190 Theory of Attractive and Repulsive Forces. 



of the fluid, a momentum equal to a mass of fluid of the 

 density of the contiguous fluid, and of the size of the sphere, 

 multiplied by the velocity with which the fluid at that instant 

 crosses a transverse plane through the centre of the sphere 

 (' Principles of Physics,' p. 284). Hence, if M be the magni- 

 tude of the sphere, pi(l + a) the density of the fluid, and V 

 its velocity at the above mentioned plane, the momentum is 

 Mp^l-fcrjV. The corresponding quantity for the rarefied 

 half of the wave is — Mpfl — a)Y. The sum of these is 



2MpiV 2 

 2Mp 1 aV , which, since V = kcixt nearly, is equal to — - — . This 



is the impulse given to the fluid at the given instant in 

 the direction of propagation, and measures the reaction of 

 the fluid on the sphere in the contrary direction. Let 



V = m sin (?«* + C). Then V =^(l -cos(^ + 2C)). 



Omitting the periodic part, we shall have for the constant 

 part of the impulse, or moving force, towards the origin of 



the waves — " 1 If the mass of the sphere be MA, the 



fca L 



2 



accelerative force is ~ — , which, it should be observed, is 



independent of the magnitude of the sphere. This result ex- 

 presses the force of gravity as due to the attractive action of a 

 molecule of a higher order as to magnitude than the molecule 

 of molecular attraction. For distinction, a molecule of this 

 superior order might be called a gravity-molecule. Its magni- 

 tude may still be considered to be so small that in comparison 

 with the magnitudes of terrestrial and cosmical masses it may 

 be treated as an infinitesimal quantity. Hence, since accord- 

 ing to the theory the attraction of each gravity-molecule is 

 independent of the attraction of all others, the process by 

 which the calculation of the attraction of masses will have to 

 be performed is in accordance with the usually received prin- 

 ciples. The factor m, relative to a given series of waves, 

 varies inversely as the distance from their origin, so that m 2 

 varies inversely as the square of the distance, which is the law 

 of gravity. It is particularly to be noticed that whereas the 

 expressions for atomic repulsion and molecular attraction in- 

 volve the magnitudes of the atoms, the force of gravity acce- 

 lerates equally atoms of different sizes, which accounts for all 

 bodies descending towards the earth with the same velocity 

 when acted upon by the earth's attraction. Lastly, it is to 

 be noticed that, on account of the large value of \ for gravity- 

 waves, they do not suffer sensible retardation or refraction in 



