OF ARTS AND SCIENCES. 177 



The times were calculated by the formula 



Time = .294 X Revolutions -|- 12.G6, 



which assumes that the engine moves with uniform velocity. As the 

 principal error in using an incorrect interpolation formula comes from 

 the calculation of the radiation, and as this formula is correct within 

 a few seconds for all the higher temperatures, we can use it in the 

 calculation of the times. 



The records of the transits of the mercury over the divisions of 

 the thermometer were nearly always made for each division, but it is 

 useless to calculate for each. I usually select the even centimeters, 

 and take the mean of the records for several divisions on each side. 



While the mercury was rising l c,n on No. 61 G3, there would be 

 about seven revolutions of the chronograph, and consequently seven 

 readings of the torsion circle, each one of which was the average for 

 a little time as estimated by the eye. 



I have obtained more than thirty series of results, but have thus 

 far reduced only fourteen, five of which are preliminary, or were made 

 with the simple jacket instead of the water jacket, the radiation to 

 which was much greater, as there was a hole at the bottom which 

 allowed more circulation of the air. The mean of the preliminary 

 results agrees so closely with the mean of the final results, that I have 

 in the end given them equal weight. 



On March 24th, the same thermometer was used for a second ex- 

 periment directly after the first, seeing that the chronograph failed to 

 work in the first experiment until 8° was reached. The error from 

 this cause was small, as the first experiment only reached to 2G° C, and 

 hence there could have been no change of zero, as this is very nearly 

 the temperature at which the thermometer was generally kept. 



Having thus calculated the work in conjunction with the tempera- 

 ture, I have next interpolated so as to obtain the work at the even 

 vol.. xv. (n. s. vn.) 12 



