may frequently be substituted.

    0
    0
  • This fact, coupled with the determination of the vapour density of the gas, establishes the molecular formula CO.

    0
    0
  • The current theological formula for this two-sided position is that the prophets are at once preachers of the law and forerunners of the gospel; and, as it is generally assumed that they found the law already written, their originality and real importance is made to lie wholly in their evangelical function.

    0
    0
  • It will be evident even from this rapid sketch, necessarily confined to a few of the most cardinal points, that Hebrew prophecy is not a thing that can be defined and reduced to a formula, but was a living institution which can only be understood by studying its growth and observing its connexion with the historical movements with which its various manifestations were bound up. Throughout the great age of prophecy the most obvious formal character that distinguished it was that the 1 One might say from the days of Habakkuk.

    0
    0
  • This equation defines log x for positive values of x; if o the formula ceases to have any meaning.

    0
    0
  • It will be observed that in the first process the value of the modulus is in fact calculated from the formula.

    0
    0
  • The logarithm is then obtained by use of the formula d l d2 l d3 2 log e (x+d) = log e x-f- - x2+3 x3 - &c., in which of course the object is to render dlx as small as possible.

    0
    0
  • The formula arrived at by Cauchy was n= A-FB+?

    0
    0
  • If suitable values are chosen for these constants, the formula can be made to represent the dispersion of ordinary transparent media within the visible spectrum very well, but when extended to the infra-red region it often departs considerably from the truth, and it fails altogether in cases of anomalous dispersion.

    0
    0
  • There are also grave theoretical objections to Cauchy's formula.

    0
    0
  • Ketteler and known as the Ketteler-Helmholtz formula, has been much used in calculating dispersion, and expresses the facts with remarkable accuracy.

    0
    0
  • P. Drude has obtained a similar formula based on the electromagnetic theory, thus placing the theory of dispersion on a much more satisfactory basis.

    0
    0
  • As A m is a wave-length corresponding to an absorption band, this formula can be used to find values of A m which satisfy the observed values of n within the region of transparency, and so to determine where the absorption bands are situated.

    0
    0
  • His refusal to subscribe unconditionally to the rigid formula of belief adopted by the theologians of Tubingen permanently closed against him the gates of his alma mater.

    0
    0
  • Rohner (Ber., 1909, 42, p. 4 0 93) obtained a yellowish white oxide, of the formula I 4 0 9, which they regard as an iodate of tervalent iodine, Millon's oxide being considered a basic iodate.

    0
    0
  • On the next topic of importance, the primacy of the pope, the project of union nearly suffered shipwreck; but here a vague formula was finally constructed which, while acknowledging the pope's right to govern the church, attempted to safeguard as well the rights of the patriarchs.

    0
    0
  • And although the God of light himself now took to the field, and with the help of new aeons (the spirit of life, &c.) inflicted total defeat upon Satan, and set the ' A is spoken of in the formula of abjuration, and an Epistola ad virginem Menoch by Augustine.

    0
    0
  • The milk-dentition, and even the early condition of the permanent dentition, is formed on the same general type as that of Sus, except that certain teeth are absent, the formula being 13 i cl, total 34; but as age advances all the teeth have a tendency to disappear, except the canines and the posterior molars, but these, which in some cases are the only teeth left in the jaws, attain an extraordinary development.

    0
    0
  • Again, like the hierophant, the sycophant publicly pronounced the formula of exclusion of certain unworthy persons from the celebration of the mysteries of the fig.

    0
    0
  • A synopsis of the leading formula connected with the circle will now be given.

    0
    0
  • Archimedes's process of unending cycles of arithmetical operations could at best have been expressed in his time by a " rule" in words; in the 16th century it could be condensed into a " formula."

    0
    0
  • Accordingly, we find in Vieta a formula for the ratio of diameter to circumference, viz.

    0
    0
  • This Rule Is Conveniently Expressed By The Formula (X 9) R, In Which X Denotes The Date, And The Symbol R Denotes That The Remainder, Which Arises From The Division Of X 9 By 28, Is The Number Required.

    0
    0
  • The Symbol X, Employed In The Formula At The Top Of The Column, Denotes The Number Of Centuries, That Is, The Figures Remaining After The Last Two Have Been Struck Off.

    0
    0
  • This number is called the Golden Number, either because will therefore be given by the formula (x 1 53) r, that is to say, add 3 totlzedate,divide the sum by 15, and the remainder is the year of the indiction.

    0
    0
  • In This Case, As The Formula Supposes The Intercalation Already Made, The Resulting Letter Is That Which Applies After The 29Th Of February.

    0
    0
  • In Order To Investigate A Formula For The Epact, Let Us Make E=The True Epact Of The Given Year; J =The Julian Epact, That Is To Say, The Number The Epact Would Have Been If The Julian Year Had Been Still In Use And The Lunar Cycle Had Been Exact;, S =The Correction Depending On The Solar Year; M =The Correction Depending On The Lunar Cycle; Then The Equation Of The Epact Will Be E=J S M; So That E Will Be Known When The Numbers J, S, And M Are Determined.

    0
    0
  • Now This Is A Condition Which Will Evidently Be Expressed In General By The Formula N (N 1).

    0
    0
  • 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.

    0
    0
  • P= 54 E 1=57 E, Or (57 E) 7 R' By Substituting One Or Other Of These Values Of P And 1, According A; The Case May Be, In The Formula P = P (L L), We Shall Have P, Orthe Number Of Days From The 21St Of March To Easter Sunday.

    0
    0
  • This Formula Gives The Following Rule For Calculating The Date Of The Commencement Of Any Year Of The Hegira, According To The Gregorian Or New Style.

    0
    0
  • Appended to the London edition of the solar and lunar tables are two short tracts - the one on determining longitude by lunar distances, together with a description of the repeating circle (invented by Mayer in 1752), the other on a formula for atmospheric refraction, which applies a remarkably accurate correction for temperature.

    0
    0
  • He describes himself when he says, "The student of Christian doctrine, because he strives after exactness of phrase, because he is conscious of the inadequacy of any one human formula to exhaust the truth, will be filled with sympathy for every genuine endeavour towards the embodiment of right opinion.

    0
    0
  • The dental formula varies from 1, c. $, 3 (total 28) in the hares and rabbits to i.

    0
    0
  • Possibly the European forms, in which the dental formula has been given as i., c. S, p, m.

    0
    0
  • Fibroin, which is analogous to horn, hair and like dermal products, constitutes about 75 to 82% of the entire mass, and has a composition represented by the formula C15H23 506.

    0
    0
  • Its formula is C15H25N508.

    0
    0
  • If within the range5100-3700A, the constants are determined once for all, the formula seems capable of giving by interpolation results accurate to o 2 A, but as a rule the range to which the formula is applied will be much less with a corresponding gain in the accuracy of the results.

    0
    0
  • Balmer's formula received a striking confirmation when it was found to include the ultra-violet lines which were discovered by Sir William Huggins' in the photographic spectra of stars.

