32S APPLIED SCIENCE 



figures for 24 evenly spaced positions of the crank, numbered as 

 shown in Fig. 46a, when the piston and connecting rod lie to the 

 left of the crank. The portion of the curve corresponding to 

 the forward or front stroke, between the positions and 12, will 

 be called the front branch; the portion corresponding to the 

 backward or back stroke, between 12 and 24, will be called the 

 back branch. In A } the front and back branches are symme- 

 trical relatively to ordinate or 12. The relation of the ordin- 

 ates of this curve to the total pressure 10O5 Ibs. on the piston 

 depends wholly on the relative velocity of the piston and a point 

 on the circumference of a circle 3 feet diameter concentric with 

 the crank shaft. There are two dead points at and 12, where, 

 for an infinitely short arc, no resistance could be overcome. 



Tn curve A 2 the front and back branches are sensibly 

 symmetrical in the present example, although not rigidly so. 

 Instead of a mere dead point we have now two dead arcs of 

 different lengths, the longest being at the end of the front and 

 beginning of the back strokes. These dead arcs together last 

 for about 2*7 per cent, of each revolution. The negative or- 

 clinates throughout these dead arcs indicate that the engine, 

 instead of driving, must be driven. The area enclosed by the 

 curves above the line OY measures the work which the steam 

 can do. The area enclosed below the line OY in A 2 measures 

 the work which must be done (not by the steam) to pull the 

 engine through the dead arcs. This work, in practical cases, is 

 done by the fly-wheel, which, if large enough, might do the 

 necessary work without allowing the speed to fluctuate sensibly 

 a condition assumed throughout the calculations. 



The whole work done by the steam is 100-5x16x12, or 

 3,216 inch Ibs. The area of Aj was found to be 3,210 inch Ibs., 

 showing the error due to defective drawing to be very trifling ; 

 the area of Aj (being the arithmetical difference between the 

 positive and negative areas) is 2,974 inch Ibs. The efficiency 



on assumption 2nd is therefore ^rrn = ^'927. 



o,zlO 



In curve A 3 the front and back branches are no longer even 

 approximately symmetrical to one another. There is no dead 

 point at the end of the front stroke, and there is a long dead arc 

 at the end of the back stroke. The maximum effort is great IT 



