CONTINUOUS CALCULATING MACHINES. 
399 
This may be resolved into 
P(1 — cot«) 
s=- 
P(1 — cot«) 
(2.) The couple 
cos y= direct pressure on bearings 
sin y= force tending to twist the plane of rotation. 
= P.op + Q.og' 
= P (op-\-oq cot a) 
= Pft(sin a+ cot a cos a) 
sin 2 a 4- cos 3 gO 
= PR 
PR 
Sill « 
Sill U 
This acts on the rim of the rollers, and if they were four in number would produce 
the effect upon each rim 
„ PR 1 
To— . X™ 
sin a. 2R 
P 
2 sin a. 
Summing, now, the total twist 
T i + T 2 =f{g^+( 1 -cot a) sin y | 
Let cl =■ half the length of roller axis—that is distance between centres of pressure 
on either side of roller. 
Then the result of this twist is 
Direct pressure on pivot or collar 
+(1— cot a) sin yl 
2 j_sm a x J 
Pressure on bearing 
Finally, since 
and 
P C 1 
--b(l— cot a) sin y 
2 [ sin a v ' ' 
, T 277-R cos y R 
JN = —t - = - cos y 
lirr r ' 
w,=? 
{(1 — cot a) cos y] -|- 
p r i 
W 2 =Ul ~— + (1 — cot a) sin y 
2 [sm a x / / 
L=2^N sin 4,(y? l+i ^L 
{--1-(l — cot a) sin y\~. 
[ sm a v ' ' \ d 
— 2wpN sin (j)- ( {(1— cot a) cosy] + - + (l — cot a) sin y 
4- 
3 cos p\ 
( - -—1-(1 — cot a) sin y j j 
ysm a ) \ 
3 F 2 
