ON THE MECHANICAL EQUIVALENT OF HEAT 



355 



The object of comparing the formula with Regnault's results at 

 temperatures so much higher than I need, is simply to test the formula 

 through as great a range of temperatures, and for as many kinds of 

 glass, as possible. If it agrees reasonably well throughout a great 

 range, it will probably be very accurate for a small range, provided 

 we obtain the constants to represent that small range the best. 



Having obtained a formula to represent any series of experiments, 

 we can hardly expect it to hold for points outside our series, or even 

 for interpolating between experiments too far apart, as, very often, a 

 small change in one of the constants may affect the part we have not 

 experimented on in a very marked manner. Thus in applying the 

 formula to points between and 100 the value of & will affect the 

 result very much. In the case of the glass Choisy-le-Eoi many values 

 of 6 will satisfy the observations besides 6 = 0. For the ordinary 

 glass, however, & is well determined, and the formula is of more value 

 between and 100. 



The following table gives the results of the calculation. 



TABLE III. REGNAULT'S RESULTS COMPARED WITH THE FORMULA. 



Kegnault does not seem to have published any experiments on Choisy- 

 le-Roi glass between and 100, but in the table between pp. 226, 227, 

 there are some results for ordinary glass. The separate observations 

 do not seem to have been very good, but by combining the total number 

 of observations I have found the results given above. The numbers in 

 the fourth column are found by taking the mean of Eegnault's results 

 for points as near the given temperature as possible. The agreement 



