Polytechnic Association. 837 



30° 0.4330. 



35° 0.4700. 



40° 0.4924. 



45° 0.5000. 



It will be seen from this table that the inertia of the piston draws 

 most heavily upon the force exerted effectively upon the crank, at the 

 end of the first octant ; and that the effect diminishes from this point 

 onward by the same law according to which it had previously 

 increased. The coefficients of resultant effective pressure would be, 

 for the first quarter = revolution, equal to sin <p — £sin.2?> ; and for 

 the second, s in ? -f £sin2?>. But they may be obtained by means 

 of a simpler formula, as follows : 



Since the force consumed in acceleration is ' *'- r cos. ?, the remain - 

 ing force not so consumed is v T2 ; r (1 — cos. <p). But 1 — cosp = 



2sin 2 \<p. Hence this remaining force is ■ ' r x 2sin 3 £? ; and 



• ) c 

 the portion of this which is effective on the crank, is v " ' r X 2 



sin 2 % <p sin <p. The coefficients will, therefore, be given equally by 

 the formula sin <p — £ sin 2 ? or the equivalent formula, 2sin <p sin 2 \ <p. 



