844 Mr. A. Stephenson on the 



therefore not really consistent with the other assumptions 

 made. In reality of course the atoms do move to some 

 extent and the electrons do influence each other, so that 

 Maxwell's law no doubt really holds good, but the absorption 

 and emission are not exactly the same as those calculated. 

 It seems likely that the absorption and emission calculated 

 should be such as to make E\ = 167raT/3\ 4 exactly. The varia- 

 tion from this obtained above when Maxwell's law is assumed 

 is no doubt due to the neglect of the motion of the atoms and 

 the mutual influence of the electrons. 



The value E\ = 167raT/3X 4 is obtained exactly when the 

 assumptions made and their consequences are strictly adhered 

 to throughout, that is when all the velocities are taken to be 

 equal. If Maxwell's law is assumed, then the mutual en- 

 counters between the electrons should also be allowed for to 

 obtain an exact result. 



The equation E\ = l67raT/3\ 4 has been very fully discussed 

 by Jeans (loc. cz7.), together with reasons why it fails in 

 practice for short waves. It now seems very probable that 

 the electron theory in its present form cannot account for 

 the observed values of E\. The observed values fall below 

 those calculated for wave-lengths which are very large com- 

 pared with those of Rontgen rays, which latter are still long 

 enough to be strongly absorbed by dense matter. Short 

 ultra-violet light is even strongly absorbed by air. 



XCII. On the Intensity of Periodic Fields of Force. 

 By Andrew Stephenson*. 



1. npHE nature of the motion of a system about a position 

 J- of equilibrium in a periodic field of force depends 

 upon the intensity of the field. In general, there is cumula- 

 tive effect within each of a series of ranges of intensity, the 

 period of the motion in the odd ranges being twice that of 

 the field, and in the even ranges equal. 



If the field is an even function of the time, the equation of 

 motion may be written 



x + 2un 2 2 OLr cos rn t . # = 0, 







where a. is regarded as a parameter measuring the intensity. 

 * Communicated by the Author. 



