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inverse

inverse

inverse Sentence Examples

  • There we proceeded from the direct to the inverse operations.

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  • In general theory the inverse rule seems to prevail.

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  • There is therefore as yet no ground for regarding any deviation from the law of inverse square as more than a possibility.

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  • It is certain that, in the general average, year after year, the force with which Mercury is drawn toward the sun does vary from the exact inverse square of its distance from the sun.

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  • Liberals were scandalized by his apparent identification of " right " with " might," implied in the demand for a strong government; and though he often declared the true interpretation to be that the right would ultimately become might, his desire for strong government seemed too often to sanction the inverse view.

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  • ii.) gave the first direct demonstration that no function of the distance except the inverse square can satisfy the condition that a uniform spherical shell exerts no force on a particle within it.

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  • The process of dispersion is the inverse of that of absorption, and exhibits similar features.

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  • It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.

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  • It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.

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  • But suddenly instead of those chances and that genius which hitherto had so consistently led him by an uninterrupted series of successes to the predestined goal, an innumerable sequence of inverse chances occur--from the cold in his head at Borodino to the sparks which set Moscow on fire, and the frosts--and instead of genius, stupidity and immeasurable baseness become evident.

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  • - The equation exists, without being shown as an equation, in all those elementary arithmetical processes which come under the head of inverse operations; i.e.

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  • In the present section, however, we return from the inverse operation to the direct; i.e.

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  • Through this space the fresh surface water finds its way, and dissolving the salt below rises in the inner tube as brine, but only to such a level that the two columns bear to one another the relation of ten to twelve, this being the inverse ratio of the respective weights of saturated brine and fresh water.

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  • On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2.000 000 161 2.

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  • Thoughts of home grew stronger the nearer he approached it--far stronger, as though this feeling of his was subject to the law by which the force of attraction is in inverse proportion to the square of the distance.

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  • A direct and an inverse calculus is thus created, the object of the former being to determine the coefficients from the generating function, of the latter to discover the generating function from the coefficients.

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  • But since an equiangular spiral having a given pole is completely determined by a given point and a given tangent, this type of orbit is not a general one for the law of the inverse cube.

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  • Similarly, in the case of a circle with the pole on the circumference we have p2=r2/2a, P=ufri, if u=8hlai; but this orbit is not a general one for the law of the inverse fifth power.

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  • the intensity of the force in the region for which r = a, nearly must diminish with increasing distance less rapidly than accordin~ to the law of the inverse cube.

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  • Several previous attempts had been made to discover the law of force, with various results, some of which correctly indicated the inverse square; in particular the German astronomer, J.

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  • Newton's researches showed that the attraction of the earth on the moon was the same as that for bodies at the earth's surface, only reduced in the inverse square of the moon's distance from the earth's centre.

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  • The law of this force, for all distances greater than say the thousandth of an inch, is an attraction varying as the inverse square of the distance.

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  • unless we increase the length of the stem in the inverse ratio of the sectional area.

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  • The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.

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  • The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.

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  • The tendency is for property valuations to decline, the estimated valuation from 1873 to 1893 decreasing 27% in Cook county and 39% in the other counties, while the assessments from 1888 to 1898 were in inverse ratio to the increase of wealth.

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  • These, with the second cathedral of St Patrick, are more conveniently described in the inverse order.

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  • The law of the inverse cube P=u u is interesting by way of contrast.

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  • Wien also used the apparatus to find the decrease of intensity with increase of distance, and found that it was somewhat more rapid than the inverse square law would give.

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  • It is also the inverse of the same curve for the same point.

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  • One was to show that the law of the inverse square not only represented Kepler's third law, but his first two laws also.

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  • Newton tells us that this agreement led him to adopt the law of the inverse square of the distance about 1665-1666, before Huygens's results as to circular motion had been published.

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  • The diminution of the star disks with increasing aperture was observed by Sir William Herschel, and in 1823 Fraunhofer formulated the law of inverse proportionality.

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  • just outside the earth's atmosphere is therefore about 4XIo 5 ergs; applying the law of inverse squares the value near the sun's surface would be I�8 ergs.

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  • It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.

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  • It is the inverse of a central conic for the focus, and the first positive pedal of a circle for any point.

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  • Meanwhile the waves are spreading out and the value of u is falling in inverse proportion to the distance from the source, so that very soon its effect must become negligible.

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  • It is a fundamental theorem in attractions that a thin spherical shell of matter which attracts according to the potential law of the inverse square acts on all external points as of a if it were concentrated at its centre.

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  • If, for example, the law be that of the inverse square, we have P=~su2, and the solution is of the form u=~1tI+ecos(Oa)), (i8;

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  • We have seen that under the law of the inverse square all finit orbits are elliptical.

