22 On the Constitution of Matter, 



whence it may be shewn that ^a,,, and consequently ^a^, vanishes 

 for all values of s except s ^ v, and 



cos V y sm u y 



h cos (2 n — 2 r + 1) u y ., ,> 



X, = ^ -. — ^ (1 — cos n^O 



sm u y 



J cos (2 « — 2 r + 1) ^\/ ■ 



= -. ; (1 cos IJit) 



sm vf/ '^ 



If the disturbance be supposed to cease, it may be shewn, as 

 before, that the subsequent motion is represented by 



b cos (2n — 2r + l)4; 

 X, — ^ — , cos IJ.t 



so that the system radiates the same kind of heat which it 

 absorbs. If ju, be greater than 2m, x^^ is small, even in comparison 

 with Ka, when n is large ; so that the system is incapable of 

 absorbing or transmitting any heat for which « is greater than 

 2m. 



Equation (8) gives 



I cos (2 « — 1) ,|/ 

 Xi = ■■ — -. (1 — cos u.t) 



So long as this coefficient is greater than a, the first of the n atoms 

 continues to be accelerated by the ether. When steady motion 

 is established, and the acceleration ceases, we have 



h cos (2 « — 1) \J/ 



sin 4/ 

 a cos (2 n — 2 r + 1) vp .-, n 



^'r = TR vn (1 — COS U,t) 



COS (2 71 1) l|/ ^ / 



^ a COS (2 r - 1) v^ ^-^ _ ^^^ ^^^ 



COS \J/ 



The principle which I have stated, if established, would afford 

 some hope of our being able to understand the facts of 

 " Spectrum Analysis." The fixed character of the bright lines 

 makes it impossible to conceive that the energy due to the 

 translation or rotation of the vapour molecules can have anything 

 to do with their production. They must be caused by the 

 internal vibrations of something of which the molecule is 

 composed. A complete knowledge of the arrangement 

 and mode of vibration of the atoms of a molecule, would involve 

 a complete knowledge of the corresponding bright lines. We 

 may imagine that the molecule of the very simple structure which 



