OF ARTS AND SCIENCES. 109 



Determination of C and m. 



I shall first discuss the determination of these for thermometers 

 Nos. 61G3, G1G.3, and G1GG, as these were the principal ones used. 



As No. 6163 extended from 0° 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 

 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 

 determine the constants for No. G1G7. 



The constants C and ^ for this thermometer were found directly 

 by observation of the 0° and 100° points; and we might assume these, 

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

 express 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 ;m equation for each temperature, 

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

 No. 6167,— 



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

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

 found, — 



Weight. 



1 Nov. 14 G = 1.85171 m = . 000217 



2 Nov. 20, 21 (7=1.85127 m = .000172 



Mean C= 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. 



