424 APPLIED MECHANICS = 
projects from the crank arm. S and T are the centrifugal forces of the 
crank arms and the parts of the crank pins which they contain. “7 
Fra. 693. ' : 
Forces P, and P,, in the planes of the circles 1 and 2 respectively, 
which will balance P, are determined from the equations 
P(e — 2a) = P(c —a), and P,(¢ — 2a) = Pa. 
Forces Q, and Q,, in the planes of the circles 1 and 2 respectively, . 
which will balance Q, are determined from the equations 
Q,(¢ — 2a) = Qa, and Q,(c — 2a) = Q(e — a). 
Forces S, and §,, in the planes of the circles 1 and 2 respectively, 
which will balance S, are determined from the equations 
S,(c — 2a) =S(c - 2a +d), and 8,(c - 2a) =Sd. 
Forces T, and T,, in the planes of the circles 1 and 2 respectively, 
which will balance Tr are determined from the equations 
T,(c — 2a) =Td, and T,(c — 2a) =T(c- 2a4+d). ; 
P, and §,, P, and 8,, Q, and T,, Q, and T,, act respectively in the . 
same straight lines and in the same directions, as shown. F 
Ry= J(Py +81 + (Qi + Ty, and R,= /(P,+8,)? + (Q,+T2), 
+T. P,+8 
tan = Ppt and tan y= | 
If P=Q, and S=T, ise P,=Q,, P2o=Q,, 8,=T,, 8,=T,, B 1 =R,, 
and 6, =6,. 
Using the same notation as for inside cylinder engines, with in addition — 
w, =the weight of one crank arm and the part of the crank pin i ich i 
contains, reduced to crank radius, then P= wr, P, = mate a fe ,Q= 
oo 
c — q 
S=wr, 8,= ees g ), T,= id , 
and R, =WR= = J{wle— a) + wc — 2a + d)}? + (wa + wd ), 
also, tan 6, = ni Pi 
, what ts w(e—a a) +w{ce-2a+d) 
