In general theory the inverse rule seems to prevail.
Thus, corresponding to the results under ï¿½ 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.
There we proceeded from the direct to the inverse operations.
The inverse symbols -, = are ambiguous, and in fact are rarely used.
It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.
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.
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.
There is therefore as yet no ground for regarding any deviation from the law of inverse square as more than a possibility.
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 process of dispersion is the inverse of that of absorption, and exhibits similar features.
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.
The limiting points are inverse points for every circle of the system.
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.
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.
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 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.
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.
And meanwhile, the very next morning after the battle, the French army advanced of itself upon the Russians, carried forward by the force of its own momentum now seemingly increased in inverse proportion to the square of the distance from its aim.
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.