112 



PROCEEDINGS OP THE AMERICAN ACADEMY 



TABLE XVI. — Ratios of Constants. 



From these we have the following, as the final most probable 

 results : — 



C u = 8.0601 C„ 

 O w = 1.31175 <7„ 

 C, — .031003 C iy , 

 C„ = .24991 C iv , 

 O lu = .040061 O iv , 



of which the last three are only used to calculate the temperatures on 

 the mercurial thermometer, and hence are of little importance in the 

 remainder of this paper. 



The value ■ of C which we have found for the old value of the 

 coefficient of expansion of glass was 



C = .056976; 



and hence, corrected to the new coefficient, it is, as I have shown, 



C, =.056962. 



Hence, O lt = .45912, 



C,„ = .074720. 



And we have finally the three following equations to reduce the ther- 

 mometers to temperatures on the air thermometer : — 



f Thermometer No. 6163: 

 T= .056962 V' — t ' — .00018 T (40— T) (l — .003 (r+40)). 



Thermometer No. 6165: 

 T=. 45912 V" — V — -00018 T (T — 40) (l —.003 (T -{- 40)). 



