172 
MR. L. N. G. FILON ON' THE ELASTIC EQUILIBRIUM OF 
rzjq. 
2 '. 
i 
r = 0. 
?• = {-2) a. 
/• = (-4) a. 
r {■Q)a. 
r = c. 1 
■ 
0 . . . . 
•00000 
•00000 
•00000 
•00000 
•00000 
f /10 . . . 
•00000 
•02148 
•05127 
•08883 
• 00000 
2 Q10 . . . 
•00000 
•03347 
•08205 
•15547 
•00000 
.3r/10 . . . 
•00000 
•03262 
•08123 
•16519 
•00000 
1 4c/10 . . . 
•00000 
•02.571 
•06262 
•13159 
•95493 
.5c/10 . . . 
•00000 
•02495 
•05701 
•11897 
• 95493 
6 c/10 . . . 
•00000 
•03718 
•08085 
•14879 
•95493 ; 
7r/10 . . . 
•00000 
•05812 
•12259 
• 20528 
•00000 
8 c/10 . . . 
•00000 
•07753 
• 15596 
•23109 
•00000 
9c/10 . . . 
•00000 
•08891 
•16969 
•21918 
•00000 
c ... . 
•00000 
•09231 
•17214 
•20992 
•00000 
Til the aliove tables it is to he remembered that rr, zz, (f)(f) are all even functions 
of s; rz is an odd function of 2 '. At the points r = a, z = ± ^ 2:2 and </)(^ are 
l)otli = + CO , while at the jioints )• = a, z = i zz and (fxf) are both = — co . 
Tlie displacements u and iv have been compared with the corresponding total 
elongation and lateral contraction u’,) '’h same cylinder under a uniform 
tension Q over its plane ends. 
Table of Displacements. 
Z, 
r = 0. 
r = (• 4) a. 
r = (•4)ff. 
r = (• 6) a. 
r = a 
0 ... . 
•00000 
•00000 
•00000 
•00000 
•00000 
f /10 . . . 
•05693 
•06005 
•06988 
•08685 
•10972 
2 c/10 . . . 
•11132 
•11693 
•13489 
•16752 
•22900 
3c/10 . . . 
•16235 
•16949 
•19259 
•23676 
• 38253 
4^10 . . . 
•21132 
•21915 
•24461 
•29489 
•592.38 
5c/10 . . . 
•26013 
•26829 
•29467 
•34706 
•67152 
6 c/10 . . . 
•30896 
•31741 
•34425 
•39538 
•68809 
7c/10 . . . 
•35493 
•36360 
•39027 
•43724 
•57421 
Sc/lO . . . 
•39299 
•40162 
•42700 
•46684 
•51756 
9r/10 . . . 
•41809 
•42646 
•45002 
•48254 
•49745 
c ... . 
•42684 
• 43506 
•45774 
•48725 
•49196 
