170 Mr. Tovey on the Elliptical Polarisation 



the first and second of the equations (4.) give, by taking the 



values ofsa? s's* ^o"^ (^^'^ 



„3 + 5 _ f^ (o- cos 6 + 0-' sin i) = , 

 „a 4- s 4- P2 (o" cos 6 — 0-' sin 6) = , 



, 0- cos 6 — tr' sin i _ (I*-) 



„= + » -0. 



0- cos & + (T^ sin i 



„2 + s' + = • 



because the sign of the sine of an arc remains the same while 

 that of the cosine changes. 



For the sake of abridgement put 



<!>(»•) +^^(r)A/ = p, 



rl/ (r) A i/ A 3 = <? , 

 w :S .2>A.r = A, mS.p'i^x = A', 



v.pAx^ = A;, ^X.p'^x^ = A/, 



JL v._pAa:'=A2, -^^g-JS-.l^'Ao^^^ A2', 



_E_r.pA^^ = A3, ^^.p'A.v* = A3', 



2.3.4.. ^•"^•* 



&c. 



7?i 5* . ? A x = B , 



&c. (16.) 



m 



S.qAx" = Bp 

 2 ^ 



^.gAj:^ = B2, 



7» 



273 



&c 



Then, since 



sin A:Aa- - /fA.r ^j- + &c., 



FA^2 ^1^4 ^ 

 cos A;Aa; =1 ^ + 2.3.4 



vers /cAa: = 1- cos/fAx, 



the formula (3.) and (10.) give 



s = - A^F + AgF-Scc. 



s, = A/. -A,^^ +8cc. (17.) 



si ^A'Jc- A,' P + &c. 

 j ^B,r--B3/c4 + &c. 

 a' ^Bk -B2F + &c. 



