840 



TRANSACTIONS OF THE AMERICAN INSTITUTE. 



The coefficients found by these formulae are the following : 



The curve of effective force corresponding to this case will be seen, 

 in the following diagram, to exhibit a more favorable distribution 

 than has been observed in any of those previously given. The work 

 done in the two successive quarter revolutions of the same stroke is 

 necessarily equal ; since that is a result of the mechanical conditions 

 intentionally introduced for the purpose of securing such equality ; 

 but it is farther true that the work is nearly the same in each of 

 the four successive octants. 



In illustration of this 

 statement, it may be ob- 

 served that the work con- 

 sumed in accelerating the 

 reciprocating Darts of the 

 engine is expressed by the 



formula, 



(2-) 2 



r' sin.*<p, 



2 .?T 2 

 and that this is equally 



divided at the point of 



the half-stroke at which 



sin 2 <p = £ ; which is true 



