ACCORDING TO THE UNDULATORY THEORY. ^95 



the m surfaces. All members which are multiplied Avitli r\ or a still 

 higher poAver of »•, must therefore become so small, in comparison with 

 those multiplied with r-, that they may be neglected. Thus the inten- 

 sities of the transmitted rays become 



a(\ — r)'" for the retardation 



a (I -r)'" .r' (/H-1) 2b 



a{\-ry .r'- {m-2){l-ry- ^b 



a(\-ry" .t"- {m-S){\-ry 6b 



a(l _^)"\r2 (m-4.)(l-r)« Sb 



a{\ -ry'\r"-{m-n) (\-rf^"-^^ 2nb, 



consequently we have 



M = a(l— r) sin2 7r//_— I 



u, = a{\ -rf\"-(>n- 1) ^51x12^ ft- -^'\cos27r — 



— cos 2 IT I < — — 1 sm 2 TT — 



«2 = rt (1 - 7-)"' r^ (m - 2) ["sin 2 tt (^ < - — ") cos 2 . 2 tt — 



- cos 2 TT (^ < - -^^ sin 2 . 2 TT —1 (I - r)"- 



„ =a(l-ry"r«(m-w) fsin 2 tt /^ < - ^"j cos w . 2 tt — 



— cos 2 TT I « — — \ smn . 2 n- — I (1 ~ V • 



If we reckon from this the resultants of all the retarded systems of 

 waves of light, i. e. all those just mentioned, with the exception of the 

 first, U', or the velocity which it represents, becomes 



U' = a (1 - rf r"- fsm2^ ( * ~ t) ["(»»- O cos 2 tt — 

 + (wi - 2) (1 - r)"- cos 2 . 2 TT — 



+ ,.{m-n)(l-r)^" ^^cos w . 2 ttI^I 

 — cos 2ir It — —\ (»i — 1) sin 2 v 



2b 

 \ 



