# Inverse Sentence Examples

- There we proceeded from the direct to the
**inverse**operations. - In general theory the
**inverse**rule seems to prevail. - There is therefore as yet no ground for regarding any deviation from the law of
**inverse**square as more than a possibility. - 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. - 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. - The process of dispersion is the
**inverse**of that of absorption, and exhibits similar features. - In the present section, however, we return from the
**inverse**operation to the direct; i.e. - 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. - 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. - 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. - 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. - 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 Iï¿½8 ergs. - 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. - 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. - 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. - The law of the
**inverse**cube P=u u is interesting by way of contrast. - 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. - 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. - - 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. - It is not yet experimentally proved that variation as the
**inverse**square is absolutely true at all distances. - 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. - 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. - 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. - 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. - It is the
**inverse**of a central conic for the focus, and the first positive pedal of a circle for any point. - Unless we increase the length of the stem in the
**inverse**ratio of the sectional area. - 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. - It is also the
**inverse**of the same curve for the same point. - One was to show that the law of the
**inverse**square not only represented Kepler's third law, but his first two laws also. - 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. - 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. - Jevons supposed induction to be
**inverse**deduction, distinguished from direct deduction as analysis from synthesis, e.g. - 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; - We have seen that under the law of the
**inverse**square all finit orbits are elliptical. - 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. - (iii.) Where the direct operation is evolution, for which there is no commutative law, the two
**inverse**operations are different in kind. - The exponential function, exp x, may be defined as the
**inverse**of the logarithm: thus x =exp y if y= log x. - 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. - 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. - If the law of attraction be that of the
**inverse**square of the distance, we have P = u/,2, and ~1=C+~. - 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. - The symbol v represents the
**inverse**of the dispersive power, its value being (nD-i)/(C-F). - 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. - 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.' - These, with the second cathedral of St Patrick, are more conveniently described in the
**inverse**order. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - In terms of x 1, x2, x3,ï¿½ï¿½ The
**inverse**question is the expression of any monomial symmetric function by means of the power functions (r) = sr. Theorem of Reciprocity.-If ï¿½1 P2 "3 01 Q 2 7 3 Al A 2 A3 X m1 X m2 X m3 ... - 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. - 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. - - 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.