Polytechnic Association. 



835 



resistance, R, regarded as constant, and reduced to the circumference 



■D 



described by the crank, we should have Psin.^ = R ; or P = — = — - 



J ' sin. (p 



= R cosec. 4'- On this supposition the variations of value of P 

 would be very large ; the limits being P=R at 90°, and P= oo at 

 0°. On the other hand, if P remain constant, the effective force is 

 equally variable, being zero at 0° and = R at 90°. 



In the first case, the following are the values which must belong to 

 P at the several angles named. 



At 



The values for the second quarter revolution are the same, in 

 reversed order. 



If P remain constant, the effective force, P, will have values as 

 follows : 



At 



0° 



1° 



5° 



10° 



15° 



. 20° 



25° 



30° 



35° 



40° 



And 



P' = 0.00. 

 P' = 0.0175 P. 

 P' = 0.0872 P. 

 P' = 0.1736 P. 

 P' = 0.2588 P. 

 P' = 0.3420 P. 

 P' == 0.4226 P. 

 P' = 0.5000 P. 

 P' = 0.5736 P. 

 P' = 0.6428 P. 



At 45°, P' == 0.7071 P. 

 50°, P' = 0.7660 P. 

 55°, P' = 0.8192 P. 

 60°, P' = 0.8660 P. 

 65°, P' = 0.9063 P. 

 70°, P' = 0.9397 P. 

 75°, P' = 0.9659 P. 

 80°, P' = 0.9848 P. 

 85°, P' = 0.9962 P. 

 90°, P' = 1.0000 P. 



as before, the values of P in the second quadrant will be 

 the same in reversed order. 



It appears from this, that the force exerted on the crank is com- 

 paratively ineffective for fifteen or twenty degrees near the begin- 

 ning of the first, and the end of the second quadrant, and is effective 

 nearly to the extent of the total pressure on the piston for about as 

 many toward tne end of the first and the beginning of the second. 



