498 Prof. Challis on the Dispersion of Light. 



no arbitrary constant being added, because we have to consider 

 no other motion than that which the waves originate, which, by 

 hypothesis, is wholly periodic. At the same time we have 



-=- = m sin — (bt + c) — V. 

 at A, 



Hence the last equation may be put under this form, 



5'+QT'=MQsin^(6/ + c), 



in which 



«=-3^( i -J)+ i -?^)- dM =K l -w) : 



Consequently by a second integration, after substituting cot ty 

 f 2irb 



iOr -ryr i /9 \ 



X{c * T'= - M sin yjr cos(^ {bt + c) + f) ■ 



Now the condition of transparency of the medium requires that 

 T', the relative velocity of the aether and the atom, should be 

 proportional, or very nearly so, to the velocity of the sether ; for 

 in that case the mean retardation of the waves is produced by 

 the atoms in motion nearly in the same manner as by the atoms 



fixed. This condition is fulfilled if ^r be very nearly equal to — , 



or if Q be a very large quantity, which is the case if (3 be very 

 small. We are thus led to conclude that the term containing ft 

 as a factor in the general value of W is insignificant when the 

 problem is to determine the dynamical effect of the sethereal 

 waves in producing vibrations of the atoms. I have elsewhere 

 shown (Phil. Mag. for November 1859, p. 332) that, in inquiring 

 whether the waves have the effect of producing permanent 

 motions of translation of the atoms, that term has to be taken 

 into account. 



Supposing, therefore, that ir=7y> the results obtained, after 



substituting for Q in the above value of M, are 



27T„. , % ., b 2 -e 2 



r = Msin^-(6/ + c), M=m 



X b*-e*+—(l--\ 



Let fx represent the ratio of the rate of propagation (tea) out of 

 the medium to the rate (b) within the medium. Then by the 

 reasoning I -have given in the article " On Double Refraction " 



