526 Dr. J. W. Nicholson on the Bending of 



If 



n + ^=kr cosh ^y—z^ cosh lf . . . (30) 



so that 



cosh/3 1 =-cosh/3, 



and /3 X is never greater than /3, 



tan^ = e 2 S 



where 



t nr — — \ log 2 + ^ (sinh j3 x — A cosh ft) . 

 Then 



tan (0„-<£ nr ) = e 2 ^— c 2<Br , 



since t» r is also very large and negative. 



For a large value of n this is evanescent, and 



The typical term of yp therefore depends on 



»(IU. f )S(l+«^. 

 But l + e 2,x » = 2/(l-itan X „] 



and R B = 2T„cosh2<„ 



s=T.e-2<.. 



under the present circumstances 



3 



^=(T„'-1)«~ 2 *» 



/ cosh 2 ^ \ a . 



_ \ sinh 3 /3 i j e 



= — £~~ n to the same order. 



The typical term therefore contains 



z cosh /3(TnT nr )* e-**-*" d? n 

 l + L e - 2t " dp ' 



which is not greater than 



£ cosh ft cosech j3 cosech /Si-r-^ * 