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  • If, for example, the law be that of the inverse square, we have P=~su2, and the solution is of the form u=~1tI+ecos(Oa)), (i8;

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  • We have seen that under the law of the inverse square all finit orbits are elliptical.

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  • Lastly, Wundt's view is an interesting piece of eclecticism, for he supposes that induction begins in the form of Aristotle's inductive syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P, S-M, S-P. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself.

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  • Lastly, Wundt's view is an interesting piece of eclecticism, for he supposes that induction begins in the form of Aristotle's inductive syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P, S-M, S-P. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself.

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  • The symbol v represents the inverse of the dispersive power, its value being (nD-i)/(C-F).

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  • p. 76, where Maxwell gives an elegant proof that if the force in the interior of a closed conductor is zero, the law of the force must be that of the inverse square of the distance.'

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  • It is not syllogism in the form of Aristotle's or Wundt's inductive syllogism, because, though starting only from some particulars, it concludes with a universal; it is not syllogism in the form called inverse deduction by Jevons, reduction by Sigwart, inductive method by Wundt, because it often uses particular facts of causation to infer universal laws of causation; it is not syllogism in the form of Mill's syllogism from a belief in uniformity of nature, because few men have believed in uniformity, but all have induced from particulars to universals.

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  • They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

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  • The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x.

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  • Jevons supposed induction to be inverse deduction, distinguished from direct deduction as analysis from synthesis, e.g.

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  • Jevons supposed induction to be inverse deduction, distinguished from direct deduction as analysis from synthesis, e.g.

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  • In its long course it varies greatly both in depth and width, in some parts being only a few feet deep and spreading out to a width of more than a mile, while in other and mountainous portions of its course its channel is narrowed to 300 or 400 ft., and its depth is increased in inverse ratio.

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  • The exponential function, exp x, may be defined as the inverse of the logarithm: thus x =exp y if y= log x.

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  • This pococurantism might easily be interpreted as an insight into the limitations of inverse method as such or as a belief in the plurality of causes in Mill's sense of the phrase.

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  • If the law of attraction be that of the inverse square of the distance, we have P = u/,2, and ~1=C+~.

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  • In its long course it varies greatly both in depth and width, in some parts being only a few feet deep and spreading out to a width of more than a mile, while in other and mountainous portions of its course its channel is narrowed to 300 or 400 ft., and its depth is increased in inverse ratio.

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  • This pococurantism might easily be interpreted as an insight into the limitations of inverse method as such or as a belief in the plurality of causes in Mill's sense of the phrase.

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  • (iii.) Where the direct operation is evolution, for which there is no commutative law, the two inverse operations are different in kind.

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  • (iii.) Where the direct operation is evolution, for which there is no commutative law, the two inverse operations are different in kind.

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  • It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.

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  • in terms of x 1, x2, x3,�� The inverse question is the expression of any monomial symmetric function by means of the power functions (r) = sr. Theorem of Reciprocity.-If �1 P2 "3 01 Q 2 7 3 Al A 2 A3 X m1 X m2 X m3 ...

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  • In the same way, a statement as to the result of an inverse operation is really, by the definition of the operation, a statement as to the result of a direct operation.

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  • - If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.

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  • J, Inverse.

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  • Though we can convert the whole of the energy possessed by any mechanical system into heat, it is not in our power to perform the inverse operation, and to utilize the whole of the heat in doing mechanical work.

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  • Worse still, Jevons proceeded to confuse analytic deduction from consequence to ground with hypothetical deduction from ground to conseguence under the common term "inverse deduction."

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  • Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.

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  • Hence the only law of force which satisfies the conditions is that of the inverse square.

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  • In the case of a central orbit described under the law of the inverse _________________ square we have v=h/SY=h.

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  • of 39 it appears that the angular velocityratio of a pair of wheels is the inverse ratio of the distances of the point of contact from the Centres respectively.

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  • Tire more general property of the mechanism corresponding to proper tions between the lengths FA and EF other than that of equality is that the curve described by the point C is the inverse of the curve described by A.

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  • Removing the summation signs in equation (52) in order to restrict its application to two points and dividing by the common time interval during which the respective small displacements ds and ds were made, it becomes Pdsfdt = Rds/dt, that is, Pv = Rv, which shows that the force ratio is the inverse of the velocity ratio.

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  • At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A.

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  • 12 a and developed the view that induction is simply an inverse employment of deduction; he treated in a luminous manner the general theory of probability, and the relation between probability and induction; and his knowledge of the various natural sciences enabled him throughout to relieve the abstract character of logical doctrine by concrete scientific illustrations, often worked out in great detail.

