836 Transactions of the American Institute. 



For the intermediate degrees, the effective force averages about five- 

 eighths of the total. 



The distribution of the effective force upon the crank over the 

 circumference of revolution may be graphically illustrated as follows : 



Upon O Q * taken equal to 

 twice the length of the crank, 

 describe the semi-circumfer- 

 ence OP Q; and subdivide 

 this into eighteen arcs of ten 

 degrees each. Draw radii 

 through the points of division ; 

 and upon these radii produced 

 beyond the circumference, set 

 off, from the circumference 

 outward, the distances a a', b b', etc., proportional to the coefficients 

 of effective pressure for the values 4> = 10°, 4> = 20°, and so on, 

 taking PP 1 = 100 parts. The curve drawn through the points thus 

 determined, will be the curve of effective force, in the case in hand. 

 2. The next case supposes the reciprocating parts to have large 

 inertia, and is that in which the steam pressure exactly suffices to 

 furnish the requisite initial accelerating force. In this case, it is 

 necessary to subtract from the effective force in the first quadrant, all 

 that would be contributed in the absence of the heavy reciprocating 

 parts, by the proportion of the total steam pressure which is required 

 to set those parts in motion, and to add an equivalent amount in the 

 second quadrant. 



The accelerating force on the piston is expressed by ' r cos. <p ; 



and the part of this which would be effective, if not consumed in 

 the acceleration, is 



. * The letters have been unfortunately omitted in this figure ; but it will be easily understood with 

 out them. 