    0
    0
  • The most complete hydrogen spectrum is that measured by Evershed 8 in the flash spectrum observed during a total solar eclipse, and contains thirty-one lines, all of which agree with considerable accuracy with the formula, if the frequency number n is calculated correctly by reducing the wave-length to vacuo.9 It is a characteristic of Balmer's formula that the frequency approaches a definite limit as s is increased, and it was soon discovered that in several other spectra besides hydrogen, series of lines could be found, which gradually come nearer and nearer to each other as they become fainter, and approach a definite limit.

    0
    0
  • Such series ought all to be capable of being represented by a formula resembling that of Balmer, but so far the exact form of the series has not been established with certainty.

    0
    0
  • C. Pickering' used in a special case, presently to be referred to, was put into a more general form by Thiele, who, however, assumes N to have the same value for all spectra, and not obtaining sufficient agreement, rejects the formula.

    0
    0
  • If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.'

    0
    0
  • A discussion of band spectra on a very broad basis was given by Thiele,' who recommends a formula - q +qi(s+c)+ +qr(s+c)r n in the discharge, except within the region of the kathode glow.

    0
    0
  • Three acids of this empirical formula are known, viz.

    0
    0
  • The widow then loosens and removes the shoe, throwing it some distance, and spits on the ground, repeating thrice the Biblical formula "So shall it be done," &c. Ilalisah, which is still common among orthodox Jews, must not take place on the Sabbath, a holiday, or the eve of either, or in the evening.

    0
    0
  • This is used as the sulphate, which has the empirical formula of (C15H21N302)2, H 2 SO 4, plus an unknown number of molecules of water.

    0
    0
  • Later, the Variata of 1540 became the creed of the lVlelanchthonians and even of the Crypto-calvinists; so the framers of the Formula of Concord, promulgated in 1580, returned to the text handed in at the Diet.

    0
    0
  • The textus receptus is that of the Formula of Concord, the divergent Latin and German forms being equally binding.

    0
    0
  • Its antiquity is attested by the symbol and formula used in its procedure, the lance (hasta) as the sign of true ownership, the oath or wager (sacramentum), the ancient formula for recovery of property or assertion of liberty.

    0
    0
  • That orthoboric acid is a tribasic acid is shown by the formation of ethyl orthoborate on esterification, the vapour density of which corresponds to the molecular formula B(0C2H5)3; the molecular formula of the acid must consequently be B(OH) 3 or H 3 B0 3.

    0
    0
  • But the free-traders did not like Mr Balfour's formula as to reversing the traditional fiscal policy of import taxes for revenue only.

    0
    0
  • As regards the recent forms, the dentition in the fully adult animal consists only of incisors and cheek-teeth, the formula being i.

    0
    0
  • Since this party in the course of years came more and more into sympathy with the representatives of the Nicene party, the Homoousians, and notably with Athanasius, the much-disputed formula became more and more popular, till the council summoned in 38L at Constantinople, under the auspices of Theodosius the Great, recognized the Nicene doctrine as the only orthodox one.

    0
    0
  • The seal is that of the fisherman's ring, hence the formula of conclusion, "Datum Romae, sub annulo Piscatoris."

    0
    0
  • It often happens that analyses of brown iron ores reveal a larger proportion of water than required by the typical formula of limonite, and hence new species have been recognized.

    0
    0
  • Schmidt xanthosiderite, from 1'avOos (yellow) and otSnpos (iron), contains Fe 2 0(OH) 4, or Fe 2 0 3.2H 2 O; whilst the bog ore known as limnite, from At vn (marsh) has the formula Fe(OH) 3, or Fe203.3H20.

    0
    0
  • Its vapour density at temperatures above 750 corresponds to the formula AlCl 3 j below this point the molecules are associated.

    0
    0
  • According to the formula FeS2, pyrites contains theoretically 46.67% of iron and 53.33 of sulphur.

    0
    0
  • For instance, following Krupp's formula, the side and barbette armour of war-vessels is now generally if not universally made of nickel steel containing about 3.25% of nickel, 0.40% of carbon, and 1.50% of chromium, deeply carburized on its impact face.

    0
    0
  • The monovalent iodine, for instance, is transformed by heating into an allotropic form, corresponding to the formula I, whereas ordinary iodine answers to I 2.

    0
    0
  • Now, in this case, the first definition expresses much better the whole chemical behaviour of ozone, which is that of "energetic" oxygen, while the second only includes the fact of higher vapour-density; but in applying the first definition to organic compounds and calling isobutylene "butylene with somewhat more energy" hardly anything is indicated, and all the advantages of the atomic conception - the possibility of exactly predicting how many isomers a given formula includes and how you may get them - are lost.

    0
    0
  • It does not, however, satisfy the Socialists, whose formula is one man, one vote.

    0
    0
  • This formula includes the vast majority of cardiac cases.

    0
    0
  • When the formula cited is not used, other somewhat nebulous expressions are sometimes employed, as, for example, that.

    0
    0
  • If Y and Z are groups which behave very differently, then there is apparently no tautomerism and a definite formula can be given to the compound.

    0
    0
  • The conductivity of the same bars was independently determined by the method of Forbes, employing an ingenious formula for the heat-loss in place of Newton's law.

    0
    0
  • He was one of the most influential supporters of the Formula Consensus Helvetica, drawn up chiefly by Johann Heinrich Heidegger (1633-1698), in 1675, and of the particular type of Calvinistic theology which that symbol embodied, and an opponent of the theology of Moses Amyraut and the school of Saumur.

    0
    0
  • During the next forty years of his life he enjoyed great influence in Geneva as the advocate of a more liberal theology than had prevailed under the preceding generation, and it was largely through his instrumentality that the rule obliging ministers to subscribe to the Formula Consensus Helvetica was abolished in 1706, and the Consensus itself renounced in 1725.

    0
    0
  • Its vapour density has been determined by Nilson and Pettersson, and corresponds to the molecular formula BeC12.

    0
    0
  • The total number of teeth is 34, with the formula i.3.

    0
    0
  • Two acids are known corresponding to this formula, normal butyric acid, CH 3 CH 2 CH 2.

    0
    0
  • Lovering's general formula suggests that the 4-month term is really less important than the 3-month term, but he gives no data for the latter at individual stations.

    0
    0
  • They had been converted to Mahommedanism in the early times of the Arab conquest, but their knowledge of Islam did not go much beyond the formula of the creed - "there is no god but God, and Mahomet is the apostle of God," - and they were ignorant of the law.

    0
    0
  • No verbal formula can really enclose the life of a people or an age, but we can best understand the significant ^ of the old Greek cities and the life they developed, when, looking at the history of mankind as a whole, we see the part played by reason, active and critical, in breaking down the barriers by which custom hinders movement, in guiding movement to definite ends, in dissipating groundless beliefs and leading onwards to fresh scientific conquests - when we see this and then take note that among the ancient Greeks such an activity of reason began in an entirely novel degree and that its activity in Europe ever since is due to their impulsion.

    0
    0
  • From 1018 the relations of C, D, E become too complicated to be expressed by any formula; sometimes all three agree together, sometimes all three are independent; in other places each pair in turn agree against the third.

    0
    0
  • The occasional visitor to the tomb is reminded by its inscriptions of the many virtues of the dead man while he yet lived, and is charged, if he be come with empty hands, at least to pronounce the funerary formula; it will indeed cost him nothing but the breath of his mouth !

