414 PROFESSOR KELLAND ON FRESNEL'S FORMULAE FOR THE 



Again 2 ((p >•' + ^ §)A ((S; _ /3) 



c^ M (IT 



= Q, (ft - /3) - ;^ T cos (p' (cos '(p'-2sm-(p')+—^—- cos ^' (cos =0' - 2 sin »0') 



and 



2'^§a/8f(c.;-a) = 2^ 8 x' 8 ,/ d a' 



= — fT- 1 cos (p sin '(B 4 J— sin ^w cos ffl + -j -y— 



J ' ' e, ax ^ f "iV 



Avbich being added to the previous term gives 



Hence 



Similarly 



f^ro C-. «V A., M,dT ,, F,dT, 

 Q, (ft - i3) - o T cos 0' + — -5— cos 0' + -^ -3-2 



'Tfi = ~o (I + R cos + T cos <p') 



^ o ^ M . /dl dR\ M, ,,dT 

 + QXft-/3) + yCos</, (^ + ^) +- cos.^ ^ 



F^ F, dT, 

 f dy f dy 



-^=--\ (l + K cos + T cos 0') 

 + Q(S-A) + -cos<^(^ + ^) +-cos0'_ 



F^, F,<rr, 



^ fdy^f dy 



10. By the same mode which we exhibited for a and a, we can shew that 



d^^ #ft_ 



and 

 also 



••• ^=ft 



2M ,/fZI (^R\ 2M, ,,c;T 



+ C0S(/) (-^- + -5— ) + COS0 -5— 



e ^ \dx dx] e, dx 



2Ffn, 2F,f^T, 

 f dy f dy 



