184 APPENDIX. 



III. TRANSMISSION OF EFFECT FROM THE CYLINDER. 



The principle that no power can be gained or lost in its transmission by means of 

 mechanism, enables us without much difficulty to trace the effective working of an engine due 

 to a given pressure in the cylinder. 



Let a denote the diameter of the cylinder in inches. 

 I the length of the stroke in feet. 

 T the temperature of the steam in the cylinders. 

 P its mean pressure in ffis. per square inch. 

 F the entire friction, estimated on the pistons, in fl5s. per square inch. 



For high pressure engines this must include the pressure of the 



atmosphere. 

 R the resistance, in ffis., overcome at the extremity of the two wheels con- 



nected with the shaft. 



n the number of strokes per minute. 

 u the velocity of the piston in feet per minute. 

 V the velocity of the circumference of the wheel in feet per minute. 

 TT 3-14159, &c. 

 Then if 1 denote the force on the pistons which would just overcome the resistance R, we 



V 



shall have, equating their powers, Q, u = R V ; and therefore Q = - - R. The area of the 



two pistons being a 2 square inches, the pressure per inch just sufficient to overcome the 



m 



resistance will be a = - = -= 5 R. To this add the friction F, and the entire 

 TT 2 TO TT a* u 



2 

 pressure per square inch on the pistons is hence, 



But since V passes through TT D, a circumference of the wheel, and u passes through 2 I, 

 twice the length of the stroke, in each revolution, - - = y ; and this being substituted 



U ' 



in (A) we get, 



P = ^R + F....(B); 



and hence, 



F=P--$-R ..... (C), 



2 Z 



R = ^(P-F) ...(D); 



which express the relations amongst the mean forces or pressures P, F, R. 



The velocities of the parts of the engine depend on the number of strokes, that of the 

 piston being, 



u = 2 n I ...... (E). 



