414 PROFESSOR KELLAND ON FRESNEL'S FORMULiE FOR THE 



Again 2 ^0 r' + tjL §^2^ ^^^'^_^^ 



= Q. ((3/ - /3) - H T cos 0' (cos ^(p' -2sin'(p')+-^-j-cos (p' (cos 20' - 2 sin *0') 



and 2^'^^^y'(a;-a)=2^ 5a;'^y5a' 



= — -^7- 1 cos 9 sm '&)' ^ p- sm V cos -f -2; -7-^ 



2 ^ ^ e, ax ^ f d-V 



Avhich being added to the previous term gives 



QX/3/-^)-9 T COS (p' + —-^- cos 0' + -7^ 



<?T, 



2 ^ e, dx f ^y 



<P^ (? 



Hence -^ = -^ (I + R cos + T cos 0') 



+ Q.(/3,-/3)4--cos0 (_ + _) +-'cos0 ^ 



F d\, ¥, dT, 



f d7j f dy 



<^i8, c2 



Similarly •^' = - 2 (I + R cos + T cos 0') 



+ Q(8_^^) + _cos0(^ + -) +-cos0'_ 



^ fdy"" f dy 

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



and ••• ^=/3. 



also ^ + ^--^^(^+^'> 



2M ,/^I ^R\ 2M, .,d1 



+ COS0(— + -Z-) + ^^^^ -JZ 



e \dx ax J e, ax 



2Y_d\ 2_¥,dT, 

 f dy f dy 



