

704 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
§ 33. Eight distinct cases have been investigated. In these examples — 
the action of the engine has been studied on four different assumptions—1st, — 
neglecting weight, mass, and friction; 2d, neglecting weight and mass; 3d, — 
neglecting friction, but taking mass and weight into account ; 4d, taking mass, 
weight, and friction into account. A comparison of the results shows the 
influence of each element of the problem on the final result. These processes 
are obtained by what in the first part of the paper are called—Ist, the dynamic 
frame ; 2d, the dynamic frame with friction ; 3d, the loaded dynamic frame ; 
4d, the loaded dynamic frame with friction. The examples will be called 
A, B, C, D, E, F, G, and H; the four assumptions will be indicated by the 
suffixes 1, 2, 3, 4, and it must be borne in mind that the suffix 4 corresponds to 
the complete solution, in which all the elements of the problem are taken into 
account. The results are graphically shown in a series of curves which will be 
called ‘Effort curves.” These were drawn to a very large scale and have been 
reduced by a photographicprocess. 
§ 34. Example A.—Speed of engine, 1 revolution per second; effective 
pressure on cylinder, 2 lbs. per square inch—uniform throughout the stroke. 
This example has been chosen to indicate the effect of running the engine with — 
a very low pressure and no expansion. The vertical ordinates of curve A,, 
fig. 45, Plate XX VL, indicate in pounds the total effort which the engine could 
exert along the assumed line of resistance, the total pressure on the cylinder 
being 100°5 Ibs. The horizontal co-ordinates indicate the are which the centre — 
of the crank-pin has traversed, measured from the position in which the crank- _ 
pin is, at the end of its stroke, nearest to the cylinder. The co-ordinates of all — 
the other curves have a similar signification. The ordinates for each curve have 
been calculated by separate figures for 24 evenly spaced positions of the crank, . 
numbered as shown in fig. 46, 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 0 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 
symmetrical relatively to ordinate 0 or 12. The relation of the ordinates of this — 
curve to the total pressure 100°5 Ibs. on the piston depends wholly on the rela- 
tive 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 0- 
and 12, where, for an infinitely short arc, no resistance could be overcome. 
In curve A, 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 27 
per cent. of each revolution. The negative ordinates throughout these dead ares 
indicate that the engine, instead of driving, must be driven. The area enclosed 
