222 



Mr. A. W. Flux on the 



, , u 2w /l# 5^ 2llu + mv /i0 ~ N .lu 2 + v 2 ^) 



, . . v 2 r ,„ ^ N 2mlu + mv, i , ~\ ■ x mu 2 + v 2 



>• («■) 



Also, from the figure, 



& = £i+i ~rcf> 2 , V2=Vi + h™r<l> 2 . 



(vii.) 



Now, if a plane be drawn through B, perpendicular to BA 

 and B / A / and cutting the latter in H, the vibration in the 

 two rays will be in the same phase at B and H. 



If, then, A denote the retardation of phase at F of the 

 vibration in FE, relative to that in FE', 



A = BC + CD+/iDE-EF-[ / uHB'+^B / E / -E / F / ] 



= 2r sin 2 1 T 1 - + V] + 9*d\± - II + (d-K) |1- VI - /^B'. 



2 \n n'j Uh n Y J J \jn n] 



\ 



(viii.) 



Now 



^BH / =/i[Z 1 (0 2 -w)4-m 1 (77 2 — v)] 



= l\ f ! — u + J — r<£ 2 | + w 1 1 77, — v + i — r<£ 2 J . 

 Inserting the values of f : and ^ in (iv.) and using in (viii.) 

 the values in (iii.) of— and — , and the values of <f> cos ->jr, 

 <f>siw*lr in (vi.), we deduce from (viii.) the following: — 

 a jl2 , o /s* s-nW 2 + v 2 . 2 rlu + mvl 2 /v ~\ 



M z + tf 



2*«-Si) : 



2 r7w + 



, n ,u 2 + v 2 



Correct to the third order, inclusive. 



This is the result obtained in equation (8) p. 211, 

 Band xii. of the Annalen der Physik. 



Section II. The same in the general case. 



Before proceeding to the use of the evaluation of the 

 retardation in Sect. I., we shall determine in a similar manner 



