ON SPHERE AND ROLLER MECHANISM FOR TRANSMITTING POWER. 493 



TABLE II. — Resistance of Friction when Hoist was running. Experiments 

 ON Sphere Hoist made at Canons Marsh, May 10, 1886. 



Load lifted direct from barrel, 5^ in. diameter. 



The different positions of the lever of the hoist in the above experi- 

 ments, resulting in difiFerent velocity ratios, are easily understood from 

 the tables, with the exception of the position 4 (Table 1.), which was the 

 position when the velocity ratio was as great as it could be made, this 

 being the limiting position in which the load could be raised. 



The above tables of results are plotted as curves on Plate IX., the 

 loads raised being measured (in lbs.) as abscissae in all the four figures. 

 The dotted lines in figs. 1 and 2 show the velocity-ratio curves, points on 

 which are obtained by setting up as ordinates the forces theoretically 

 required for various loads, supposing no loss in friction to take place. 

 The three cases of velocity-ratio are respectively numbered 1, 2, and 3, 

 and all the dotted lines representing them necessarily pass through the 

 origin of co-ordinates. The centres of the small circles are points obtained 

 by setting up as ordinates the forces actually required. The results 

 are not perfectly regular, but the irregularity obviously arises from 

 the difficulty of conducting such experiments with very great accuracy, 

 although every care was taken to obtain trustworthy results. 



It is, however, not difiBcult to see that the curves which practically 

 represent the results are straight lines drawn in full on figs. 1 and 2. 

 Although in the first set of experiments these lines all pass through one 

 point, showing that the friction of the machine when starting from rest 

 is independent of the velocity -ratio, yet they do not in either set of experi- 

 ments pass through the origin, since this could only occur for the case of 

 a frictionless machine. Thus the equations representing the curves are — 



(1) For velocity-ratio, 



y=:'mX. 



(2) For actual results of experiment, 



y=nx + c, 



where m, n, and c are constants which can easily be obtained. 



The curves in figs. IB and 2E are those of efficiency obtained by 

 plotting the corresponding results given in Tables I. and II., the equa- 

 tions of the various efficiency curves being of the form 



y- 



mx 



nx+c 



and since y=0 when a!=0, they evidently all pass through the origin. 



