196 
MR. L. N. G. FILON OX THE ELASTIC EQUILIBRIUM OF 
rz-= /xE 
■ [l(-y + + rh - |(2y + l)i 
+ (2r + i)-^s-^, i;w™ 7 
■ic-a-y ^ - 1 )" 
77 - 7 n- 
2r+ l)a+ ;;(8y-f 1) r,-(8y + 4)I, 
^ • ( 104 ), 
7a^(Io— If)- Ir 
L . 
Sill 
mrz 
where, putting in for f. r/, h in (98) their values, 
(105). 
. § 17. Numerical Example. 
Let us now consider a concrete example. Take a cylinder whose diameter is 
nearly equal to its length. This corresponds about to the dimensions used in practice 
for test pieces under pressure. We will take ira/c = 3 in order to simplify the 
calculation of the I-functions. 
Further, we shall assume uniconstant isotropy, so that y = 2/3. 
We then find : 
liy 7^ - ^^(-10695), 
ih = - 
u^ = 
= -(’070057), 1 
aq = — - (*090552), 
ib\ — — -x(l'd6046), 
fxa- 
u 
h = ^.(l’01193), , 
E= ^,(1*13842), 
/xer ' 
E' = - -^(1*01193), 
/xfr ' ' 
F = 
- -,(2*52982), ; 
L) 7= (1*63584) , 
/xc- 
D' = 
'‘,(ri0970), 
fj,a~ ' 
^ = 2*036847, 
j 
/’= — rU (*451889), 
r/ = (*093947) , 
h = ■ 
-(d(*455329) ! 
( 106 ), 
