422 Mr. J. H. Jeans on the 



judgment the view ultimately arrived at, together with the 

 account of the phenomena of matter to which it leads, in so 

 far as it has been found possible to examine these phenomena. 

 The theory will not, it is hoped, be judged as an attempt 

 to attain to ultimate truth. At most the author hopes that 

 by attempting a definite and consistent hypothetical interpre- 

 tation of certain phenomena, some kind of clue may be 

 suggested as to the real significance of these phenomena, and 

 perhaps something of the nature of a foreshadowing of the 

 real truth arrived at. 



Analytical Expression for the Radiation from a Gas. 



§ 2. It will be best to begin by a consideration of the 

 general question of spectroscopy. 



We shall suppose the radiation emitted by a gas to be the 

 aggregate of contributions from a great number of similar 

 vibrators. Each of these vibrators will be supposed to be 

 capable of vibrating with certain definite frequencies of 

 vibration, and the disturbances of the sether which are set up 

 by these vibrations constitute the radiation. 



Let us, in the first place, consider only the radiation pro- 

 pagated along a certain line of sight, say the axis of x, and 

 polarized in a certain plane, say that of xy. If the vibrator 

 were at rest in space, this radiation might be represented, so 

 long as the vibrator was undisturbed by collisions, by 



A cos (pt + e), 



in which A and e would be constants, which would, in general, 

 depend upon the orientation of the vibrator. 



If, however, the vibrator is rotating with an angular 

 velocity w about some axis fixed in space, the above expression 

 will no longer represent the radiation in question. This 

 radiation may, however, be represented by 



A cos pt + B sin pt, 



where A, B are themselves periodic functions of the time, of 

 period 27r/w. 



If we expand A and B in Fourier-series, the foregoing ex- 

 pression can be at once expressed as a series of simply 

 harmonic terms of frequencies 



Pi Pi w ? p + 2w, . . . &c. 



Suppose, to take a particular case, that the vibrator is an 

 electrical doublet of strength A cos pt, rotating about a fixed 

 axis with angular velocity w, the axis of the doublet always 



