06 Mr. H. M. Macdonald. The Bending of [May I'-', 



hence ^ is negative, and -^ diminishes as the absolute value of T,, 

 increases, therefore-^ 1 - is, when M + i ; , at most of an order 

 (/t +)-*. Since ^' l is always negative the series 8 4 vanishes, and 

 since ^ is always negative, and 3*t is always very small, the series 



S 8 vanishes. 



It remains to evaluate the series S 3 ana ^:- Wn 

 the exponent in the series S 3 becomes 



and the coefficient of v in this vanishes, if 



2 3* + ^ o,* 



and putting Mi + i- = : sin a, this becomes 



2a-7r + ^ = 0, 

 and the sum of the corresponding group of terms in the series S ; < is 



V aJ 



now 



</>, = .s cos a - Iniir + (/<i + i) a, 

 that is 



whence 



-^.s, + O^i + i) ^ -= ^ COS a 4- iir, 



and the sum of the group of terms, therefore, is 



that is, since, neglecting all but the terms of highest order, 



L / ~~2~ 



f, (ft*) ~4 5 \ / - -- z 2.: a sin "a. 

 4K- cos a V TT- sin a sin 



* This cqutttioii canuot be satislied, by the preceding, for a value >, of <, which 

 is not such that z (n+ ) is positive and of higher order than ^. 