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  • The volumes of their publication, Resultate aus den Beobachtungen des magnetischen Vereins, extend from 1836 to 1839; and in those for 1838 and 1839 are contained the two important memoirs by Gauss, Allgemeine Theorie des Erdmagnetismus, and the Allgemeine Lehrscitze - on the theory of forces attracting according to the inverse square of the distance.

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  • we have a memoir On the Attraction of Homogeneous Ellipsoids, and the already mentioned memoir Allgemeine LehrsÃtze, on the theory of forces attracting according to the inverse square of the distance.

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  • Its history does not run parallel with the scientific side, but rather varies in inverse ratio with scientific activity.

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  • inverse orientation of the tissues, x, Xylem.

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  • Eichler, one of the chief supporters of the simpler view, does not recognize in the inverse orientation of the vascular bundles an argument in support of the axillary-bud theory, but points out that the seminiferous scale, being an outgrowth from the surface of the carpellary scale, would, like outgrowths from an ordinary leaf, naturally have its bundles inversely orientated.

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  • The apparent hexagonal bipyramid is really a combination of two rhombohedra, the direct rhombohedron r{ loo} and the inverse rhombohedron z{221{.

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  • Speaking generally, the Ozark region is characterized by reddish clays, mixed with gravels and stones, and cultivable in inverse proportion to the amount of these elements; northern Missouri by a generally black clay loam over a clay subsoil, with practically no admixture of stones; the southern prairies, above referred to, share the characteristics of those north of the Missouri.

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  • Now under the law of attraction according to the inverse square of the distance, or any other inverse power beyond the first, the energy of even a single pair of material points is unlimited, if their possible closeness of approach to one another is unlimited.

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  • Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

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  • But by observing the distance through which a body would fall in one second of time at the earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the earth's attraction at the distance of the moon would draw a body through 15 ft.

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  • In January 1684 Sir Christopher Wren, Halley and Hooke were led to discuss the law of gravity, and, although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established.

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  • It appears that Hooke professed to have a solution of the problem of the path of .a body moving round a centre of force attracting as the inverse square of the distance; but Halley, finding, after a delay of some months, that Hooke " had not been so good as his word " in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult Newton on the subject.

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  • Excepting in the correspondence with Flamsteed we hear nothing more of the preparation of the Principia until the 21st of April 1686, when Halley read to the Royal Society his Discourse concerning Gravity and its Properties, in which he states " that his worthy countryman Mr Isaac Newton has an incomparable treatise of motion almost ready for the press," and that the law of the inverse square " is the principle on which Mr Newton has made out all the phenomena of the celestial motions so easily and naturally, that its truth is past dispute."

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  • He knew indeed that before Newton had announced the inverse law Hooke and Wren and himself had spoken of it and discussed it, and therefore justice demanded that, though none of them had given a demonstration of the law, Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration.

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  • This scholium was- " The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

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  • (iii) The inclusion of the four processes under one general head fails to indicate the essential difference between addition and multiplication, as direct processes, on the one hand, and subtraction and division, as inverse processes, on the other (§ 59).

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  • Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.

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  • Results of Inverse Operations.

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  • But, in attempting the inverse processes of subtraction, division, and either evolution or determination of index, the data may be such that a process cannot be performed.

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  • I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and my hopes upon weaker convictions.

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  • Ward in his Gifford lectures for 1896-1898 (Naturalism and Agnosticism, 1899), Huxley's challenge ("I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and my hopes upon weaker convictions") is one which a spiritualistic philosophy need not shrink from accepting at the hands of naturalistic agnosticism.

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  • The first minors, each divided by the determinant itself, form a system of elements inverse to the elements of the determinant.

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  • The discovery of Neptune in 1846 by Adams and Leverrier marked the first solution of the " inverse problem " of perturbations.

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  • The cissoid is the first positive pedal of the parabola y2+8ax=o for the vertex, and the inverse of the parabola y 2 = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion.

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  • For a given degree of opposition this burden will be shared between the conflicting presentations in the inverse ratio of their strength.

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  • Biot further ascertained that this rotation of the plane of polarization varies as the distance traversed in the plate and very nearly as the inverse square of the wave-length, and found that with certain specimens of quartz the rotation is in a clockwise or right-handed direction to an observer receiving the light, while in others it is in the opposite direction, and that equal plates of the rightand lefthand varieties neutralize one another's effects.

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  • C, I are seldom pronounced like s; but a feature more peculiar to the Andalusians is the inverse process, the softened and interdental pronunciation of the s (the so-called ceceo): zeor (sehor), &c. Before a consonant and at the end of a word s becomes a simple aspiration: mihmo (mismo), Dioh (Dios), do reales (dos reales).

