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.
The limiting points are inverse points for every circle of the system.
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.
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.
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.
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.
It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.
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.
In the present section, however, we return from the inverse operation to the direct; i.e.
There is therefore as yet no ground for regarding any deviation from the law of inverse square as more than a possibility.