    0
    0
  • Often the formula was written on a strip of rag or a scrap of papyrus and tied round the neck of the person for whom it was intended.

    0
    0
  • Up to that time all the leaders had been united in accepting the naturalistic formula, which was combined with an individualist and a radical tendency.

    0
    0
  • The formula employed by P is "and Pharaoh's heart was strong (pin)," or, "and Pharaoh made strong (p'in) his heart," as in E, but it is distinguished from E's phrase by the addition of "and he hearkened not unto them as Yahweh had spoken."

    0
    0
  • The emperors Zeno and Anastasius had been strongly suspected of it, and the Roman bishops had refused to communicate with the patriarchs of Constantinople since 484, when they had condemned Acacius for accepting the formula of conciliation issued by Zeno.

    0
    0
  • One of Justinian's first public acts was to put an end to this schism by inducing Justin to make the then patriarch renounce this formula and declare his full adhesion to the creed of Chalcedon.

    0
    0
  • Titanotherium, of the Oligocene of the Dakotas and neighbouring districts, was a huge beast, with the hinder upper premolars similar in character to the molars, a pair of horn-cores, arising from the maxilla, overhanging the nose-cavity, four front and three hind toes, only twenty dorso-lumbar vertebrae, and an almost continuous and unbroken series of teeth, in which the canines are short; the dental formula being i.

    0
    0
  • Whether or no the so-called "fourth formula" (Hahn, § 156) is to be ascribed to a continuation of this synod or to a subsequent but distinct assembly of the same year, its aim is like that of the first three; while repudiating certain Arian formulas it avoids the Athanasian shibboleth "homoousios."

    0
    0
  • The chlorine is not completely precipitated by silver nitrate in nitric acid solution, the ionization apparently not proceeding to all the chlorine atoms. Thallic iodide, T11 3, is interesting on account of its isomorphism with rubidium and caesium tri-iodides, a resemblance which suggests the formula T11 (12) for the salt, in which the metal is obviously monovalent.

    0
    0
  • He was, as he called himself, a " mystic "; and his creed was too vague to be put into any formula beyond a condemnation of atheism.

    0
    0
  • Heidegger was the principal author of the Formula Consensus Helvetica in 1675,which was designed to unite the Swiss Reformed churches, but had an opposite effect.

    0
    0
  • A wide knowledge of the Old Testament supplies him with a text to illustrate one incident after another; and so deeply is he impressed with the correspondence between the life of Christ and the words of ancient prophecy, that he does not hesitate to introduce his quotations by the formula " that it might be fulfilled which was spoken by the prophet."

    0
    0
  • Metternich was anxious to secure an apparent unanimity of the powers to back the Austrian intervention in Naples, and every device was used to entrap the English representative into subscribing a formula which would have seemed to commit Great Britain to the principles of the other allies.

    0
    0
  • This derivation of the word Mass, which would connect it with the special formula of dismissal still preserved in the Roman liturgy - Ite, missa est- once generally accepted, is now disputed.

    0
    0
  • A graver mistake, according to some critics, is that Hegel, far from giving a law of progress, seems to suggest that the history of the world is nearing an end, and has merely reduced the past to a logical formula.

    0
    0
  • Its composition approaches the formula CaOC1 2, and it is regarded as a double salt of calcium chloride and hypochlorite, which by the action of water splits up into a mixture of these salts.

    0
    0
  • Their formula in Na 2 CO 3, 10H 2 O, corresponding to 37% of dry sodium carbonate.

    0
    0
  • Jefferson seems to have been the first discoverer of an exact formula for the construction of mould-boards of least resistance for ploughs.

    0
    0
  • The magnifying power is computed by the same formula as in the case of the Gregorian telescope.

    0
    0
  • This flamen also sacrificed on the 1st of May to Maia, who in an old prayer formula (Gellius 13.23) was coupled with Volcanus as Maia Volcani.

    0
    0
  • This quantity is now, as the result of further experiments, added to the values of h, and also represented in the formula for the specific heat itself by the cubic term.

    0
    0
  • It is a black powder, the composition of which is never quite definite, but approximates to the formula given above.

    0
    0
  • It is an advance on this when Heraclitus 2 opposes to the eyes and ears which are bad witnesses " for such as understand not their language " a common something which we would do well to follow; or again when in the incommensurability of the diagonal and side of a square the Pythagoreans stumbled upon what was clearly neither thing nor image of sense, but yet was endowed with meaning, and henceforth were increasingly at home with symbol and formula.

    0
    0
  • The result is a selflimiting dialectic. This higher dialectic is a logic. It is no accident that the first of the philosophical sophists, Gorgias, on the one hand, is Eleatic in his affinities, and on the other raises in the characteristic formula of his intellectual nihilism' issues which are as much logical and epistemological as ontological.

    0
    0
  • The one in the many, the formula which lies at the base of the possibility of predication, is involved in the Socratic doctrine of general concepts or ideas.

    0
    0
  • Yet from the points of view alike of an absolute pluralism, of a flux, and of a formula of bare identity - and a fortiori with any blending of these principles sufficiently within the bounds of plausibility to find an exponent - all knowledge, because all predication of unity, in difference, must be held to be impossible.

    0
    0
  • The formula for an indefinite number of particular things in particular places at particular times, and all of them presentable in sensuous imagery of a given time and place, is not itself presentable in sensuous imagery side by side with the individual members of the group it orders.

    0
    0
  • Plato replies with the doctrine of the interpenetration of ideas, obviously not of all with all, but of some with some, the formula of identity in difference within thought itself.

    0
    0
  • Once embarked upon such an analysis, where valid process from assured principles gave truth, Aristotle could find little difficulty in determining the formula of demonstrative knowledge or science.

    0
    0
  • The point of view is to be modified profoundly by what follows - by the doctrine of the class-concept behind the class, of the form or idea as the constitutive formula of a substance, or, again, by the requirement that an essential attribute must be grounded in the nature or essence of the substance of which it is predicated, and that such attributes alone are admissible predicates from the point of view of the strict ideal of science.

    0
    0
  • The question is as to membership of a class, and the dominant formula concet.

    0
    0
  • Syllogism as formula for the exhibition of truth attained, and construction or what not as the instrumental process by which we reach the truth, have with writers since Hegel and Herbart tended to fall apart.

    0
    0
  • The individualism with which he starts, howsoever afterwards mitigated by his doctrine of To Ti v eivac or eiSos constituting the individual in a system of intelligible relations, confined him in an inadmissible way to the subject-attribute formula.

    0
    0
  • The Aristotelian theory of the universal of science as secure from dependence on its instances and the theory of linking in syllogism remain a heritage for all later logic, whether accepted in precisely Aristotle's formula or no.

    0
    0
  • The method now proceeds on the basis of the first table to set f p rth the possible suggestions as to a general explanatory formula for the quality in question.

    0
    0
  • If one suggestion, and one alone, survives the process of attempted rejection it is the explanatory formula required.

    0
    0
  • It is the recipe for, and at the same time is, heat, much as H 2 O is the formula for and is water.

    0
    0
  • Had Bacon analysed bodies into their elements, instead of their qualities and ways of behaviour, he would have been the logician of the chemical formula.

