120 Mr. Morrow on Lateral Vibration of Bars of 



The correct value of the numerical constant in the 

 numerator is tt 2 , so that the ratio of the two values is 0*9996. 



The last expression for the displacement may be con- 

 veniently compared with the exact type. Thus it may be 

 written 



f '17066 , r -08433 d' 4 '00030 x 10 -00005 a 11 \ 



~ I -10386"? -10386 Z 4 -10386/ 10 -10386Z 11 J 



whilst the method indicated at the commencement of this 

 paper gives, by the insertion of the end conditions, 



. TTX 



y gc sm -p 



or 



;/-AVJ"l * > (?IW + « , (*W ^(x/iy^ _ 



Comparing the coefficients of «u 2 , # 4 , &c. inside the bracket 

 shows how the accuracy alters in passing from the lower to 

 the higher powers. For example, 



17086 ... K tt 2 1fl , K 



= 1*645. — = l*b4o. 



10386 6 



08433 



TT 4 



= -8120. -„ = -8117 



10386 |5 



0(1030 000289. £°= -000235. 



10386 ' (11 



5. Free- Free Bar. 



In the case in which both ends are free and no external 

 forces act on the bar, the conditions at each end are 



Assuming 



y = A + Bw + Car 2 + B^ + Ez i + SV + Qx% 

 the conditions at x = give 



A=y„ C = D = 0, 

 and those at x — l give 



B=-iGf, E = |GZ 2 , F=-3GZ. 



