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PROFESSOR 0. REYNOLDS AND MR. W. H. MOORBT 
(1.) The moment of effort on the crank being constant, and the resistance constant, 
and equal to the effort, the energy of motion of all the parts is constant. 
Putting CO = 27rN/60, and ^ jg, 
4- sin hit — C, 
where C is constant, t is the time since the axis of the crank-pin has crossed the 
axis of the cylinder and n is Wq, the mean value of co or 27 rN/ 60 . 
Whence neglecting i as compared with I, the extreme variation of co is 
approximately 
O ^ 1 ^ 
ZCij &)q ^ -y- (Oq 
whence 
(2.) In the same way, considering the effect of the crank effort alone, with a moderate 
expansion, the energy that has to be absorbed and given out by the revolving parts 
is about one-fourth part of the work per stroke, and 
— -|-U cos 2n {t — T) = C, 
where nT, say ^ is the angle of the crank at which co^ is a minimum. 
The extreme fluctuations in velocity are 
^0 0 1 U 
CO = Wo j 1 + COS 2 {nt — ivr) j . 
(3.) The effect of the weight of the reciprocating parts acting alone, causes v 
fluctuation on the revolving parts of 2rW ; thus approximately 
- lo)^ — rW cos nt = C, 
and 
CO = coq (1 -b j —3 cos nt 
giving an extreme fluctuation on the angular velocity of 
Wr 
2<^3^COq = 2 