    0
    0
  • Hobbes developed the nominalism which had been the hallmark of revolt against scholastic orthodoxy, and, when he brings this into relation with the analysis and synthesis of scientific A notable formula of Bacon's Novum Organum ii.

    0
    0
  • Hume derived from him the explanatory formula of the association of ideas, 8 which is, however, still with Hobbes a fact to be accounted for, not a theory to account for facts, being grounded physically in " coherence of the matter moved."

    0
    0
  • Berkeley, though at length the notions of spirits, acts and relations 6 give him pause, prefers the formula which Hume expresses in the phrase that " some ideas are particular in their nature but general in their representation," 7 and the afterhistory of " abstraction " is a discussion of the conditions under which one idea " stands for " a group. Not from those for whom general ideas mean schematic concepts, not imageable.

    0
    0
  • Apart from the adoption by Hume of the association of ideas as the explanatory formula of the school - it had been allowed by Malebranche within the framework of his mysticism and employed by Berkeley in his theory of vision - there are few fresh notes struck in the logic of sensationalism.

    0
    0
  • They had undermined the foundations of scientific certainty, and so far as the fecundity of contemporary science did not give them pause, were ready, notwithstanding the difference of their starting-point, to acquiesce in the formula as well as the temper of Pyrrhonism.

    0
    0
  • So again in determining the " import " of propositions, it is no accident that in all save existential propositions it is to the familiar rubrics of associationism - co-existence, sequence, causation and resemblance - that he refers for classification, while his general formula as to the conjunctions of connotations is associationist through and through.

    0
    0
  • It is a shorthand formula of registration.

    0
    0
  • But that truth is not what Mill expounds, nor is it capable of development within the limits imposed by the associationist formula.

    0
    0
  • Again the formula of the Joint-Method, which contemplates the enumeration of cases " which have nothing in common but the absence of one circumstance," is ridiculously unsound as it stands.

    0
    0
  • The latter becomes a mere memorandum or formula of registration.

    0
    0
  • It is the oscillation which Mill manifests between the conception of his formula as it is actually applicable to concrete problems in practice, and the conception of it as an expression of a theoretical limit to practical procedure.

    0
    0
  • Finally, it is on the whole in keeping with Mill's presuppositions to admit even in the case of the method of difference that in practice it is approximative and instructive, while the theoretical formula, to which it aims at approaching asymptotically as limit, if exact, is in some sense sterile.

    0
    0
  • Mill may well have himself conceived his methods as practically fruitful and normally convincing with the limiting formula in each case more cogent in form but therewith merely the skeleton of the process that but now pulsed with life.

    0
    0
  • The formula of identity passed in another form to Herbart and therefore to Lotze.

    0
    0
  • His general theory of knowledge deriving from Kant and Reid, and including among other things a contaminatio of their theories of perception, 3 in no way sustains or mitigates his narrow view of logic. He makes no effective use of his general formula that to think is to condition.

    0
    0
  • Schleiermacher's formula obviously ascribes a function in knowledge to thought as such, and describes in a suggestive manner a duality of the intellectual and organic functions, resting on a parallelism of thought and being whose collapse into identity it is beyond human capacity to grasp. It is rather, however, a statement of a way in which the relations of the terms of the problem may be conceived than a system of necessity.

    0
    0
  • There was scope for diversity of view and there was diversity of view, according as the vital issue of the formula was held to lie in the relation of intellectual function to organic function or in the not quite equivalent relation of thinking to being.

    0
    0
  • Finally it must not be forgotten that the host of writers who were in reaction against Hegelianism tended to take refuge in some formula of correlation, as a half-way ho-use between that and formalism or psychologism or both, without reference to, and often perhaps without cdnsciousness of, the way in which historically it had taken shape to meet the problem held to have been left unresolved by Kant.

    0
    0
  • Fichte cannot be said to have developed a logic, but this rhythm of thesis, antithesis and synthesis, foreshadowed in part for Fichte in Spinoza's formula, " omnis determinatio est negatio," and significantly in Kant's triadic grouping of his categories, gave a cue to the thought of Hegel.

    0
    0
  • To the formalist proper it was self-condemned in its pretension to develop the content of thought and its rejection of the formula of bare-identity.

    0
    0
  • The comparison of Sigwart with Lotze is instructive, in regard both to their agreement and their divergence as showing the range of the epistemological formula.

    0
    0
  • But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method.

    0
    0
  • The most important apparent exceptions to Raoult's law in dilute solutions are the cases, (I) in which the molecules of the dissolved substance in solution are associated to form compound molecules, or dissociated to form other combinations with the solvent, in such a way that the actual number of molecules n in the solution differs from that calculated from the molecular weight corresponding to the accepted formula of the dissolved substance; (2) the case in which the molecules of the vapour of the solvent are associated in pairs or otherwise so that the molecular weight m of the vapour is not that corresponding to its accepted formula.

    0
    0
  • The highest pressures recorded for cane-sugar are nearly three times as great as those given by van't Hoff's formula for the gas-pressure, but agree very well with the vapour-pressure theory, as modified by Callendar, provided that we substitute for V in Arrhenius's formula the actual specific volume of the solvent in the solution, and if we also assume that each molecule of sugar in solution combines with 5 molecules of water, as required by the observations on the depression of the freezing-point and the rise of the boiling-point.

    0
    0
  • Zeuner, at a later date (La Chaleur, p.441) employing the empirical, formula pv= BO +Cp 25 for saturated steam, found the value S = 568, which further increased the discrepancy.

    0
    0
  • Perry (Steam Engine, p. 580), assuming a characteristic equation similar to Zeuner's (which makes v a linear function of the temperature at constant pressure, and S independent of the pressure), calculates S as a function of the temperature to satisfy Regnault's formula (10) for the total heat.

    0
    0
  • If the steam at A were dry and saturated, we should have, assuming Regnault's formula (to), H A -H D = 305 (0'-O), whence, if S = .475, we have zL = .3 0 5 (0 '- 0)-.

    0
    0
  • It is evident that this is a very delicate method of determining the wetness z, but, since with dry saturated steam at low pressures this formula always gives negative values of the wetness, it is clear that Regnault's numerical coefficients must be wrong.

    0
    0
  • If we assume Regnault's formula (10) for the total heat, we have evidently the simple relation S=0.305(0'-0)/(0"-o), supposing the initial steam to be dry, or at least of the same quality as that employed by Regnault.

    0
    0
  • The method of deducing the specific heat from Regnault's formula for the variation of the total heat is evidently liable in a greater degree to the objections which have been urged against his method of determining the specific heat, since it makes the value of the specific heat depend on small differences of total heat observed under conditions of greater difficulty at various pressures.

    0
    0
  • The rate of increase of the total heat, instead of being constant for saturated steam as in Regnault's formula, is given by the equation dH/d0 =S(1 - Qdp/d0).

    0
    0
  • The formula of Dalton would make the pressure increase in geometrical progression for equal increments of temperature.

    0
    0
  • Observing that this rate of diminution is approximately as the square of the reciprocal of the absolute temperature, we see that the almost equally simple formula log p=A+B/0 represents a much closer approximation to experiment.

    0
    0
  • The values so found are necessarily erroneous if formula (io) for the total heat is wrong.

