Purser — Applicdfion^ of Bcssel'.s Finicfioiis (<> Pf/f/s/cs. 57 



first root of tho (Mpiation of condition maJJ^ma) - hJ^{m(i) ^ 0. We 

 have, tluMi, by wliat wu liavo proved above, 



J r(j){r)Ji{mr) dr, 



for m different from 0, 



Now, remembering that k = 2, we have 



•« 1 2 f 



r'^Jx{mr) = - — + — rJJ^ma) 



J u ^ 



2 1 



= —aJAma) — d^Jlma) = 0. 

 m 



We have, then, 

 for M different from 0, while to determine <•„ we have 



3 



I (r) dr. 



Let now, for <^ (r), be taken the supposed given distribution 

 of shear over terminal ; then we have to determine the 



A^^ mA,„hnl = ^ja^J^ {ma) ^ rc{> {r) Ji{})ir) dr. 

 In m = we have 



3 f* 



mAmJi {mr) = c^r = — rch (r) dr. 



^ Jo 



The corresponding terms in n, v will be 



Suppose, now, c^^ = 0. This will be the case when the total torque 

 vanishes over each terminal, i. e., the forces over tliis t(^rmiiial 

 constitute a system in rigid equilibrium. 



In this case the stresses and strains dejjend for eacli Icrm in j/i, 



K.I. A. PUOC, VOL. XXVI., SEC. A.] iv 



