108 PROCEEDINGS OP THE AMERICAN ACADEMY 



It now remains to determine from these experiments the most 

 probable values of the constants in the formula, comparing the air 

 with the mercurial thermometer. The formula is, as we have found, 



t= T—at (t 1 — t) (b — t); 



but I have generally used it in the following form : — 



t = G V— t — mt (100 — t) (1 — n (100 -4- t)), 

 t = C V— t' — 7nt(A0 — t) ( 1 — n (40 -f t)). 



And the following relations hold anions; the constants : — 

 G = C (1 4- m (60 — 8400 n)), nearly, 



In these formula3 t is the temperature on the air thermometer; Fis 

 the volume of the stem of the mercurial thermometer, as determined 

 from the calibration and measured from any arbitrary point; and 

 G', t' , m, and n are constants to be determined. 



The best way of finding these is by the method of least squares. 

 G' must be found very exactly ; t is only to be eliminated from the 

 equations ; m must be found within say ten per cent, and n need only 

 be determined roughly. To find them only within these limits is a 

 very difficult matter. 



Determination of n. 



As this constant needs a wide range of temperatures to produce 

 much effect, it can only be determined from thermometer No. Gl 67, 

 which was of the same glass as Gl 03, 01 60, and 1 0(J. It is unfortunate 

 that it was broken on November 21, and so we only have the experi- 

 ments of the first and second series. From these I have found 

 n = .003 nearly. This makes b = 233°, which is not very far from 

 the values found before from experiments above 100° by Regnault 

 on ordinary glass.* 



* Some experiments with Baudin thermometers at high temperatures have 

 given me about 240°, — a remarkable agreement, as the point must be uncertain 

 to 10° or more. 