    0
    0
  • This leads immediately to the simple formula loge (p/po) = (t/90t/6)L/R,.

    0
    0
  • A formula of this type has been widely employed by van't Hoff and others to calculate heats of reaction and solution from observations of solubility and vice versa.

    0
    0
  • The formula evidently applies to the vapour-pressure of the pure solvent as a special case, but Kirchhoff himself does not appear to have made this particular application of the formula.

    0
    0
  • He proceeds to calculate from this expression the difference of vapour-pressures of ice and water in the immediate neighbourhood of the melting-point, but does not observe that the vapour-pressures themselves may be more accurately calculated for a considerable interval of temperature by means of formula (23), by substituting the appropriate values of the latent heats and specific heats.

    0
    0
  • They give the following numerical values The error of the formula for water is less than t mm.

    0
    0
  • A formula of the same type was given by Athenase Dupre (Theorie de chaleur, p. 96, Paris, 1869), on the assumption that the latent heat was a linear function of the temperature, taking the instance of Regnault's formula (io) for steam.

    0
    0
  • It is generally called Dupre's formula in continental text-books, but he did not give the values of the coefficients in terms of the difference of specific heats of the liquid and vapour.

    0
    0
  • It was employed as a purely empirical formula by Bertrand and Barus, who calculated the values of the coefficients for several substances, so as to obtain the best general agreement with the results of observation over a wide range, at high as well as low pressures.

    0
    0
  • Applied in this manner, the formula is not appropriate or satisfactory.

    0
    0
  • The true application of the formula is to low pressures, at which it is very accurate.

    0
    0
  • It is easy, however, to correct the formula for these deviations, and to make it thermodynamically consistent with the characteristic equation (13) by substituting the appropriate values of (v-w) and L =H -h from equations (13) and (is) in formula (21) before integrating.

    0
    0
  • Omitting w and neglecting the small variation of the specific heat of the liquid, the result is simply the addition of the term (c-b)/V to formula (23) log p=A+B/B - I - C log B-f-(c-b)IV..

    0
    0
  • The value of c is determined by the throttling experiments, so that all the coefficients in the formula with the exception of A are determined independently of any observations of the saturationpressure itself.

    0
    0
  • The most uncertain data are the variation of the specific heat of the liquid and the value of the small quantity b in the formula (13).

    0
    0
  • But this neglects the latent heat of solution, unless we may suppose it included by writing the internal latent heat L i in place of L in Callendar's formula.

    0
    0
  • But in order to deduce the values of c by the Joule-Thomson method, it is necessary to assume an empirical formula, and the type c=co(6019) n is chosen as being the simplest.

    0
    0
  • The latent heat L (formula 9) is found by subtracting from H (equation 15) the values of the heat of the liquid h given in the same article.

    0
    0
  • The values of the specific heat in the next column are calculated for a constant pressure equal to that of saturation by formula (16) to illustrate the increase of the specific heat with rise of pressure.

    0
    0
  • The values of the saturation-pressure given in the last column are calculated by formula (25), which agrees with Regnault's observations better than his own empirical formulae.

    0
    0
  • Every sort of pressure was brought to bear upon him to make his submission, and at last, broken in health and spirit, he consented to sign a formula which the cardinal de Noailles claimed as a recantation.

    0
    0
  • The chemical formula CuFeS 2 corresponds with the percentage composition Cu = 34' 5, Fe = 30' 5, S =35.0.

    0
    0
  • Ammonia does not react with tungsten or the dioxide, but with trioxide at a red heat a substance of the formula W 5 H 6 N 3 0 5 is obtained, which is insoluble in acids and alkalis and on ignition decomposes, evolving nitrogen, hydrogen and ammonia.

    0
    0
  • Originally any inhabitant holding a certain measure of land, freehold or subject to the mere nominal ground-rent abovementioned, was a full citizen independently of his calling, the clergy and the lord's retainers and servants of whatever rank, who claimed exemption from scot and lot, to use the English formula, alone excepted.

    0
    0
  • The prophets use the formula, " Thus saith the Lord," but he goes beyond them and speaks in his own name, " Amen, I say unto you."

    0
    0
  • The answer is given in the Nicene formula, which is characteristically Greek.

    0
    0
  • The formula (16) expresses that the squared radius of gyration about any axis (Ox) exceeds the squared radius of gyration about a parallel axis through G by the square of the distance between the two axes.

    0
    0
  • This indicates an experimental method of determining g with considerable accuracy, using the formula g 41r2l/T2.

    0
    0
  • It follows from the formula 15 (10) for the internal kinetic energy of a system of particles that as a result of the impact this energy is diminished by the amount i m1mi 2(1 _ei)m+m(ui_uf)1.

    0
    0
  • This formula is due to Mbius.

    0
    0
  • The formula (13) may be easily verified in the case of the compound pendulum, or of the solid rolling down an incline.

    0
    0
  • As a first application of Lagranges formula (II) we may form the equations of motion of a particle in spherical polar co-ordinates.

    0
    0
  • The length L of an endless belt connecting a pair of pulleys whose effective radii are r,, r,, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.

    0
    0
  • The story goes that, having been deeply impressed by Ramananda's teaching, he sought to attach himself to him; and, one day at Benares, in stepping down the ghat at daybreak to bathe in the Ganges, and putting himself in the way of the teacher, the latter, having inadvertently struck him with his foot, uttered his customary exclamation" Ram Ram,"which, being also the initiatory formula of the sect, was claimed by Kabir as such, making him Ramananda's disciple.

    0
    0
  • In this sect, children are solemnly admitted to full membership at the early age of four, and even two, years of age, when a rosary, or necklace, of 108 beads of basil (tulsi) wood is passed round their necks, and they are taught the use of the octo-syllabic formula Sri-Krishnah saranam mama, " Holy Krishna is my refuge."

    0
    0
  • It has the formula C 10 H 12 0 4, and on hydrolysis is converted into cantharinic acid, C10H1405.

    0
    0
  • Modernists deny that the spirit of religion can be thus imprisoned in an unchangeable formula; they hold that it is always growing, and therefore in continual need of readjustment and restatement.

    0
    0
  • Two acids corresponding to this empirical formula are known - namely ethylene succinic acid, H0 2 C CH 2 CH 2 CO 2 H and ethylidene succinic acid CH3 CH(C02H)2.

    0
    0
  • Calixtus saw himself under the necessity of abandoning his friends and setting up a mediating formula designed to harmonize the Trinitarian and the Modalistic positions.

    0
    0
  • The mediation formula, however, proposed by Calixtus became the bridge by which, in the course of the decades immediately following, the doctrine of the Trinity made its way into the Roman Church.

    0
    0
  • This appears, on the one hand, in the use of expressions having a Modalistic ring about them - see especially the poems of Commodian, written about the time of Valerian - and, on the other hand, in the rejection of the doctrine that the Son is subordinate to the Father and is a creature (witness the controversy between Dionysius of Alexandria and Dionysius of Rome), as well as in the readiness of the West to accept the formula of Athanasius, that the Father and the Son are one and the same in substance (O,uoou6coc).

    0
    0
  • This act fixed the formula of subscription to be signed by all ministers.

