410 Lord Rayleigh on Interference Bands. 



harmonic occur, fcut not to the same extent. When n is 

 nearly equal to 2m, the terms rise to great relative magnitude. 

 The most important are thus 



cos -^ ( 1 ± 5— ), cos -^- ( 1 + Tz- \ &c. ; 



/ \ 2m J I \ — 2m J 



and it is especially to be remarked that what might at first 

 sight be regarded as the principal, if not the solitary, wave- 

 length, viz. I, does not occur at all. 



Besides communication of energy to the ether, and dis- 

 turbance during encounters with neighbours, the motion of 

 the molecule itself has to be considered as hostile to homo- 

 geneity of radiation. The effect, according to Doppler's 

 principle, of motion in the line of sight was calculated by me 

 on a former occasion and is fully regarded in your paper. 

 But there is another, and perhaps more important, consequence 

 of molecular motion, which does not appear to have been 

 remarked. Besides the motion of translation there is the 

 motion of rotation to be reckoned with. The effect of the 

 latter will depend upon the law of radiation in various 

 directions from a stationary molecule. As to this we do not 

 know much, but enough to exclude the case of radiation alike 

 in all directions, as from an ideal source of sound. Such a 

 symmetry is indeed inconsistent with the law of transverse 

 vibrations. The simplest supposition is that the radiation is 

 like that generated in an elastic solid, at one point of which 

 there acts a periodic force in a given direction. In this case 

 the amplitude in any direction varies as the sine of the angle 

 between the ray and the force, and the direction of (trans- 

 verse) vibration lies in the plane containing these two lines. 

 A complete investigation of the radiation from such molecules 

 vibrating and rotating about all possible axes would be rather 

 complicated, but from one or two particular cases it is easy to 

 recognize the general character of the effect produced. 

 Suppose, for example, that the axis of rotation is perpen- 

 dicular to the axis of vibration, and consider the radiation in 

 a direction perpendicular to the former axis. If co be the 

 angular velocity, the amplitude varies as cosa>£, and the 

 vibration may be represented by 



2 cos cot . cos ht = cos (n -f co) t + cos (n — co) t. 



The spectrum would thus show a double line, whose compo- 

 nents are separated by a distance proportional to co. 



Again, if the ray be parallel to the axis of rotation, the 

 amplitude is indeed constant in magnitude, but its direction 