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  • of it constitutes a special fund to be apportioned among eligible counties in proportion to their school population but in inverse ratio to their taxable property; to have the use of any portion of this special fund a county must levy for the maintenance of common schools a tax not less than forty cents on each $loo of taxable property, a tax of $2 on each taxable poll, and such privilege taxes as the state permits it to levy for school purposes.

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  • additive inverse of any number is a unique number.

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  • admissible argument of the operation Inverse, which may sometimes return ' fail ' .

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  • Figure 1. atmospheric carbon dioxide mirrors plankton growth in inverse relationship.

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  • The use of inverse phase gas chromatography to study the glass transition temperature of a powder surface.

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  • This change becomes prominent in advanced stages of the cancer and shows a strong inverse correlation with protein expression.

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  • partial correlation coefficients suggest that geographic range is the most important predictor of description date, and shows an inverse relationship.

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  • The inverse cosine is defined only in the domain from ` -1 ' to ` 1 ' .

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  • calculate the inverse covariance of the full Gaussian, and use the partitioned inverse equations to obtain the covariance for the known data.

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  • demon lord and killed by Lina Inverse.

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  • A homeomorphism that has at least one continuous derivative (w.r.t. z) and a continuously differentiable inverse is a diffeomorphism.

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  • He derived the distances from inverse square law of brightness: clusters farther away should appear dimmer.

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  • Figure 1. atmospheric carbon dioxide mirrors plankton growth in inverse relationship.

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  • equal in magnitude to the inverse of d 010.

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  • The adjustable rate escapement shown in below resembles the inverse escapement in **** .

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  • factorized inverse transversal is a Schreier tree.

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  • Simple methods define an arbitrary law, such as an inverse square relationship, or a linear falloff.

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  • Using this domain derive a formula for the inverse function.

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  • The use of inverse phase gas chromatography to study the glass transition temperature of a powder surface.

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  • generalized inverse, P # .

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  • For Newton-Raphson calculations, the inverse Hessian is output after each exact recalculation, but not after updating.

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  • Sequence analysis at the site of transgene insertion by inverse PCR yielded 1 to 4 DNA fragments differing in size in each sample.

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  • inverse of a matrix?

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  • inverse of a generator is represented by the corresponding capital letter.

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  • inverse of a group algebra element.

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  • The inverse of a function The inverse of a function The inverse of a function is the function which reverses the effect of the original function.

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  • inverse of any number is a unique number.

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  • P is its own generalized inverse, P # .

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  • Based on these three analytic inverses, three formulae were developed for computing the inverse numerically.

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  • It calculates the inverse of a group algebra element.

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  • finding the inverse of a matrix: an example Find the inverse of the matrix A = 2 3 -4.

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  • This generalized inverse, called a g2 inverse, has two important properties.

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  • Example 11.. 7 The matrix A = does not have an inverse.

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  • IsmultiplicativeElementWithInverse contains objects obj for which a multiplicative inverse contains objects obj for which a multiplicative inverse can be obtained by forming obj ^-1.

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  • The additive inverse of any number is a unique number.

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  • inverse kinematics.

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  • inverse cosine is defined only in the domain from ` -1 ' to ` 1 ' .

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  • inverse phase gas chromatography to study the glass transition temperature of a powder surface.

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  • inverse FFT for the reconstruction.

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  • inverse telecine WAS added in the release for HDP or that it WILL be added next.

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  • inverse fast Fourier transform, which gives the structure factor.

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  • Negative powers are computed using the matrix inverse of the positive power.

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  • The numerical method used is multisection for eigenvalues [16] and repeated inverse iteration and orthogonalization for eigenvectors [17] .

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  • inverse kinematics Given knowledge of an achieved pattern of movement, calculation of the component elements of movement required to produce the observed movement.

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  • The aim of this project is to provide an algorithm that computes the stable manifold without using the inverse map at all.

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  • Note that the inverse general mapping of a mapping map is in general only a general mapping.

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  • measurable quantity by solving an inverse problem.

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  • multiplicativeElementWithinverse contains objects obj for which a multiplicative inverse can be obtained by forming obj ^-1.

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  • Explore our research pages to see some stunning images of opal and inverse opal and to learn more about these exciting materials.

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  • In this paper, the surface energies of various thermoplastic polyolefins (TPO) have been measured via Inverse Gas Chromatography (IGC ).

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  • Note The passage on inverse probability is reproduced in Likelihood and Probability in R. A. Fisher's Statistical Methods for Research Workers.

