Prof. (Jhallis on the Force of Gravity. 449 



a collection of atoms would be acted upon in tlie same manner 

 and degree as if it were alone ; and hence by reference to (1) it 

 will appear that the acceleration of all masses will be the same, 

 whatever be their composition or state of aggregatiori. 



5. If there be several series of waves propagated in different 

 directions, and having different values of m and \, the velocity 

 and condensation due to a single additional series may still be 

 expressed to the first order of small quantities by the function 



m sin f— i-c J, because to quantities of this order the hydro- 

 dynamical equations arc linear. But the complete expression 

 will be of the form 



mf (0 + m%{t) + mm%{t) + mm'%{t) + &c., 



because the modification which the new waves undergo by reason 

 of the existing condensations and velocities of the other waves, 

 must be expressed by terms of a higher order than the first, 

 which all vanish if vi = 0, and vanish severally if m' = 0, m" = 0, 

 &c. The functions /g, /j, &c. will all be periodic, because the 

 modifying action is periodic. Hence the effect of the additional 

 series in producing a permanent motion of translation of the 

 atom, being proportional to the non-periodic part of the square 

 of the above quantity, will vary as m'^+ terms of the fourth 

 order, and consequently, excluding terms of that order, will be 

 the same as if the other waves did not exist. Thus different 

 series of waves from different origins, acting simultaneously, will 

 each produce the same motion of translation of the atom as if it 

 acted separately. 



6. In the mathematical investigation of the pi'essure of a 

 series of waves upon an atom, it was assumed that the atom was 

 fixed. Actually it is subject to a vibratory motion by the 

 action of the waves under consideration, as well as of other 

 waves. The effect of this circumstance upon the motion of 

 translation of the atom will be taken into account by calculating 

 independently the pressure of the waves on the atom supposed 

 fixed, and that due to the motion of the atom in the fluid at rest. 

 Now, by the solution of Problem III., which gives the complete 

 value of the pressure at any point of a small sphere in motion, it 

 appears from the equation («), that there is no resulting dyna- 

 mical action between the sphere and the fluid depending on the 

 square of the velocity of the former, and that the effective 

 pressure on its surface is wholly periodic. On this account the 

 movement of translation of the atom is the same, whether or not 

 its vibratory motion be included in the investigation. 



The foregoing inferences seem to account sufficiently for the 

 known laws of gravity. It must, however, be borne in mind 

 Phil. Mag. S. 4. Vol. 1 8. No. 133. Dec. 1859. 2 G 