    0
    0
  • The formula adopted by the assembly of 1711 had still to be signed by ministers, and was felt to be much too strict.

    0
    0
  • Wislicenus also investigated the reaction very thoroughly and accepted the Frankland-Duppa formula (Annalen, 1877, 186, p. 163; 1877, 19 0, p. 257).

    0
    0
  • Hubert and Mauss show in their penetrating analysis of sacrifice that after the rite has been brought to its culminating point there follows as a pendant a ceremony of re-entry into ordinary life, the idea of which is preserved in the Christian formula Ite, miss y est.

    0
    0
  • Or the relation between the inferior deities and the most exalted may be conceived politically and explained by Tertullian's formula, " Imperium penes unum, officia penes multos."

    0
    0
  • Still a further reduction was made in the number of members, and a small residuum consisting of five Catholics and five Protestants undertook the task of devising a formula on which the two churches might unite with regard to the question of the Communion.

    0
    0
  • It melts at below red heat to a brown mass, and its vapour density at both red and white heat corresponds to the formula Cu 2 C1 2.

    0
    0
  • If W is the weight required to depress the attracted disk into the same sighted position when the plates are unelectrified and g is the acceleration of gravity, then the difference of potentials of the conductors tested is expressed by the formula V - V'=(d - d') /87 W where S denotes the area of the attracted disk.

    0
    0
  • The formula indicates that the sensibility of the instrument should increase with the charge of the Leyden jar or needle, whereas Hopkinson found that as the potential of the needle was increased by working the replenisher of the jar, the deflection due to three volts difference between the quadrants first increased and then diminished.

    0
    0
  • He found that when the potential of the needle exceeded a certain value, of about volts, for the particular instrument he was using (made by White of Glasgow), the above formula did not hold good.

    0
    0
  • His "Eloisa to Abelard" (1717) is carefully modelled on the form of Ovid's "Heroides," while in his Moral Essays he adopts the Horatian formula for the epistle.

    0
    0
  • An ordinary formula for obtaining it is 1 S for highpressure engines, and S for condensing engines, where D is the diameter of the piston in inches and S the length of the stroke in feet, though varying numbers are used for the divisor.

    0
    0
  • It is, in the words of the old formula, Curare, cito, tuto, et jucunde, to cure quickly, safely, and pleasantly.

    0
    0
  • If Watermeyer's formula, " In all things political, purely despotic; in all things commercial, purely monopolist," was true of the government of the Dutch East India Company in the 18th century, it was equally true of Kruger's government in the latter part of the 19th.

    0
    0
  • The dental formula, when completely developed, is incisors i, canines o, premolars 31 molars - on each side, giving a total of 34 teeth.

    0
    0
  • The various laws are clearly defined by the formula " I am Yahweh," or " I am Yahweh your God," phrases which are especially characteristic of chaps.

    0
    0
  • A formula, similar to (5), may be given for the frequencies of vibration of a spherical mass of liquid under capillary force.

    0
    0
  • Goldschmiedt (Monats., 1883-1889), who determined its constitution (formula I., below) by a study of its oxidation products, showing that papaveraldine, which it gives with potassium permanganate, is a tetramethoxybenzoylisoquinoline.

    0
    0
  • Formulae have been proposed by Pschorr and Knorr explaining this and other decompositions (in Pschorr's formula the morphine ring system is a fusion of a phenanthrene and pyridine nucleus); another formula, containing a fusion of a phenanthrene with a pyrrol ring, was proposed by Bucherer in'1907.

    0
    0
  • As regards the isomerism of the pyridine substitution products, three mono-derivatives are known, the different positions being indicated by the Greek, letters a, s and y, as shown in the inset formula.

    0
    0
  • The formula for the obliquity of the ecliptic, as derived from the laws of motion of it and of the equator, may be developed in a series.

    0
    0
  • Herbert Spencer's formula that life is "the continuous adjustment of internal relations to external relations" was the result of a profound and subtle analysis, but omits the fundamental consideration that we know life only as a quality of and in association with living matter.

    0
    0
  • It occurs in a colourless crystalline powder, having the formula C20H24N202.2HC1.3H20.

    0
    0
  • It may be added that, where a systematic account of duties is actually given, the connexion of the particular duties with the universal formula is in general more formal than real.

    0
    0
  • His Pantheisticon, sive formula celebrandae sodalitatis socraticae, of which he printed a few copies for private circulation only, gave great offence as a sort of liturgic service made up of passages from heathen authors, in imitation of the Church of England liturgy.

    0
    0
  • His formula relies on a sulfuric paste applied to arrows and shot at enemy targets.

    0
    0
  • The formula then becomes I = Ioe kt (2) where e is the base of Napierian logarithms, and k is a constant which is practically the same as j for bodies which do not absorb very rapidly.

    0
    0
  • The law of absorption expressed by the formula (2) has been verified by experiments for various solids, liquids and gases.

    0
    0
  • The formula of the acid is not quite definite.

    0
    0
  • It exists in two forms, one having the formula P 4 5 10, and the other a lower molecular weight.

    0
    0
  • In the catchword Homousios, which had been added to the creed at Nicaea, he too recognized the best formula for the expression of the mystery, although in his own writings he made but sparing use of it.

    0
    0
  • He was in fact less concerned with the formula than with the content.

    0
    0
  • With the help of counsellors more subtle than discerning, the emperor, with the object of uniting the various parties in the Church at any cost, sought for the most colourless possible formula of belief, which he hoped to persuade all the bishops to accept.

    0
    0
  • He propounds as the comprehensive formula of the new Christianity this precept - "The whole of society ought to strive towards the amelioration of the moral and physical existence of the poorest class; society ought to organize itself in the way best adapted for attaining this end."

    0
    0
  • For the application of the above formula it is necessary to measure (R) and (r) very accurately, by reason of the high powers involved, but when this has been carefully done the formula may be relied upon.

    0
    0
  • Thus in the case of a spring for which the values of the quantities were W =7 lb, n = 51, R = .30 in., .038 in., E = io,50o,000, the formula gives extension =1.764 in., while direct experiment gave extension =1.75 in.

    0
    0
  • And with a very long and weak spring for which the values of the quantities were W =1 oz., /1=233, R = 35 in., 0085 in., E = io,50o,000, the formula gives extension =22.78 in., while direct experiment with the spring gave 23.5 in.

    0
    0
  • Dorp (Rec. Pays Bas, 1885, 4, 125); its formula is shown in the inset.

    0
    0
  • Where the nitrous fumes prevail and there is less water present, sulphur dioxide combines with nitrous acid and oxygen to form nitroso-sulphuric acid, a crystalline substance of the formula SO 2 (OH)(ONO).

    0
    0
  • The trinitarian formula and trine immersion were not uniformly used from the beginning, nor did they always go together.

    0
    0
  • The Teaching of the Apostles, indeed, prescribes baptism in the name of Father, Son and Holy Ghost, but on the next page speaks of those who have been baptized into the name of the Lord - the normal formula of the New Testament.

    0
    0
  • The formula of Rome is, " I baptize thee in the name of Father and Son and Holy Spirit."

