-282 Prof. L. Natanson on the Molecular Theory 



where X is the wave-length and h = 4:7rKfK, represents Lord 

 Rayleigh's "coefficient of transmission." Thus divesting 

 our equations of: perhaps unnecessary generality (for it is 

 doubtful in how far we may consider the calculation 

 applicable unless /c is small) we revert to Lord Rayleigh's 

 fundamental theorem. 



It may be well to observe, by way of caution, that (2) 

 and (3) are quite independent of the form assumed by the 

 term which appears in the numerator of the left-hand 

 member of (1). It must be borne in mind, in this connexion, 

 that we can adopt a view of the damping action (experienced 

 by the electron) which departs widely from that here contem- 

 plated without necessarily invalidating the general form of 

 (1) and (2). If we do so, the expression for the left-hand 

 member of (1) may not become substantially modified, 

 whereas (2) will in general he quite different. This con- 

 sideration is serviceable in illustrating the intimate connexion 

 which exists between Lord Rayleigh's equation and the 

 hypothesis from which we have started as to the nature of 

 the frictional effect generated during the vibration of the 

 electron. If we were to adopt, for instance, Helmholtz's 

 tentative supposition (beautifully exemplified in H. A. 

 Lorentz's theory of impacts) according to which the 

 vibrating electron experiences a resisting force in simple 

 proportion to its instantaneous velocity of motion, we should 

 have to put \ 2 , instead of A, 4 , in the denominator of the 

 right-hand member of (3) (and to modify besides the value 

 of the constant). 



§ 8. "We now proceed to consider the electric field in vacuo 

 where ~<0. This field consists of the effect of the incident 

 wave 



E£ ) =A (l) €* , <'- a *+*) (I) 



and the cumulative electric effect 



-27ranNA< 2) f °° dz^~ &*o+«(*-*b)+?] 



Jo 



— _ -^^ e *n(t + az+Q) (9\ 



- i(bc+l) € ' * ' W 



produced by negative secondary waves which are emitted, in 

 the negative direction of the axis of z, by every stratum of 

 the material medium, from r = to r = oo . We will assume 

 that (2) simply represents the reflected wave thrown back 