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  • prudent to avoid feeding a ration consisting of a large amount of ingredients with an inverse calcium:phosphorus ratio.

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  • An inverse association was also found for increasing quintiles of beta-carotene among premenopausal women who consumed 15 g or more of alcohol per day.

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  • It is the inverse of the price-earnings ratio, with a few refinements.

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  • The political processes in the two countries have a lot do with this inverse regionalism.

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  • During the seventeenth century it was becoming clear that fluxions and quadrature were intimately related in fact, that they are inverse processes.

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  • The process, called inverse electron spin resonance, uses the magnetic field to deflect electrons and to modify their magnetic direction.

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  • The inverse sine is defined only in the domain from ` -1 ' to ` 1 ' .

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  • see also matrix singularity, matrix inverse, generalized inverse.

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  • Kay Bell disliked what she saw as inverse snobbery in the attitudes of the book.

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  • The inverse tangent is the value whose tangent is ` x ' .

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  • transpose of the matrix is a right inverse of the generator matrix.

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  • Another name for a factorized inverse transversal is a Schreier tree.

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  • viepanky is a sort of inverse Divine rail-thin but still vying to be the most disgusting person on earth.

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  • In passing from one part of the spectrum to another, A is the only quantity which varies, and we have the important law: - When light is scattered by particles which are very small compared with any of the wave-lengths, the ratio of the amplitudes of the vibrations of the scattered and incident lights varies inversely as the square of the wave-length, and the ratio of intensities as the inverse fourth power.

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  • The incident light being white, the intensity of the component colours scattered in this direction varies as the inverse eighth power of the wave-length, so that the resultant light is a rich blue.

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  • Though we can convert the whole of the energy possessed by any mechanical system into heat, it is not in our power to perform the inverse operation, and to utilize the whole of the heat in doing mechanical work.

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  • The explanation of the action of the shunt is that all slowly varying currents affect the coil of the receiving instrument and its shunt in inverse proportion to their respective resistances; whereas with the comparatively rapid variations of current used in signalling the coil is forced at the beginning of each element of A v

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  • When he wrote his Logic he had learned from Comte that the a posteriori method - in the form which he chose to call "inverse deduction" - was the only mode of arriving at truth in general sociology; and his admission of this at once renders the essay obsolete.

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  • In general theory the inverse rule seems to prevail.

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  • It is also the inverse of the same curve for the same point.

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  • in terms of x 1, x2, x3,�� The inverse question is the expression of any monomial symmetric function by means of the power functions (r) = sr. Theorem of Reciprocity.-If �1 P2 "3 01 Q 2 7 3 Al A 2 A3 X m1 X m2 X m3 ...

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  • Several previous attempts had been made to discover the law of force, with various results, some of which correctly indicated the inverse square; in particular the German astronomer, J.

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  • 4 Poisson assumed the existence of two dissimilar magnetic fluids, any element of which acted upon any other distant element in accordance with Coulomb's law of the inverse square, like repelling and unlike attracting one another.

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  • A direct and an inverse calculus is thus created, the object of the former being to determine the coefficients from the generating function, of the latter to discover the generating function from the coefficients.

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  • - The equation exists, without being shown as an equation, in all those elementary arithmetical processes which come under the head of inverse operations; i.e.

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  • In the same way, a statement as to the result of an inverse operation is really, by the definition of the operation, a statement as to the result of a direct operation.

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  • Thus, corresponding to the results under � 15 (2), we have the iollowing: (i) Where the inverse operation is performed on the unknown quantity or number: (i.) If A=X-B, then X=A+B.

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  • (iii.) (a) If a= then x = aP. (b) If p = log a x, then x = aP. (2) Where the inverse operation is performed with the unknown quantity or number: (i.) If B=A-X, then A=B+X.

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  • There we proceeded from the direct to the inverse operations; i.e.

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  • In the present section, however, we return from the inverse operation to the direct; i.e.

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  • They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

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  • The inverse symbols -, = are ambiguous, and in fact are rarely used.

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  • The inverse operation is free from ambiguity, and, in fact, A 1 - B 1 = E (a i - 130ei.

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  • The diminution of the star disks with increasing aperture was observed by Sir William Herschel, and in 1823 Fraunhofer formulated the law of inverse proportionality.

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  • The symbol v represents the inverse of the dispersive power, its value being (nD-i)/(C-F).

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  • One was to show that the law of the inverse square not only represented Kepler's third law, but his first two laws also.

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  • Newton's researches showed that the attraction of the earth on the moon was the same as that for bodies at the earth's surface, only reduced in the inverse square of the moon's distance from the earth's centre.

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  • On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2.000 000 161 2.

