102 Mr. W. H. L. Russell on 



we obtain at once 



f w ot r e r sin rxdx f w « r sin rxdx_ a, r e r _ a. r 

 JO e 77 ^ — e— nX Jo e 71 '*— e _7nr 4 4 



Hence, if we put 



\_ f w c&» /9 sin x 



J o ( 1 - 2/9 cos a; + /a 2 ) (e^ - e~^) 



we have 000 fe)=J j^" J • "fy 



e 



so also 0(^+0(04-^-- 



e e 



and continuing the process 



P P 



1 p 1 6 . 1 6 2 



(111.) W=i • r ^---- + ---_ a . 



6 e 2 



In like manner we obtain 



Jo e«* 



sin (/> sin ^) 1 1 £ 1 £ 1 £ . 

 (112.) I -- L=- 6 P— - e e +- <? e s— - e e s + 



; 7r*_ c -7r* 4 2 2 2 



In a similar way also we may find the values of 



dx 



and 



■ 2a COS X + a?) (jF* + e"^) 

 JO e™ + (F™~ 



Let us now return for a moment to the equations 



p 3 + 2 3 + r2 + s 2 =«. 2jpg[ + 2gr + 2rs: 



2jpr 4- 2^ = 7. 2ps = 8. 



Then a + /3 + 7 + £ gives us 



p + q + r + s= V(* + (3 + 1 + 8), 



x — /3 + 7 — 8 gives us 



£> — q + r— s= V (at— /S + 7— 8) 7 



