of Attractive and Repulsive Forces. 189 



group ; and it might be supposed that the attractive action 

 would be proportionately increased, so as to be capable of pro- 

 ducing sensible effects at distances from the boundaries of 

 bodies much beyond the sphere of activity of capillary attrac- 

 tion. This, as matter of experience, is not the case ; and the 

 fact that such effects are uot perceived is theoretically accounted 

 for as follows : — 



24. It is to be considered, first, that the motions resulting 

 from the composition of all the minor waves must consist of 

 harmonic vibrations, because the opposite motions of any 

 particle towards and from the centre of the waves must be 

 equal — and, again, that the value of X for the breadth of these 

 composite waves is greater as the number of the components, 

 and consequently the intensity of the compound wave, is 

 greater. Although as respects the getherial vibrations con- 

 cerned in atomic repulsion and molecular attraction the ex- 

 cursus of an setherial particle might not exceed, and might 

 even be much less than, the diameter of the atom on which 

 they are incident, in the case of the much larger vibrations 

 compounded as above stated the excursus of the particle must 

 be supposed very much to exceed that diameter. In fact the 

 total motion would in this case approximate to that of a stream 

 in the direction of the propagation w T hile the condensed half 

 of the wave is passing the fixed sphere, and of a stream in the 

 contrary direction while the rarefied half is passing. Now it 

 is known that if a uniform steady stream be incident on a 

 fixed sphere, the consequent condensation at the surface of 

 the sphere will be symmetrical with respect to a transverse 

 plane passing through its centre, and that thus there will be 

 no accelerative action on the sphere. Accordingly it may be 

 supposed that the two streams above mentioned produce 

 separately little effect, and that, as they flow in opposite direc- 

 tions, the residual effect is extremely small. This will account 

 for the molecular attraction of a very large group of atoms 

 not being proportionate to the magnitude of the group. 



25. There is, however, a residual effect, which, in fact, is 

 the attraction of gravity r , the origin and amount of which may 

 be ascertained by reference to Poisson's well known solution 

 of the problem of the resistance of the air to a ball-pendulum. 

 According to that solution the ball at a given instant is com- 

 municating to the air in the direction opposite to that of its 

 motion a momentum equal to a mass of air of its own size 

 multiplied by its velocity at that instant. By analogous 

 reasoning it is proved, in the case of waves incident on a fixed 

 sphere, that there is communicated to the fluid by the reaction 

 of the sphere at a given instant, in the direction of the motion 



