286 OF THE APPLICATION [SECT. ix. 



if a be the diameter of the piston, and p = the pressure on a circular inch, we 

 have, 



a" p = (A - D) sin. i + (A + D) q + C S. 

 From this the diameter of the cylinder is easily found, and in all cases 



where R is the radius of the wheels of the carriage, r that of the axles, and / the 

 friction, when the pressure is 1. 

 Also 



s = iZ 

 x ' 



where X is the diameter of the pulleys, and x that of the axes. When the railway 

 is level, 



a 2 p = (A + D) q + C S. 



In these equations the piston of the engine, and the load, are supposed to move 

 at the same velocity. 



592. STEAM CARRIAGES. The engines of steam carriages are double non- 

 condensing engines, of the kind described in art. 372. They have generally two 

 cylinders. If, 



p be the mean effective pressure on the piston, 

 a the diameter of the cylinders, 

 v the velocity in feet per minute ; 

 i the angle of inclination of the rails of the road, 

 q the friction of all the axes, 

 W the weight of the carriages and their loads, 

 V their velocity in feet per minute, 

 and E the weight of the engine. 



Then, V (W + E) (g + sin. z) = 2 a* p v, in ascending the inclination ; 

 and, V (W + E) (q sin. t) = 2 a z p v, in descending the inclination. 



Also 



E (-08 cos. sin. i) _ -^ 

 q + sin. 



so that the engine may not slide in ascending ; and 



E (-08 cos. i + sin. i) _ w 



- : - : -- W, 



5 sin. t 

 when it will not slide in descending. 



