Measurement of Mechanical and Electrical Forces. 85 



Part II. 

 The practical value of the tangent principle depends on the 

 fact, that the only operation required of the function to be in- 

 tegrated is that of turning more or less a spindle and tangent - 

 wheel, which ruay he as light and delicate as any part of a 

 ■watch, and of which the moment of inertia may be inappre- 

 ciable. This is in marked contrast to what is necessary in 

 radius machines: the friction in the common double disk or 

 disk and cone integrator, or the inertia of the ball in Sir 

 James Thomson's machine, would be quite sufficient to make 

 the former useless for the integration of such delicate forces as 

 depend on the actions of electricity, or the latter inapplicable 

 to machinery in rapid movement. Another point about tan- 

 gent machines is, that the whole process of integration is the 

 result of pure rolling, and any doubt that may be felt as to 

 the effect of the sliding action on the accuracy of cosine 

 machines is here removed. The rest of this paper describes 

 some applications of the disk-cylinder integrator some of which 

 are likely to be of practical value. 



Engine-power Meter. 

 As work is motion multiplied by pressure, the work done 

 in an engine may be found by integrating the difference of 

 pressure on the two sides of the piston with respect to the 

 motion of the piston. For any one stroke, this is usually 

 done by measuring the areas of the indicator-diagrams, one 

 taken at each end of the cylinder, and repeating, so as to get 

 an average value. But as the work done, or the area of the 

 diagram, is subject to variation depending on the load, pres- 

 sure, and speed, only guesses can be made as to the whole 

 amount of work that has been done by an engine during any 

 length of time. Any machine, therefore, that will automati- 

 cally find the total work done should be of value, not onlv to 

 users of engine-power, but especially to experimentalists who 

 are engaged on testing the efficiency of engines, and on other 

 subjects where total work done should be known. It is only 

 fair to mention that Messrs. Ashton and Story have an engine- 

 power meter in which the integration is effected by a double- 

 disk integrator acting on the radius principle : but it necessa- 

 rily suffers from the defects common to all radius machines. 

 The disk-and-cylinder is especially applicable to this particular 

 case; for it is only necessary to make the cylinder reciprocate 

 with the piston of the engine, the motion being of course re- 

 duced to a convenient amount, and to make the tangent of the 

 inclination of the disk vary with the difference in pressure on 



