48 

 The first term or — „ '" , " contains no term of the form 



B cos {» — tt) 



The second term or — ^j^rjr* ^^^ ^^ ' — 2"*") gives a term 



r— = ■ COS (i' — v) ( I ) 



The third term gives a term 



5nr-eA /■ n SnfAe 



hw^ «•* 



V — t) =: cos \v — t) (_2} 





»,/5 



a'lt 



-J- sm {2v — 2 mt) — 5—— . -r— sm (2 »— 2mc) 



4-' 6 1/ COS (2v—2mii) 



The first and third terms do not afford any term of the required 

 form B cos (i- — tt) 



•^^t— 2^^- -^ ^'" (2;-— 2mO gives 



I (1 — 2m) ^ e cos (►—3-) (3) 



3, Tlie variation of 



= (substituting - instead oi ~ -{■ t()y^- "„T„s" ^'' ^in {2v—2u) 



■^fl&d.y. cos (2.-20 -(^ + a«)/£.^-- (2-20 

 The first two terms give a term 



_ ^ (1 + m) ^ e cos (»— 5r) (4) 



The third term gives a term 



3m^ (1— 2m)^— 1 ^ x -e, 



— — . ^-7, ~- cos (»— t) (5) 



o 4 (1 — m) ^ ^ ^ ' 