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  • It is certain that, in the general average, year after year, the force with which Mercury is drawn toward the sun does vary from the exact inverse square of its distance from the sun.

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  • There is therefore as yet no ground for regarding any deviation from the law of inverse square as more than a possibility.

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  • - If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.

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  • p. 76, where Maxwell gives an elegant proof that if the force in the interior of a closed conductor is zero, the law of the force must be that of the inverse square of the distance.'

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  • ii.) gave the first direct demonstration that no function of the distance except the inverse square can satisfy the condition that a uniform spherical shell exerts no force on a particle within it.

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  • It is a fundamental theorem in attractions that a thin spherical shell of matter which attracts according to the potential law of the inverse square acts on all external points as of a if it were concentrated at its centre.

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  • The process of dispersion is the inverse of that of absorption, and exhibits similar features.

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  • The law of this force, for all distances greater than say the thousandth of an inch, is an attraction varying as the inverse square of the distance.

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  • It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.

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  • Meanwhile the waves are spreading out and the value of u is falling in inverse proportion to the distance from the source, so that very soon its effect must become negligible.

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  • Wien also used the apparatus to find the decrease of intensity with increase of distance, and found that it was somewhat more rapid than the inverse square law would give.

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  • just outside the earth's atmosphere is therefore about 4XIo 5 ergs; applying the law of inverse squares the value near the sun's surface would be I�8 ergs.

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  • It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.

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  • The exponential function, exp x, may be defined as the inverse of the logarithm: thus x =exp y if y= log x.

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  • The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x.

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  • From comparative anatomy alone it is possible to arrange a series of living forms which, although structurally a convincing array because placed in a graded series, may be, nevertheless, in an order inverse to that of the actual historical succession.

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  • It is the inverse of a central conic for the focus, and the first positive pedal of a circle for any point.

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  • These, with the second cathedral of St Patrick, are more conveniently described in the inverse order.

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  • The limiting points are inverse points for every circle of the system.

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  • unless we increase the length of the stem in the inverse ratio of the sectional area.

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  • Newton tells us that this agreement led him to adopt the law of the inverse square of the distance about 1665-1666, before Huygens's results as to circular motion had been published.

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  • J, Inverse.

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  • teath the ground lay a dark and mysterious region, now con- obs~ red as an inverse heaven (Nenet), now as a vast series of pail ems whose gates were guarded by demons.

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  • Through this space the fresh surface water finds its way, and dissolving the salt below rises in the inner tube as brine, but only to such a level that the two columns bear to one another the relation of ten to twelve, this being the inverse ratio of the respective weights of saturated brine and fresh water.

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  • Liberals were scandalized by his apparent identification of " right " with " might," implied in the demand for a strong government; and though he often declared the true interpretation to be that the right would ultimately become might, his desire for strong government seemed too often to sanction the inverse view.

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  • The tendency is for property valuations to decline, the estimated valuation from 1873 to 1893 decreasing 27% in Cook county and 39% in the other counties, while the assessments from 1888 to 1898 were in inverse ratio to the increase of wealth.

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  • Worse still, Jevons proceeded to confuse analytic deduction from consequence to ground with hypothetical deduction from ground to conseguence under the common term "inverse deduction."

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  • It is not syllogism in the form of Aristotle's or Wundt's inductive syllogism, because, though starting only from some particulars, it concludes with a universal; it is not syllogism in the form called inverse deduction by Jevons, reduction by Sigwart, inductive method by Wundt, because it often uses particular facts of causation to infer universal laws of causation; it is not syllogism in the form of Mill's syllogism from a belief in uniformity of nature, because few men have believed in uniformity, but all have induced from particulars to universals.

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  • Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.

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  • rotation will bring a point from C to C and that the second will bring it back to C; the result is therefore equivalent to a rotation about OC. We note also that if the given rotations had been effected in the inverse order, the axis of the resultant rotation would have been OC, so that finite rotations do not obey the commutative law.

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  • If the law of attraction be that of the inverse square of the distance, we have P = u/,2, and ~1=C+~.

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  • But since an equiangular spiral having a given pole is completely determined by a given point and a given tangent, this type of orbit is not a general one for the law of the inverse cube.

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  • Similarly, in the case of a circle with the pole on the circumference we have p2=r2/2a, P=ufri, if u=8hlai; but this orbit is not a general one for the law of the inverse fifth power.

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  • The law of the inverse cube P=u u is interesting by way of contrast.

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  • the intensity of the force in the region for which r = a, nearly must diminish with increasing distance less rapidly than accordin~ to the law of the inverse cube.

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  • Hence the only law of force which satisfies the conditions is that of the inverse square.

