838 



Transactions of the American Institute. 



In the following diagrams, the lighter shaded portion of the area of 

 the curve of effective force belongs to that portion of this force which 

 is absorbed by the inertia of the reciprocating parts of the engine : 



This diagram illustrates 

 the great disturbance in the 

 symmetry of distribution of 

 effective force acting on the 

 crank, introduced into the 

 reciprocating steam-engine 

 working without cut-off by 

 the use of heavy pistons. 



3. The case next presented is that of a similar engine working with 

 short cut-off, the reciprocating parts being supposed to be without 

 inertia. In calculating the coefficients of effective force, the logarithmic 

 theory, or the law of Marriotte, is used, although the pressures of expand- 

 ing steam thus deduced are somewhat above the truth. If P is the 

 original pressure, 7c the cut-off expressed in terms of radius or length 

 of crank r, and^ the pressure after expansion begins, we shall have 



p = P - — = p \ == p * . 



■^ r v. s. <p r (1 — cos. <p) 2 r sin. 3 £ <p 



Putting, for simplicity, — — = q, the formula for the coefficient of 



the pressure will be 



= q cosec. 2 \ <p ; and that for the coeffi- 



sin. 2 \ <p 



cient of effective force exerted on the crank, = q cosec. 2 $ <p sin. p . 

 From this formula are deduced the following values, on supposition 

 of a cut-off at one-eighth of the length of the stroke, or \r ; but it is 

 to be observed that, up to the point where rv. s.<p — k, the coeffi- 

 cients are those corresponding to case first, in which the coefficient 

 is, simply, sin. <p. This point is that which <p == 4:1-^°, nearly. 



First quarter revolution. Second quarter revolution. 



<P sin. <p 