    0
    0
  • In " Truth," starting from the formula " the Ent (or existent) is, the Nonent (or non-existent) is not," Parmenides attempted to distinguish between the unity or universal element of nature and its variety or particularity, insisting upon the reality of its unity, which is therefore the object of knowledge, and upon the unreality of its variety, which is therefore the object, not of knowledge, but of opinion.

    0
    0
  • If, for instance, three terms of a proportion are given, the fourth can be obtained by the relation given at the end of § 57, this relation being then called the Rule of Three; but this is equivalent to the use of an algebraical formula.

    0
    0
  • Calculation of Square Root.-The calculation of the square root of a number depends on the formula (iii) of § 60.

    0
    0
  • An analogous method of finding cube root, based on the formula for (a+b) 3, used to be given in text-books, but it is of no practical use.

    0
    0
  • More generally, if we have obtained a as an approximate value for the pth root of N, the binomial theorem gives as an approximate formula p,IN =a+6, where N = a P + pap - 19.

    0
    0
  • In a sense not; but our analysis may not give all that is there, and we ought not at once to impose that analysis or any formula on history.

    0
    0
  • Besides, the tendency of applying a formula of this sort to history is to assume that the elements are developed in a certain regular or necessary order, whereas this may not at all be the case; but we may find at any epoch the whole mixed, either crossing or co-operative, as in the consciousness of the individual himself.

    0
    0
  • The milk-dentition is expressed by a similar formula, d for deciduous, being added before the letter expressive of the nature of the tooth.

    0
    0
  • It also dissolves in alcohol and ether; boiling point determinations of the molecular weight in these solutions point to the formula FeCl3.

    0
    0
  • Ferrous sulphate forms large green crystals belonging to the monoclinic system; rhombic crystals, isomorphous with zinc sulphate, are obtained by inoculating a solution with a crystal of zinc sulphate, and triclinic crystals of the formula FeSO 4.5H 2 O by inoculating with copper sulphate.

    0
    0
  • The Church's first creed had been " the Fatherhood of God and the Messiahship of Jesus " (A Ritschl); but the " Rule of Faith " (Irenaeus; Tertullian, who uses the exact expression; Origen)- that summary of religiously important facts which was meant to ward off error without reliance on speculations such as the Logos doctrine - built itself up along the lines of the baptismal formula of Matt.

    0
    0
  • To find the distinctive technicalities of Lutheranism we have to leave Melanchthon's system (and his great Reformation creed, the Augsburg Confession) for the Formula of Concord and the lesser men of that later period.

    0
    0
  • This is not fully formulated even in the Lutheran Formula of Concord, nor yet in the Calvinistic canons of Dort and Confession of Westminster, though these and other Protestant creeds have various instalments of the finished doctrine.

    0
    0
  • This creed may almost rank with the Lutheran Formula of Concord as summing up post-Reformation Protestant orthodoxy.

    0
    0
  • Sacraments are a republication of the " Word " of the Gospel; we have to content ourselves with this rather evasive formula, so often employed by the Reformers.

    0
    0
  • The free life of personal beings is no more to be mastered by a formula than it is to be assigned to caprice.

    0
    0
  • Thus his famous general formula for virtue, that it is a mean or middle state, always to be found somewhere between the vices which stand to it in the relation of excess and defect, scarcely avails to render his treatment more systematic.

    0
    0
  • It ought to be said that Aristotle does not present the formula just discussed as supplying a criterion of good conduct in any particular case; he expressly leaves this to be determined by " correct reasoning, and the judgment of the practically-wise man (6 cppovcµos)."

    0
    0
  • Its demands were met by the Stoic school which separated the moral from the worldly view of life, with an absoluteness and definiteness that caught the imagination; which regarded practical goodness as the highest manifestation of its ideal of wisdom; and which bound the common notions of duty into an apparently coherent system, by a formula that comprehended the whole of human life, and exhibited its relation to the ordered process of the universe.

    0
    0
  • The Stoics, on the other hand, not only worked out a detailed system of duties - or, as they termed them, " things meet and fit " (Ka6 r i Kovra) for all occasions of life; they were further especially concerned to comprehend them under a general formula.

    0
    0
  • Thus the formula of " living according to nature," in its application to man as the " rational animal," 1 Hence some members of the school, without rejecting the definition of virtue = knowledge, also defined it as " strength and force."

    0
    0
  • And during the period of a century and a half between Antiochus and Plutarch, we may suppose the school to have maintained the old controversy with Stoicism on much the same ground, accepting the formula of " life according to nature," but demanding that the " good " of man should refer to his nature as a whole, the good of his rational part being the chief element, and always preferable in case of conflict, but yet not absolutely his sole good.

    0
    0
  • Such are the evangelical principle of " doing as you would be done by the principle of justice, or " giving every man his own, and letting him enjoy it without interference "; and especially what More states as the abstract formula of benevolence, that " if it be good that one man should be supplied with the means of living well and happily, it is mathematically certain that it is doubly good that two should be so supplied, and so on."

    0
    0
  • As regards "material" goodness of actions, 'he adopts explicitly and unreservedly the formula afterwards taken as fundamental by Bentham; holding that " that action is best which procures the greatest happiness for the greatest numbers, and the worst which in a like manner occasions misery."

    0
    0
  • The third is merely the general rule of benevolence stated in the somewhat vague Stoical formula, that " no one is born for himself only."

    0
    0
  • When, however, we look closer, we find that the principle of order, or obedience to government, is not seriously intended to imply the political absolutism which it seems to express, and which English common sense emphatically repudiates; while the formula of justice is given in the tautological or perfectly indefinite proposition " that every man ought to have his own."

    0
    0
  • Whewell, indeed, explains that this latter formula must be practically interpreted by positive law, though he inconsistently speaks as if it supplied a standard for judging laws to be right or wrong.

    0
    0
  • Of the primary, secondary and tertiary alcohols having the same empirical formula, the primaryhave the highest, and the tertiary the lowest boiling point; this is in accordance with the fairly general rule that a gain is symmetry is attended by a fall in the boiling point.

    0
    0
  • He reconstructs, as he declares, ontology, and begins with the "ideal formula," "the Ens creates ex nihilo the existent."

    0
    0
  • Civilization is a conditioned mediate tendency to perfection, to which religion is the final completion if carried out; it is the end of the second cycle expressed by the second formula, the Ens redeems existences.

    0
    0
  • Thenceforward public opinion, which was looking for something quite different from the superannuated formula of 1614, abandoned the panements, which in, their turn disappeared from view; for the struggle beginning between the privileged classes and the government, now at bay, hadgiven the public, through the states-general, that means of expression which they had always lacked.

    0
    0
  • This formula only holds for the Platonic solids.

    0
    0
  • In strictness the angle is dependent upon the frequency, but if the dispersion be weak relatively to the double refraction, the product sin 24 - a)sin 2Ni - (3) has sensibly the same value for all terms of the summation, and we may write I=cos 2 (1 3 - a)/a 2 - sin 2 (1 ' - a) sin 2 (t ' - a 2 sin 2 2 This formula contains the whole theory of the colours of crystalline plates in polarized light.

    0
    0
  • When light from an extended source is made to converge upon the crystal, the phenomenon of rings and brushes localized at infinity is obtained.The exact calculation of the intensity in this case is very complicated and the resulting expression is too unwieldy to be of any use, but as an approximation the formula for the case of a parallel beam may be employed, the quantities and p therein occurring being regarded as functions of the angle and plane of incidence and consequently as variables.

