THE PRESSURE OF A CYLINDRICAL AXIS ON ITS BEARINGS. 
557 
But by equation ( 1 .), substituting ~6 and — for 6 and 6^, 
M /d&y_ 2ffh{cosd-cos 6^) + {k^ + P)m^ 
\dt ) k^ + — 2ah cos fl + v v 
2 
2«A(cos 9— cos 9,) + + 
-{9\_ ‘9 
\aj Z:^ + G^— 2aAcos 9 + A® 
— 2ah cos 9, + {k’^-{-r ^)~ — (k^ + a^ + h^—2ah cos 9) 
9 
\a) k‘^ + a^— 2ah cos, ’ 
(«) + h^- 2ah cos 9 ~ ^ J 
Observing that a^+A^— 2 aA cos ^i=P. 
Differentiating this equation and dividing by ^^^5 
■ ^ (A|2 + a2 + /j2_2fl4cos9f 
Substituting these values of M and N in equation (30.), and reducing, 
„ WAsin9J {k^-\-P){k^ + h^ — ah cos ^){g + a(x>^)'\ \ 
® 1 g[li^ + a^ + h^—2ah cos J v v 
WAf/fl! \ (F + /^)(_ 5 f + to^){fl4cos®9— (F + e^ + A^) cos9 + «A} I 
^(F + «^ + A2-2«Acos9)^ • (3^-) 
The rotation of a body about a cylindrical axis of small diameter. 
Assuming a=0 in equations (31.), (33.), and Z)i=0, we have 
A/r 2^4(cos9-I) , 2 gh sin^ 
‘^= +■" 
Therefore, by equation (30.), 
WAro/«(2— 3 cos9) ol . ^ . X 
('* 0 .) 
■^7 tur 1 WAro/«(3cos^9 — 2cos9 — 1) , , . . 
Y=W+— ^+<v’cos«| (41.) 
The last equation may be placed under the form 
Y=W+pq:;^ 2 ||cos^+ 3 (-^^ - Vj “V ~3f 
If be numerically less than unity, whether it be positive or nega- 
tive, there will be some value of 6 between 0 and t for which this expression will be 
equalled, with an opposite sign, by cos 6, and for which the first term under the 
4 c 
MDCCCLI. 
