Ng ia a dbl a slalenie h h ail =| rn ae ee 
BALANCING __ 423 
i ‘the right-hand crank. P and Q are the centrifugal forces of the revolving 
masses and two-thirds of the reciprocating masses at crank radius, as 
- already explained. P and Q are in ar equal, 
Forces P, and P,, in the planes of the circles 1 and 2 respectively, 
which will balance P, are determined from the equations 
P,(2a +c) =P(a+e), 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 +c) = Qa, and Q,(2a +c) = Q(a +c). 
R,, the resultant of P, and Q,, and Ry, the resultant of P, and Q,, 
can now be determined. R,= Aan Oh and R,= JP +Q)). The 
angles 0, and @, are determined from tan =Q,/P, and tan 4, = P,/Q,: 
If P=Q, then P| =Q,, P,=Q,, R,=R,, and 0,=9,. 
Let w=weight at each crank pin, including equivalent revolving 
weight and two-thirds of the reciprocating weight for one cylinder. 
W=weight of each balance weight. r=radius of cranks. R=radius 
of circles described by the centres of gravity of balance weights. 
~ _wr(a+e) fe 
Then P=wr, P, re ae Q,= ret and 
V(a+c)?+a?, also tan =. 
356. Outside Cylinder Uncoupled Locomotives.—These engines 
have two cylinders placed outside the frames, and the two cranks, which 
are at right angles to one another, are placed at the ends of the driving 
axle, which is straight. Generally the crank arms are formed in the 
driving wheels. 
Referring to Fig. 693, 1 and 2 are the circles described by the centres 
of gravity of the required balance weights which are placed in the driving 
R,=WR= oh 
_ wheels. P and Q are the centrifugal forces of the weights which are 
considered as revolving at the centres of the crank pins A and B respec- 
tively. The weight considered as revolving at each crank pin includes 
two-thirds of the weight of the reciprocating parts for one cylinder, two- 
thirds of the weight of that part of the connecting-rod which is reckoned 
as reciprocating, the weight of that part of the connecting-rod which is 
reckoned as revolving, and the weight of the part of the crank pin which 
