78 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OP R. 



R = * terms independent of the quantities h 



- f { T *'.« + ^' *=°' ' + *''^ *'°' ^ '■■'■' ^"^ } 



- ^ { T *3.o + *3,i cos r + 43,2 cos 2 r +, &c. } 



+ ^Vi - ^) cos (r + 2 >,,) + 2^'cos (r - 2 , + 2 »,,) 



+ y^.(,_^_^')cos(,-,)-^'(i-^-^>oB (, + >/)} 



- H^ { ¥ *5,o + *5,i COS r + «5,2 COS 2 r +, &c. } 



o "12 



|/^+^)cosr-^cos(r-2;?)-^cos(r + 2?7^)-yy,cos(;?-?j,)+7yyCOs(^ + ^/) j 



= |^ + Z^V51^J^l+cos2r} +{-^-5:^'}{cos(2r-2,)+cos2,} 



+ I _ y^' _ ^ j {cos (2 r + 2 pjj + cos 2 ;? J 



+ I - "^ - ^'j {cos (r + ?j -»?,) + cos (r -;? + ^,)} 



^ + ^ j {cos (r + »j 4- ^;) 4- cos (r - ;? - ;j^)} 

 + ^ { 1 + cos (2 r - 2 ;?) } + ^' (cos (2 T - 2 ;j + 2 ;j^) + cos (2 pj - 2 ;? j } 

 H- ^ {cos (r - ;j - ^^) + cos (t - 3 ?7 + ;?j} 



+ ^ {cos (r - ;? + ;?>+ cos (r - 3 ;?-;?,)}+ ^ {1 + cos (2 r - 2 ;7^)} 

 + ^ {cos (r - »j + ;?^) + cos (r ~ ^ + 3 ;j,n + ^ { 1 + cos (2 ;j - 2 p? j } 



3 2 2 2 



-'^{cos2;j4-cos2;7,} + ^{1 + cos (2;j + 2 ??^)}. 



* It is useless to consider these terms, because as 22 contains no term multiplied by — , if the other part is 



«/- 



found to contain any term multiplied by — it must be neglected, that is to say, got rid of by adding a simi- 

 lar term independent of the quantities h, and with a contrary sign. 



