Ox THE MECHANICAL EQUIVALENT OF HEAT 379 



The results for m are then as follows : 



From direct comparison of Xo. 6167 with the air thermometer -000187 

 From direct comparison of Xo. G163 with the air thermometer -000154 

 From comparison of Xo. 6163 with Xo. 6167 -000213 



The first and last are undoubtedly the most exact numerically, but 

 they apply to Xo. 6167, and are also, especially the first, derived from 

 somewhat higher temperatures than the 20 point, where the correc- 

 tion is the most important. The value of m, as determined in either 

 of these ways, depends upon the determination of a difference of tem- 

 perature amounting to 0-30, and hence should be quite exact. 



The value of m, as obtained from the direct comparison of Xo. 6163 

 with the air thermometer, depends upon the determination of a differ- 

 ence of about 0-05 between the mercurial and the air thermometer. 

 At the same time, the comparison is direct, the temperatures are the 

 same as we wish to use, and the glass is the same. I have combined 

 the results as follows: 



m from Xo. 6167 -000200 



m from Xo. 6163 -000154 



Mean 00018 1 



It now remains to deduce from the tables the ratios of the constants 

 for the different thermometers. 



The proper method of forming the equations of condition are as 

 follows, applying the method to the first series : 



Weight. 



4 21-25 C llt = 115-33 C l i\ 



4 255-80 C llt = 422-84 C, r, 



4 34 1 -05 C llt = 534-71 C t r. 



5 431-71 C llt = 653-49 C t i\ 



where (?, is the constant for Xo. 6166, C, is that for Xo. 6163, and 

 r is a constant to be eliminated. Dividing by C lt the equations can 



be solved for jw. The following table gives the results : 

 "t 



16 See Appendix to Thermometry, where it is finally thought best to reject the 

 value from No. 6167 altogether. 



