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.
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.
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.
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.
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.
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.
- 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 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.
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.
(iii.) Where the direct operation is evolution, for which there is no commutative law, the two inverse operations are different in kind.
(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.
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.
The exponential function, exp x, may be defined as the inverse of the logarithm: thus x =exp y if y= log x.
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.
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.
Jevons supposed induction to be inverse deduction, distinguished from direct deduction as analysis from synthesis, e.g.
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.
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 law of the inverse cube P=u u is interesting by way of contrast.
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.
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.
We have seen that under the law of the inverse square all finit orbits are elliptical.