16 On the Constitution of Matter, 



If « be considerable, but \|/ so small that (2 « +1) rf/ is not 

 nearly equal to 1, sin 4' will be small, and the relative disturbance 



small compared with a for all values of r. This shews that a 

 slow external disturbance, corresponding to a small value of /x,. 

 will cause a general oscillatory motion of the whole system, but 

 very little internal relative vibration of the atoms. 



If (2 w -^ 1) 4/ be equal to 1, or to any odd multiple of it, 



x^ — a:r_i becomes infinite, indicating the well known change in 

 the form of the solution from A cos ftt to At sin ^ut. I will 

 defer the consideration of this particular case, and suppose 



(^n + 1) \I/ to be nearly equal to some odd multiple of Z, so 



Ji 

 that cos {2n + 1) ^1/ is small, but a so small that the character 

 of the vibrations is maintained. Since 



Sin (2 ?i — 2 r + 2) 4/ = cos (2 r —1) r\> 

 nearly, the relative displacement is a maximum and large com- 

 pared with a for such values of j' as make (2.r — 1) vf/ a multiple 

 of TT or most nearly so ; and this of course occurs at regular 

 intervals, li p be the whole number most nearly satisfying the 

 condition 2 ^ vp =7r, the atoms are arranged in groups of p each, 

 where jj is a number depending upon the wave length of the dis- 

 turbance, and the nature of the system, and not at all upon a, or 

 the intensity of the disturbance. Suppose now a, or the 

 temperature to increase gradually ; the groups remain the same, 

 but become more and more isolated. Each group acquires an 

 oscillatory motion as a whole in addition to the vibratory motion 

 of its atoms amongst themselves ; and the time of this oscillation 

 corresponds nearly to the fundamental or lowest note of a group 

 of ^ atoms vibrating without restraint, for in that case 



ju-i = 2 w sin — = 2 w sin \J/ = a nearly 



The disturbance a cos fjit representing the prevailing heat, fu, and 

 therefore \[/ also, for atoms of a given kind, has a certain very 

 limited range of value. We may suppose then that there is some 



one particular value of -^ making — = ^; an integer ; and that 



2\[/ 



particular wave length corresponds exactly to the fundamental 

 note of the group, or molecule, of p atoms. 



If we suppose now that a increases until the maximum value of 

 the relative dasplacement exceeds a certain quantity, the severance 

 becomes complete. This does not necessarily take place at aU 



