Messrs. Newcomb and Holden in their work, entitled "Astronomy for High Schools and Colleges," sixth edition, 1889, apparently accept the theory, and proceed to explain and support it by showing what would be the action of a hollow spherical shell of any substance on a particle of it, say the bob of a pendulum, placed on the outside and also on the inside of the shell; and give us two theorems which are supposed to comprehend both cases. These are:--
(1) "If the particle be outside of the shell, it will be attracted as if the whole mass of the shell were concentrated at its centre."
(2) "If it be inside the shell, the opposite attractions in every direction will neutralise each other, no matter whereabouts in the interior the particles may be, and the resultant attraction of the shell will therefore be zero."
To the first theorem no objection can be made: The particle on the outside of the shell will undoubtedly be attracted by every particle in the shell, with the same force as if the attractive power of all the particles composing it were concentrated in the centre. Not so with the second theorem: for it can be objected that it altogether ignores the Law of Attraction laid down by Sir Isaac Newton, where it asserts that the resultant attraction of the shell for the particle will be zero, when it is placed anywhere on the inside. In fact the theorem supposes a case impossible for the Harton Colliery experiments, in order to demonstrate their accuracy; for it makes use of the bob of the pendulum--a particle of matter--as if it were transferable to any part of the interior of the earth instead of being confined within the bounds of its swing. That the attraction of the shell--1260 feet thick all round the earth--on the pendulum bob inside of it continues in all its force, and is only divided into two opposing parts, is made plain by Fig. 1. Supposing O to represent the bob of the pendulum at the bottom of the mine, and the space between the two circles the shell of the earth. Then the line B C will show where the attraction of the shell for the bob is divided into two parts acting in opposite directions. Supposing these two parts to be separated from each other, only far enough to admit the bob--a particle to all intents and purposes--between them; the part B A C will attract the bob as if its whole attractive force were collected at its centre of gravity, and the part B D C as if the whole of its attractive force were collected, not at the centre B of the shell, but at its centre of gravity, a very little distance from B in the direction towards D. This is an incontrovertible fact, because it is in strict accordance with Newton's Law of Attraction, which is: _Every particle of matter in the universe attracts every other particle with a force directly as their masses, and inversely as the square of the distance which separates them._