Polytechnic Association. 839 



The distribution of effective force in this case is shown in the fol- 

 lowing diagram to be even more disadvantageous than in the case 

 preceding ; but the work is here principally thrown upon the first 

 quarter revolution, instead of on the second, as in that. 



4. We have finally to consider 

 the case of the heavy piston en- 

 gine, werking with short cut-off, 

 and with such weight in the 

 reciprocating parts as is indicat- 

 ed by theory to be that which 

 most equally distributes the 

 work over the circumference 

 described by the crank. The 

 cut-off for which the calculations 

 are made is, as in the case last considered, one-eighth. In computing 

 the coefficients of effective force for this case, it must be borne in 

 mind that the initial steam pressure must be 2.6 times as great as 

 that which would do the same work without cut-off; and the part 

 of this which, according to what has gone before, it is most advanta- 

 geous to use in overcoming inertia in the reciprocating parts of the 

 engine, is to the total initial pressure, as 1.1 to 2.6, for a one-eighth 

 cut-off. Hence, therefore, the formula for the coefficient will be 



<2COsec. 2 \4> sin.^ — ^-— sin.2. ? 



The sign connecting the terms is negative ; but when <p exceeds 

 90°, 2<p exceeds 180°, and sin.2^ beoomes essentially negative ; so 

 that, during the second half stroke, the coefficient is the sum and not 

 the difference of the two terms of the formula. The first form of 

 this formula is only to be used for the values of <p in which r v. s. p 

 exceeds Tc. For values less than this, the formula is 



1.1 . 



sin. — — —sin. 2 . 

 0.2 



