834 Transactions of the American Institute. 



total pressure, and 7c), then P'a is the initial pressure employed in 

 accelerating the piston. But the initial force required to produce the 



proper degree of acceleration is represented by - v Ta ' r ; and the 



relation of this to gravity is - r 2 % r. Hence, if w represent the 



weight of the piston, the following ought to be true, viz. : 



(2*) 2 -p/ a gT*P'a 



-±-nw r w —- r'a: and w = —^ — ^ — ■ 

 g L* (2 izy r. 



If we wish, with a one-eighth cut-off, to do the work of a full head 

 of steam of 30 pounds pressure per square inch, upon a piston 16 

 inches in diameter, with a two-foot-stroke, and 120 revolutions to the 

 minute, we shall find P' to be 33 pounds, and P' a = 6,633 pounds. 

 Also, the initial accelerating force will be nearly five times gravity 

 (4.9), and vj = 1,350 pounds. But if, the other data remaining the 

 same, the length of stroke be increased to 30 inches, the initial accele- 

 rating force will be increased to a little over six times gravity (6.1), 

 and w becomes something less than 1,100 pounds (1080). 



It may be remarked that, while the weights thus assigned are 

 mathematically the best,* in reference to the equality of distribution 

 of work over the stroke, yet there can^be considerable variation from 

 these values without affecting injuriously, to any very marked degree, 

 the performance of the engine. 



It having thus been shown what is necessary to the most favorable 

 distribution of work, in the heavy-piston engine, it is proposed now 

 to illustrate by tabular coefficients, and by diagrams, the effective tan- 

 gential force exerted upon the crank, at every point of the revolution, 

 under several hypotheses in regard to the admission of steam, and to 

 the presence or absence of large inertia in the reciprocating parts of 

 the engine. 



1. The first case considered will be that in which the steam 

 pressure is constant throughout the stroke, and the reciprocating 

 parts of the engine are supposed to be without inertia. 



Referring to Fig. 2, the pressure on the piston transmitted to the 

 crank by the connecting rod, may be represented by C I, which is 

 resolvable into the rectangular components C K and K I, of which 

 the second only is effective in turning the crank round D. This 

 effective component is, therefore, = P sin. </'. If it were possible to 

 make P vary so that the turning force might always be equal to the 



*This is on supposition of the correctness of the logarithmic theory of pressures. As the 

 actual pressures of expanding steam are considerably less, the values of w found by employing a. 

 more exact formula, as for instance that of Pambour, would be greater. 



