448 Prof. Challis on the Force of Gravity. 



but by the same principles m varies inversely as the distance 

 from the origin of the waves. Hence tlie acceleration varies 

 inversely as the sijuare of the distance. 



Also if there be several series of waves propagated from the 

 same centre, having different values of m and A,, the condensa- 

 tion and velocity resulting from them at a given point are 

 expressed to the first order of small quantities by a function of 

 the form 



m sm 



f-^ + cj + m' sm f — 7-+c'j + &c. 



But, from what has been shown, the pressure which gives to an 

 atom a permanent motion of translation, depends on the non- 

 periodic part of the square of this expression, and therefore 

 varies as Am^ + B»/^ + &c. Hence, as each of the quantities m, 

 m', &c. varies inversely as the distance from the centre, it follows 

 that the acceleration of an atom produced by a compound series of 

 waves emanating from a centre, varies inversely as the square of 

 the distance from the centre, 



3. By the mathematical theory it is shown that there is no sen- 

 sible dynamical action between the medium and the atom if 

 the latter move uniformly, the pressures on opposite hemi- 

 spheres just counteracting each other. Also if the motion be 

 variable, and the variation be extremely slow compared to that 

 of the vibratory motion of the particles of the medium, no 

 sensible action of the medium on the atom results from this 

 motion, because such action could only be expressed by means 

 of a periodic function in which A, is immensely large compared 

 to the \ of the waves. Consequently the acceleration of the 

 atom is independent of the acquired velocity. 



4. In waves for which X is very small, the dynamical action 



depending on the first power of m may be very great, because the 



principal term of the first order in the value of a^ (s — a), viz. 



c dW 



-g . —-J- cos 6, contains \ in the denominator. On this account, 



since action and reaction must be equal, the vibratory motion of 

 the waves of light in transparent substances may be greatly im- 

 peded by the mean counteraction of the inertia of the atoms, and 

 the rate of their propagation be consequently diminished. But 

 as the above expression for waves 1 foot in breadth, m being 

 given, has only ^-o-oVott^^i P^^'^ <^f the value it has for waves 

 of light, it is quite possible that that expression may be extremely 

 small for waves having much larger values of m and \ than those 

 of light-undulations. In that case they would be transmitted 

 through solid bodies without sensible alteration of character, or 

 retardation of the rate of propagation. Thus each individual of 



