OF ARTS AND SCIENCES. 



87 



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 0° and 100° the value of b will affect the 

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

 values of b will satisfy the observations besides b = 0. For the 

 ordinary glass, however, b is well determined, and the formula is of 

 more .value between 0° and 100°. 



The following table gives the results of the calculation. 



TABLE III. — Regnault's Results compared with the Formula. 



Regnault does not seem to have published any experiments on 

 Choisy-le-Roi glass between 0° and 100°, but in the table between 

 pp. 22G, 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 Regnault's results for points as near the given temperature 

 as possible. The agreement is only fair, but we must remember that 

 the same specimens of glass were not used in this experiment as in the 

 others, and that for these specimens the agreement is also poor above 

 100°. The values a = .000 000 44 and b = 2G0° are much better 



