APPLICATION OF GRAPHIC METHODS 327 



shaft, the tangent being so inclined as to cut the centre line of 

 the engine 19 - 2" from the crank-shaft centre on the side 

 towards the piston. This line may be regarded as the direction 

 of the resistance exerted at the teeth of a spur-wheel. The 

 position of this line exercises a very material influence on the 

 results obtained, which must not, therefore, as was said before, 

 be considered as applicable to engines generally. The coefficient 

 of friction has been taken as = ^. 



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 fric- 

 tion ; 2nd, neglecting weight and mass ; 3rd, neglecting friction, 

 but taking mass and weight into account ; 4th. 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 1st. the simple dynamic frame ; 2nd, the 

 dynamic frame with friction; 3rd, the loaded dynamic frame; 

 4th, 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 photographic process. 



34. Exo.mple A. Speed of engine, 1 revolution per second ; 

 effective pressure on cylinder. 2 Ibs. per square inch uniform 

 throughout the stroke. This example has been chosen to indi- 

 cate the effect of running the engine with a very low pressure 

 and no expansion. The vertical ordinates of curve A,, Fig. 46, 

 indicate in pounds the total effort which the engine could 

 exert along the assumed line of resistance, the total pres- 

 sure on the cylinder being 100*5 Ibs. The horizontal co- 

 ordinates indicate the arc 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 



