KINETIC THEORIES OF GRAVITATION. 275 



The corpuscular bypotbesis is clearly invented j)ro hac vice. Nor can 

 ■even an analogue of the invention be found in the corpuscular theory 

 of gases ; for in the latter case, the free path of the particle is assumed 

 to extend only for the short distance between neighboring molecules, 

 and by reason of incessant collision and deflection among the elements 

 the hydro-dynamic pressure of the medium is equal in all directions, 

 quite irrespective of the number or character of intervening obstruc- 

 tions: while the gravific or ultramundane corpuscle must ex hypothesi 

 travel from infinity in a perfectly straight and undisturbed path to fulfill 

 its appointed mission. It is therefore a special creation, neither ascer- 

 tained nor suggested by any other consideration. 



Secondly, even if a vera causa, it is wholly insufiBcient. The first 

 great triumph of the corpuscular assumption was its supposed happy 

 expression of the distance-ratio of gravitative intensity : and this 

 appears to have been admitted by all the mathematicians who have 

 referred to the problem. But a very brief consideration will show that 

 while this may be approximately true for small masses, there is a limit 

 of magnitude as well as of number in the masses of gross matter, beyond 

 which no assignable number of corpuscles is capable of acting. Let us 

 suppose for deflniteness (not as even suggesting a higher limit) that 

 normal to a plane whose area is d^ {d representing the distance between 

 two adjacent molecules of ice or of water,) a million million corpuscles 

 are passing simultaneously with any desired frequency. This neglects 

 for the moment the far greater number passing through the same area 

 iit all other angles. The molecule of ice or water being a very small 

 though appreciable fraction of the value of rf, (a not improbable estimate 

 of which value may be the five hundred millionth of an inch,) it is ob- 

 vious that with an equable distribution of the material molecules in a 

 continued right prism having d? for its base, no very great depth is 

 required for a million million of such molecules to lie each in the line of 

 motion of one of the parallel moving corpuscles. Beyond this depth or 

 distance, of any number of molecules continued, no one will receive an 

 impact, or in other words, will have any gravitation.* This reasoning 

 remains true, whatever be the number and direction of the prisms chosen, 

 and whatever be the number of corpuscles passing through its base 

 d". If it be said that this number is infinite, this is simply an uncondi- 

 tional surrender of the hypothesis. It is proved then that the number 

 of corpuscles passing through a large mass must be very much less than 

 the number impinging on its exposed strata or passing through a small 

 mass; and that if the mass be large enough, the side presented toward 

 another mass will receive no gravitative impulse thereto ; and a tidal 



' This idea may be more popularly illustrated by supposing ou a plane of indefinite 

 extent a grove of small, vertical trees, planted at irregular but equable intervals, at; 

 any assignable distance apart. It is evident that it. would require no indefiuite extension 

 of the woods to absolutely exclude a horizontal ray of light in any direction, eveu 

 though suns or electric lights were blazing with unimaginable splendor. 



