312 REPORT— 1841. 



of revolutions, or rather parts of a revolution, which it is made to describe 

 during any exceedingly small period of time, beginning from that instant, is 

 dependent upon two causes ; first, upon the angle which the cone describes 

 about its axis during that small period of time, and secondly, upon the distance 

 of its point of contact K with the cone from the apex of the cone at that time. 

 Moreover, that if either of these two elements of variation remained always 

 the same, then the number of revolutions, or parts of a revolution, made by 

 the wheel, would vary directly as tiie other, whence it follows, by a well-known 

 principle of variation, that when (as in the present case) both these elements 

 vary, it varies as their product ; or that the number of revolutions, or parts of 

 a revolution, made by the integrating wheel during any exceedingly small 

 period of time, varies directly as the product of two factors, of which one is 

 the angle described during that time by the cone, and the other the distance 

 of the point of contact K of the cone and wheel from the apex of the cone. 



Now the former of these factors has been shown to vary directly as the 

 space described during that small period of time by the piston of the engine, 

 and the latter to vary directly as the effective pressure which the steam is 

 then exerting upon the piston of the engine*. 



Thus, then, it appears that the number of revolutions, or parts of a revolu- 

 tion, made during any exceedingly small period of time by the integrating 

 wheel, varies as the product of the space described by the piston of the engine 

 during that time, by the effective pressure of the steam upon it during that 

 time, that is, it varies as the work or dynamical effect of the steam upon the 

 piston during that time. And this being true in respect to every small pe- 

 riod of the time during which the stroke of the engine is in progress, is true 

 of the whole stroke; whence it follows, that the number of revolutions, and 

 parts of a revolution, made by the integrating wheel during the stroke is pro- 

 portional to the whole work, or dynamical effect of the steam upon the piston 

 during the stroke. 



The integrating wheel carries round with it the frame G H, on the hollow 

 axis of which frame is fixed a pinion running into a wheel, whose axis turns 

 upon bearings fixed to the frame of the instrument, and the number of whose 

 teeth is to that of the teeth in the pinion as ten to one. This wheel carries 

 also a pinion running into a second wheel, their numbers of teeth being in 

 the same proportion, and so through a train of five wheels and pinions. The 

 circumference of each of the four last wheels is divided into ten equal parts 

 and numbered, and the circumference of the first into 100. The number of 

 revolutions of the integrating wheel is thus registered to five places of inte- 

 gers, and to one place of decimals. 



Now this number of revolutions has been shown to be proportional, in re- 

 spect to each stroke, to the work done by the steam upon the piston during 

 that stroke ; if therefore the action of the indicator continued the same during 

 successive strokes, or if the direction of the pressure of the steam upon the 

 piston, and that of the motion of the piston, were not reversed at every stroke, 

 then would the number registered during any number of strokes of the en- 

 gine be directly proportional to the work done by the steam upon its piston 

 whilst that number was registered. At the return-stroke of the piston of the 

 engine, the pulley N, however, revolves backwards, and supposing it to carry 



* The position of the integrating wheel upon the piston-rod is so adjusted, that before 

 the steam is admitted the integrating wheel may be brought by the elasticity of the springs 

 exactly to the apex of the cone. In order to prevent it fi'om being stopped by the apex of 

 the cone, if accidentally it should be made to pass it, a solid piece projects from the frame of 

 the instrument, having its surfaces adjusted so as to receive the edge of the wheel when it is 

 forced beyond the apex of the cone, and to serve as a stop to the motion of the cone in the 

 direction of its spindle when the resistance of the wheel is thus removed from it. 