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  • In the case of a central orbit described under the law of the inverse _________________ square we have v=h/SY=h.

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  • of 39 it appears that the angular velocityratio of a pair of wheels is the inverse ratio of the distances of the point of contact from the Centres respectively.

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  • Tire more general property of the mechanism corresponding to proper tions between the lengths FA and EF other than that of equality is that the curve described by the point C is the inverse of the curve described by A.

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  • Removing the summation signs in equation (52) in order to restrict its application to two points and dividing by the common time interval during which the respective small displacements ds and ds were made, it becomes Pdsfdt = Rds/dt, that is, Pv = Rv, which shows that the force ratio is the inverse of the velocity ratio.

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  • At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A.

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  • 12 a and developed the view that induction is simply an inverse employment of deduction; he treated in a luminous manner the general theory of probability, and the relation between probability and induction; and his knowledge of the various natural sciences enabled him throughout to relieve the abstract character of logical doctrine by concrete scientific illustrations, often worked out in great detail.

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  • The volumes of their publication, Resultate aus den Beobachtungen des magnetischen Vereins, extend from 1836 to 1839; and in those for 1838 and 1839 are contained the two important memoirs by Gauss, Allgemeine Theorie des Erdmagnetismus, and the Allgemeine Lehrscitze - on the theory of forces attracting according to the inverse square of the distance.

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  • we have a memoir On the Attraction of Homogeneous Ellipsoids, and the already mentioned memoir Allgemeine LehrsÃtze, on the theory of forces attracting according to the inverse square of the distance.

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  • Its history does not run parallel with the scientific side, but rather varies in inverse ratio with scientific activity.

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  • inverse orientation of the tissues, x, Xylem.

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  • A peculiarity of these leaves is the inverse orientation of the vascular tissue; each of the two veins has its phloem next the upper and the xylem towards the lower surface of the leaf; this unusual position of the xylem and phloem may be explained by regarding the needle of Sciadopitys as being composed of a pair of leaves borne on a short axillary shoot and fused by their margins (fig.

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  • Eichler, one of the chief supporters of the simpler view, does not recognize in the inverse orientation of the vascular bundles an argument in support of the axillary-bud theory, but points out that the seminiferous scale, being an outgrowth from the surface of the carpellary scale, would, like outgrowths from an ordinary leaf, naturally have its bundles inversely orientated.

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  • The apparent hexagonal bipyramid is really a combination of two rhombohedra, the direct rhombohedron r{ loo} and the inverse rhombohedron z{221{.

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  • Speaking generally, the Ozark region is characterized by reddish clays, mixed with gravels and stones, and cultivable in inverse proportion to the amount of these elements; northern Missouri by a generally black clay loam over a clay subsoil, with practically no admixture of stones; the southern prairies, above referred to, share the characteristics of those north of the Missouri.

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  • Now under the law of attraction according to the inverse square of the distance, or any other inverse power beyond the first, the energy of even a single pair of material points is unlimited, if their possible closeness of approach to one another is unlimited.

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  • Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

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  • But by observing the distance through which a body would fall in one second of time at the earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the earth's attraction at the distance of the moon would draw a body through 15 ft.

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  • In January 1684 Sir Christopher Wren, Halley and Hooke were led to discuss the law of gravity, and, although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established.

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  • It appears that Hooke professed to have a solution of the problem of the path of .a body moving round a centre of force attracting as the inverse square of the distance; but Halley, finding, after a delay of some months, that Hooke " had not been so good as his word " in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult Newton on the subject.

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  • Excepting in the correspondence with Flamsteed we hear nothing more of the preparation of the Principia until the 21st of April 1686, when Halley read to the Royal Society his Discourse concerning Gravity and its Properties, in which he states " that his worthy countryman Mr Isaac Newton has an incomparable treatise of motion almost ready for the press," and that the law of the inverse square " is the principle on which Mr Newton has made out all the phenomena of the celestial motions so easily and naturally, that its truth is past dispute."

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  • He knew indeed that before Newton had announced the inverse law Hooke and Wren and himself had spoken of it and discussed it, and therefore justice demanded that, though none of them had given a demonstration of the law, Hooke especially should receive credit for having maintained it as a truth of which he was seeking the demonstration.

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  • This scholium was- " The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

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  • (iii) The inclusion of the four processes under one general head fails to indicate the essential difference between addition and multiplication, as direct processes, on the one hand, and subtraction and division, as inverse processes, on the other (§ 59).

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  • Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.

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  • Results of Inverse Operations.

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  • But, in attempting the inverse processes of subtraction, division, and either evolution or determination of index, the data may be such that a process cannot be performed.

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  • I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and my hopes upon weaker convictions.

