M. Bessel's Correction of the Thermometer. 309 



210°. By this assumption the lower parts of the scale were 

 determined by the upper ones, the latter being supposed cor- 

 rect for the first approximation; the lower ones, thus approxi- 

 matively determined, were again compared to the upper ones, 

 and these latter thus likewise approximatively determined! 

 These approximate values were again employed to determine 

 the lengths of the columns of mercury, and the former calcu- 

 lation was repeated, by which means a second approximation 

 was obtained, which was already so near, that a third one o- a ve 

 no sensible differences. In this manner, the following values 

 of <px were deduced, which agree with the single readino-s to 

 such small quantities as are within the limits of the uncertainty 

 of the readings themselves. 



I determined the freezing point bv imbedding the thermo- 

 meter in pounded ice, and found it, "by the mean of very nu- 

 merous experiments instituted in various manners, but almost 

 perfectly agreeing in their results, = 32°-53 : for ascertaining 

 the point of boiling water, the height of the barometer (the 

 temperature of which is that of melting ice) beino- =o™6 the 

 apparatus proposed by Cavendish was employed; and I found 

 it by the mean of different experiments =212°-71. These 

 results, and the above table for <?x t give, therefore, e + <a e= 

 32°-86 and 5 + p 5 = 212°-79, and hence 



= -0 o -873 + Jg 3 (x4-^.) 



The corrections to be applied to the readings of the ther- 

 mometer resulting from this formula are as follows : 



