14 On the Constitution of Matter, 



The nature of the vibrations will be the same, and the term 



, denoting the general motion of translation of the system, 



be avoided, by supposing tbe initial conditions to be 



^ (r) = - 2 sin (2 r — 1) 5 7 , fi (r) = 



then £c, = - 2 sin (2 r — 1) s y cos /x, ^ 



s= 1 



Since 2 ni: = y, it is evident that 



so that the motion is symmetrical about the middle point. If « be 

 an odd number the central atom will remain at rest. These con- 

 clusions hold for the higher approximations as well as for the 

 first. 



The whole energy is and the vibratory energy, which 



alone is represented in the above value of x^, is m^a^. The 



2 n 



heat developed as temperature for the r*^ atom is 



— — 2 sm- s y sin- (2 r — 1) sy = ~~i 



n^ ' 4 w* 



and is the same for all, the mass of an atom being here supposed 

 to be unity. 



Subject to no external disturbance whatever, any number of 

 atoms might vibrate together in the manner indicated, but this is 

 a condition which can never exist, for the atoms of a molecule of 

 vapour, even during the interval between its encounters, are 

 subject to acceleration or retardation, as the ease may be, from 

 the action of the ether in which they must be supposed to be 

 immersed. A notion may be formed of the effect of an external 

 disturbance upon such a system as that under consideration, by 

 supposing an additional atom at the beginning of the series, con- 

 strained to move according to a particular law. Let cCo be the 

 displacement of this atom, and suppose 

 Xo = a cos[j!,t 

 a being small compared with h. The equations of motion are 

 q Xi = x„ + x-2 



q Xr=' Xr-l + a-r+l 

 (q — 1) X^ =iCn-l 



