432 HENEY A. KOWLAND 



which is the work on the calorimeter during one revolution of the 

 engine. 



The equation of the motion of the calorimeter, supposing it to be 

 nearly stationary, and neglecting the change of torsion of the suspend- 

 ing wire, is 



m dV WD , nt f- 2* A 2 A 



+ Cvl (1 + c cos - - = 0, 



TIT ^ 



g dt* 2 \ a 



where m is the moment of inertia of the calorimeter and its attach- 

 ments, <p is the angular position of the calorimeter, W is the sum of 

 the torsion weights, and D is the diameter of the torsion wheel. Hence, 



= L j J/ \_Cvl (I + 



til (_ 



When WD = 2Cv Q z (I -\- -|c 2 ), the calorimeter will merely oscillate 

 around a given position, and will reach its maximum at the times t = 0, 

 a, a, &c. 



The total amplitude of each oscillation will be very nearly 



,,,_,,/ _ Cfrfra'c = WDga'c 

 v*m 2x*m ' 



If x is the amplitude of each oscillation, as measured in millimetres, 

 on the edge of the wheel of "diameter D, we have <p <p' =. -?. 



Hence . c = ^, 



where n is the number of revolutions of the engine per second. 

 Having found c in this way, the work will be, during any time, 



w = TT WDN(l + c 2 ) , 

 where N is the total number of revolutions of the paddles. 



A variation of the velocity of ten per cent from the mean, or twenty 

 per cent total, would thus only cause an error of one per cent in the 

 equivalent. 



Hence, although the engine was only single acting, yet it ran easily, 

 had great excess of power, and was very constant as far as long periods 

 were concerned. The engine ran very fast, making from 200 to 250 

 revolutions per minute. The fly-wheel weighed about 220 pounds, and 

 had a radius of 1 feet. At four turns per second, this gives an energy 

 of about 3400 foot-pounds stored in the wheel. The calorimeter re- 

 quired about one-half horse-power to drive it; and, assuming the same 



