140 



formulae of §§ 1 and 2 maj- still be used, provided we substitute for 



the coefficient g the value 



2w 

 f/, = — (14) 



T 



Here r denotes the average time between two succeeding collisions 

 of one and the same electron. The formula is based on the assump- 

 tion that each collision wholly destroys the original vibration. If 

 some part of it remained after an impact, we should have to take 

 for T a larger or smaller multiple of the time between two collisions. 

 We may also remark that the expression (14) has a more general 

 meaning. We may understand by t the time during which a vibration 

 can go on without being much disturbed or considerably damped, 

 and use the formula, whatever be the cause of the disturbance or 

 tiie damping. If there were e.g. a true frictional resistance the equation 

 for the free vibrations would be 



mr =—fr — gr , 

 and we should have 



a< 



cos \ / t. 



V in 4m' 



The time during which the amplitude decreases in the ratio e : i 

 would therefore be 



2m 



T = , 



which agrees with (14). Thus, the formula also applies to cases in 

 which there is a radiation resistance only; for g we have then to 

 substitute the value (11). 



Returning to the question of impacts, we may remark ihat in the 

 case of a gaseous medium, it would be natural to take for t in (14) 

 the mean time between two collisions of a molecule. There are, 

 however, cases where we find in this way a value much too high 

 for g, . 



Let us consider e.g. the propagation of yellow light (^/:= 6000 A. Ü.) 



through air of 0° and under a pressure of 76 cm, and compare the 



values of _(/, and g^. In calculating this latter coefficient we shall 



use the values liühluig foi' nitrogen. If u denoies the mean velocity 



of I lie molecules, / the mean length of path beiweeii two collisions, 



I 



we fiud, putting t = -, trom (14) and (11) 



n 



g^ 271" c ' Rl' 



