314 REPORT — 1841. 



that it performs a similar operation in the up-stroke, and deducts the corre- 

 sponding amount as a correction from the first. 



The above must be received as an attempt to place the theory of the in- 

 strument under a general and popular form. A mathematical discussion of 

 it accompanies this Report, in which the corrections due to friction and other 

 causes are fully considered. 



The instrument will be observed to differ from that invented by M. Morin 

 for applying the same principle of M. Poncelet to estimate the traction of 

 carriages, as well in those contrivances which are specially required by its 

 application to the steam-engine, as in the following important particulars, 

 which are wholly independent of that particular application. 



First, the surface of a cone is here substituted for the plane surface of a cir- 

 cular disc, an arrangement by which the rapidity of the changes of velocity 

 due to corresponding changes in the position of the integrating wheel is di- 

 minished in the same proportion in which the sine of one half the angle of the 

 cone is less than unity ; and the force necessary to drive the integrating wheel 

 is diminished in the same proportion, and therefore the chance of an error 

 arising from the slipping of the edge of the integrating wheel on the surface, 

 which gives it motion in the like proportion. 



Secondly, it differs from the Compteur of M. Morin in the separation of 

 the registering apparatus from the integrating wheel, by the contrivance of 

 the frame and guides, by which separation, whilst the springs are relieved 

 from the effect of the momentum and the friction due to the weight of the re- 

 gistering apparatus, this last being brought to a state of quiescence, the re- 

 gistration is made legible whilst the indicator is in action. 



Theory of the Indicator. 



Let N represent the number of revolutions, and parts of a revolution, made 

 by the integrating wheel and registered by the indicator, whilst L feet are 

 described by the piston of the engine. 



Also let — represent the space described in the same time by the cord 



which passes over the pulley N, this cord being supposed to move precisely 

 as the piston of the engine does, but through one mth of the space. 



Let R represent the radius of the pulley N in inches. 



Let r represent the radius of the piston of the indicator in inches. 



Let p represent the radius of the integrating wheel I K in inches. 



Let I represent half the angle at the apex of the cone. 



A N the number registered by the indicator, whilst the exceedingly small 

 space A L is described by the piston of the engine. 



A. the additional separation of the springs in inches due to each additional 

 pound of strain upon the springs, or to each additional pound of effective 

 pressure on the piston-rod of the indicator. P the effective pressure of the 

 steam on the piston of the engine, and therefore on that of the indicator, in 

 pounds per square inch, at that period of the stroke when the space A L begins 

 to be described and the number A N to be registered. F the whole friction 

 opposed to the motion of the piston-rod in the direction of its length. The 

 effective pressure upon the piston-rod of the indicator at that time in pounds 

 is represented, therefore, by tt r^ P + F, the sign -\- being taken according 

 as the steam pressure is in the act of increasing or diminishing, or the piston 

 of the indicator moving in the direction of the pressure of the steam upon it, 

 or in the opposite direction ; and since each pound of this pressure produces 

 a separation of X inches in the springs, therefore the whole separation of the 

 springs, or the whole distance of the point of contact of the integrating wheel 



