OF ARTS AND SCIENCES. 



101 



As the error is so small, I have not thought it worth while to entirely 

 recalculate the tables, but have calculated a table of corrections as 

 follows, and have so corrected them : — 



TABLE IX. — Table of Corrections. 



T= T> {1 -f 373 (b' m - b m ) - (273 + T) (b> - b)}. 

 T— T' {1 — .000858 + (273 -f T 1 ) (b — b')}. 



T = .99975 T' approximately between and 40°. This last is 

 true within less than T ^j^ of a degree. 



The two bulbs of the air tbermometer used were from the same 

 piece of glass tubing, and consequently had nearly, if not quite, the 

 6ame coefficient of expansion. 



In the reduction of the barometer and other mercurial columns to 

 zero, the coefficient .000162 was used, seeing that all the scales were 

 of brass. 



In the tables the readings of the thermometers are reduced to 

 volumes of the tube from the tables of calibration, and they are cor- 

 rected for the pressure of water, which increased their reading, 

 except at 0°, by about 0°.01 C. 



The order of the readings was as follows in each observation : — 

 1st, barometer; 2d, cathetometer; 3d, thermometers forward and 

 backward ; 4th, cathetometer ; 5th, barometer, &c, — repeating the 

 same once or twice at each temperature. In the later observations, 

 two series like the above were taken, and the water stirred between 

 them. 



The following results were obtained at various times for the value 

 of a with the first bulb : — 



