ON THE MECHANICAL EQUIVALENT OF HEAT 377 



found as if we obtained the constants directly by comparison with the 

 air thermometer. 



The constants of 6163 can be found either by comparison with 6167, 

 or by direct comparison with the air thermometer. I shall first deter- 

 mine the constants for No. 6167. 



The constants C and t for this thermometer were found directly 

 by observation of the and 100 points; and we might assume these, 

 and so seek only for m. In other words, we might seek only to ex- 

 press the difference of the thermometers from the air thermometer 

 by a formula. But this is evidently incorrect, seeing that we thus 

 give an infinite weight to the observations at the and 100 points. 

 The true way is obviously to form an equation for each temperature, 

 giving each its proper weight. Thus from the first series we find for 

 No. 6167, 



Weight. Equations of Condition. 



4 = 6-147 C t , 



4 17 -427 = 15-685 C 1 930m, 



4 23-793 = 19-157 C t 1140m, 

 &c. &c. &c. 



5 100 =60-156 C t , 



which can be solved by the method of least squares. As t is unim- 

 portant, we simply eliminate it from the equations. I have thus 

 found, 



Weight. 



1 Nov. 14 (7 = 1-85171 m= -000217 



2 Nov. 20, 21 (7 = 1-85127 m= -000172 



Mean = 1-85142 m= -000187 



The difference in the values of m is due to the observations not being 

 so good as were afterwards obtained. However, the difference only 

 signifies about 0-03 difference from the mean at the 50 point. After 

 November 20 the errors are seldom half of this, on account of the 

 greater experience gained in observation. 



The ratio of C for 6167 and 6163 is found in the same way. 



Weight. 



1 Nov. 14 -0310091 



2 Nov. 20 -0309846 



Mean -0309928 



