OF ARTS AND SCIENCES. 1G5 



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

 Hence, 



\_\bir- a 2 it- \ a /J ) 



When WD = 2 Cc (l 2 (1 -f- \ c 2 ), the calorimeter will merely oscil- 

 late 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 



C r,! 1 fj a 1 c W D g <>' c 



f — # = 



2ir* 



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



2 x 



on the edge of the wheel of diameter D, we have \j/ — \p' = -jr. 

 Hence, c - 



2 CDg ' 



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

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



W = 7T WD N{\ -\-c 2 ), 



where iV^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 2;10 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 required about one-half horse-power to drive it ; and, 

 assuming the same for the engine friction, we have about 140 foot 

 pounds of work required per revolution. Taking the most unfavorable 

 ease, where all the power is given to the engine at one point, the 

 velocity changes during the revolution about four per cent, or c would 

 nearly equal .02, causing an error of 1 part in 2500 nearly. By 

 means of the shaking of the calorimeter, I have estimated c as follows, 

 the value of m being changed by changing the weight on the inertia 

 bar, or taking it off altogether. The estimate of the shaking was 

 made by two persons independently. 