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  • Ward in his Gifford lectures for 1896-1898 (Naturalism and Agnosticism, 1899), Huxley's challenge ("I know what I mean when I say I believe in the law of the inverse squares, and I will not rest my life and my hopes upon weaker convictions") is one which a spiritualistic philosophy need not shrink from accepting at the hands of naturalistic agnosticism.

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  • The first minors, each divided by the determinant itself, form a system of elements inverse to the elements of the determinant.

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  • Ismael Bouillaud (1605-1694) stated in 1645 the fact of planetary circulation under the sway of a sun-force decreasing as the inverse square of the distance; and the inevitableness of this same " duplicate ratio " was separately perceived by Robert Hooke, Edmund Halley and Sir Christopher Wren before Newton's discovery had yet been made public. He was the only man of his generation who both recognized the law, and had power to demonstrate its validity.

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  • The discovery of Neptune in 1846 by Adams and Leverrier marked the first solution of the " inverse problem " of perturbations.

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  • The cissoid is the first positive pedal of the parabola y2+8ax=o for the vertex, and the inverse of the parabola y 2 = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion.

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  • For a given degree of opposition this burden will be shared between the conflicting presentations in the inverse ratio of their strength.

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  • Biot further ascertained that this rotation of the plane of polarization varies as the distance traversed in the plate and very nearly as the inverse square of the wave-length, and found that with certain specimens of quartz the rotation is in a clockwise or right-handed direction to an observer receiving the light, while in others it is in the opposite direction, and that equal plates of the rightand lefthand varieties neutralize one another's effects.

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  • C, I are seldom pronounced like s; but a feature more peculiar to the Andalusians is the inverse process, the softened and interdental pronunciation of the s (the so-called ceceo): zeor (sehor), &c. Before a consonant and at the end of a word s becomes a simple aspiration: mihmo (mismo), Dioh (Dios), do reales (dos reales).

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  • of it constitutes a special fund to be apportioned among eligible counties in proportion to their school population but in inverse ratio to their taxable property; to have the use of any portion of this special fund a county must levy for the maintenance of common schools a tax not less than forty cents on each $loo of taxable property, a tax of $2 on each taxable poll, and such privilege taxes as the state permits it to levy for school purposes.

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  • The proportion of freedom to inevitability decreases and increases according to the point of view from which the action is regarded, but their relation is always one of inverse proportion.

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  • An inverse association was also found for increasing quintiles of beta-carotene among premenopausal women who consumed 15 g or more of alcohol per day.

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  • It is the inverse of the price-earnings ratio, with a few refinements.

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  • The political processes in the two countries have a lot do with this inverse regionalism.

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  • During the seventeenth century it was becoming clear that fluxions and quadrature were intimately related in fact, that they are inverse processes.

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  • The process, called inverse electron spin resonance, uses the magnetic field to deflect electrons and to modify their magnetic direction.

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  • The inverse sine is defined only in the domain from ` -1 ' to ` 1 '.

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  • See also matrix singularity, matrix inverse, generalized inverse.

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  • Kay Bell disliked what she saw as inverse snobbery in the attitudes of the book.

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  • The inverse tangent is the value whose tangent is ` x '.

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  • The transpose of the matrix is a right inverse of the generator matrix.

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  • Spanky is a sort of inverse Divine rail-thin but still vying to be the most disgusting person on earth.

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  • The inverse is true with low credit scores.

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  • Although you may want to focus on last minute deals, don't forget about their inverse: early bird bookings.

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  • Inverse psoriasis occurs in the armpits and groin, under the breasts, and in other areas where skin flexes or folds.

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  • This inverse association was stronger than that for omega-3 fatty acid intake alone.

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  • They are linked to inverse operations, many algebraic functions, and proportions.

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  • This can be mirrored on the other side by what is known as an inverse belly button piercing.

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  • Inverse navel piercings run through the lower lip of the navel and extend upwards into the center of the belly button.

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  • Placement is commonly through the upper lip of the navel, but navel piercings can be placed at any point around the navel, including the inverse lip or either side.

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  • Among the watch's high-tech attributes are inverse chrono functions, chrono sub dials, bi-directional rotating bezel and screw-in mineral crystal.

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  • Some lessons will be geared 75-100 percent towards the babies, and others will be the inverse of that.

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  • The inverse is true as well, as activities like yoga do not require as sturdy a bra.

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  • Is popularity a factor - or does popularity have an inverse relationship with great music?

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  • When he wrote his Logic he had learned from Comte that the a posteriori method - in the form which he chose to call "inverse deduction" - was the only mode of arriving at truth in general sociology; and his admission of this at once renders the essay obsolete.

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