376 HENET A. EOWLAND 



And the following relations hold among the constants : 



C = G' (1 + m (60 8400 )) , nearly , 

 a = mn, 



b = ~ 100, 

 n 



T=CVt 9 , 

 i t 



*t l o n' ' 



In these formulae t is the temperature on the air thermometer; V is 

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

 from the calibration and measured from any arbitrary point; and C", 

 f , m, and n are constants to be determined. 



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

 C" 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. 6167, which 

 was of the same glass as 6163, 6165, and 6166. It is unfortunate that 

 it was broken on November 21, and so we only have the experiments 

 of the first and second series. From these I have found w = -003 

 nearly. This makes b = 233, which is not very far from the values 

 found before from experiments above 100 by Eegnault on ordinary 

 glass." 



Determination of C and m 



I shall first discuss the determination of these for thermometers 

 Nos. 6163, 6165, and 6166, as these were the principal ones used. 



As No. 6163 extended from to 40, and the others only from 

 to 30, it was thought best to determine the constants for this one 

 first, and then find those for 6165 and 6166 by comparison. As this 

 comparison is deduced from the same experiments as those from which 

 we determine the constants of 6163, very nearly the same result is 



15 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. 