    0
    0
  • The legend according to which Galileo, rising from his knees after repeating the formula of abjuration, stamped on the ground, and exclaimed, "Eppur si muovel" is, as may readily be supposed, entirely apocryphal.

    0
    0
  • We conclude by applying Ohm's law that the electromotive force, E, of the thermocouple may be approximately represented for small differences of temperature by the formula E=CR=p(t-t').

    0
    0
  • Similar phenomena occur in the case of many other couples, and it is found that the thermoelectric power p is not in general a constant, and that the simple linear formula (I) is applicable only for small differences of temperature.

    0
    0
  • In the majority of cases it is found that the observations can be represented within the limits of experimental error by a fairly simple empirical formula, at least for moderate ranges of temperatures.

    0
    0
  • We have also the relations dE/dt = b+2ct and d 2 E/dt 2 =2C. The first relation gives the thermoelectric power p at any temperature, and is probably the most convenient method of stating results in all cases in which this formula is applicable.

    0
    0
  • He does not record any systematic deviations from the formula.

    0
    0
  • Their observations were probably free from immersion errors, but they record some deviations from the formula which they consider to be beyond the possible limits of error of their work.

    0
    0
  • The values of d 2 E/dt 2 agree as well as can be expected, considering the difference of the ranges of temperature and the great variety in the methods of observation adopted; they are calculated assuming the parabolic formula, which is certainly in many cases inadequate.

    0
    0
  • He states that the deviations from the formula were " quite within the limits of error introduced by the alteration of the resistance of the circuit with rise of temperature, the deviations of the mercury thermometers from the absolute scale, and the non-correction of the indications of the thermometer for the long column of mercury not immersed in the hot oil round the junctions."

    0
    0
  • This is the equation to a parabola, and is equivalent to the empirical formula of Avenarius, with this difference, that in Tait's formula the constants have all a simple and direct interpretation in relation to the theory.

    0
    0
  • If we suppose that s is not quite constant, but increases or diminishes slightly with change of temperature according to a linear formula s=50-1-2cT (in which so represents the constant part of s, and c may have either sign), we obtain a more general formula which is evidently the sum of the two previous solutions and may be made to cover a greater variety of cases.

    0
    0
  • According to this formula, the Peltier effect is a linear function of the temperature.

    0
    0
  • In many cases a formula of the last type would be quite inapplicable, as Stansfield remarks, but the difference between the three is often much less than might be supposed.

    0
    0
  • In this particular case the parabolic formula appears to be undoubtedly inadequate.

    0
    0
  • This might be appropriately represented, as already suggested, by a linear formula s=so - cT.

    0
    0
  • In some reactions it behaves as having the first formula, in others as having the second.

    0
    0
  • This multiplicity of titles was more than a mere formula of the royal chancery.

    0
    0
  • Theology sank into a branch of dialectic; whatever would not fit in with a logical formula was cast aside as useless.

    0
    0
  • The dentition of the horse, when all the teeth are in place, is expressed by the formula i.

    0
    0
  • From this formula it follows, for example, that one obtains a system of a in.

    0
    0
  • From the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed numerical aperture can be perceived.

    0
    0
  • For microscopy the Fraunhofer formula is best written S =X/A.

    0
    0
  • The resolution in the case of oblique illumination is given by the formula 6=X/2A.

    0
    0
  • The Fraunhofer formula permits the determination of the most useful magnification of such an objective in order to utilize its full resolving power.

    0
    0
  • Supposing, however, there is oblique illumination, then formula (5) can always be applied to determine the magnifying power attainable with at least one objective.

    0
    0
  • Chandler has constructed empirical formulae representing the motion, with the results already given, while Albrecht has determined the motion of the pole from observation simply, without trying to represent it either by a formula or by theory.

    0
    0
  • The formula is parallel to that in 2 Sam.

    0
    0
  • In optics, he developed the wave theory, and his name is associated with the simple dispersion formula.

    0
    0
  • He had accepted the Formula Concordiae, a Lutheran document promulgated in June 1580, and sought to prevent any departure from its tenets.

    0
    0
  • Public opinion, however, in Brandenburg was too strong for him, and he was compelled to fall back upon the Lutheran Formula and the religious policy of his father.

    0
    0
  • Its formula is (C6H1005)2H20, and it forms compounds with nearly all bases which are easily soluble in water.

    0
    0
  • I seem to have stolen the formula that will grant Immortal or demon this same immunity.

    0
    0
  • For simple organic molecules, including alkanes, alkenes and cycloalkanes, construct appropriate isomeric forms, given a molecular formula 11.

    0
    0
  • They never found a mathematical formula that worked, much less anything capable of becoming the basis for a universally applicable model.

    0
    0
  • Formula 4 Feet contains the amino acid arginine, which is the precursor for the formation of nitrous oxide in the tissue circulation.

    0
    0
  • It finally banished the memory of my Formula 3000 accident in 1988.

    0
    0
  • The natural citric formula is non toxic & completely biodegradable & is safe to use on all metal, plastic & glass components.

    0
    0
  • The musical biopic is hardening into a formula of lots of suffering and then final salvation.

    0
    0
  • Graviola makes up 50 percent of the N-Tense formula, which also consists of smaller amounts of the rainforest botanicals described below.

    0
    0
  • For mothers who do not breast-feed, an approved infant formula is the only alternative.

    0
    0
  • Total Foot Care Cream is a luxurious conditioning formula that softens and eliminates calluses, and heals chapped areas of the foot.

    0
    0
  • Trikatu formula increases the digestive fire, which then burns away these accumulated toxins and cleanses the alimentary canal.

    0
    0
  • To aid sleep consider the short term use of Valerian & Passion flower formula, and drink chamomile flower tea.

    0
    0
  • There is great synergy between the Class 1 powerboat championship and the Honda Formula 4-Stroke series.

    0
    0
  • The formula in the notes applies to the general case, only failing if points actually become coincident.

    0
    0
  • Some people believe that colic is caused from gas or intolerance to breast milk or even baby formula.

    0
    0
  • Verily there was no formula by which the Tathagata attained the consummation of Incomparable Enlightenment.

    0
    0
  • This Formaldehyde free formula penetrates thick, dry cuticles leaving them soft and transparent.

    0
    0
  • Polanski's vision is thus deepened by his confrontation with the traditional horror formula.

    0
    0
  • At that time there were others manufacturing artificial stone, but without success because their methods and formula proved deficient.

    0
    0
  • If you do freeze infant formula you should make sure it is properly defrosted before heating.

    0
    0
  • Virtually all of the phytic acid was removed (using enzymatic degradation) from the experimental formula.

    0
    0
  • A Bessel formula is applied to interpolate the energy levels of the restricted asymmetric rotor.

    0
    0
  • For direct solution, it must be possible to rearrange the equations so that a formula can be written for every unknown.

    0
    0
  • The Deep Sanderson formula junior is now nearing completion and is looking exquisite.

    0
    0
  • I have omitted them from the formula in the heading above because they didn't come out well in the italic font I used.

    0
    0