Temperatures above the Boiling-point of Mercury. 429 



serve as starting-points, by which the graduation may be from 

 time to time adjusted. 



If one wished to extend the graduation below the zero-point 

 down to —100°, it would be necessary to fix upon some other 

 determinate point, situated as low as possible ; we should thus 

 possess a far more accurate instrument than the alcohol-ther- 

 mometer generally employed for low temperatures. 



An instrument constructed in the foregoing manner gives, 

 above 300°, indications at least as exact as those of a mercurial 

 thermometer, especially if one considers the amount of correc- 

 tion required by the latter if a considerable portion of the column 

 happens to be unimmersed in the heated space. The errors due 

 to the different expansions of different kinds of glass are equally 

 great in the two instruments. M. Regnault's experiments have 

 shown that even in the best-constructed mercurial thermometers 

 the error produced by this expansion may amount to 5° or 6° at 

 temperatures above 300°. 



The indications of the new thermometer present another ad- 

 vantage, namely that they correspond to those of the air-ther- 

 mometer ; at 350° the indications of the latter instrument differ 

 from those of the mercurial thermometer by 10° at least. 



The new thermometer is especially useful for temperatures 

 beyond 330° ; for the greater number of mercurial thermometers 

 disagree among themselves above that point. When properly 

 constructed, its indications are seldom more than 2° or 3° in 

 error, even at a temperature of 500°. 



III. Theory of the Instrument. 



The trustworthiness of the instrument depends upon two fun- 

 damental conditions, namely, the empirical construction of a 

 curve of temperatures by means of fixed points experimentally 

 determined, and the relatively very minute quantity of air con- 

 tained in the capillary portion of the instrument as compared 

 with the amount of air in the cylindrical reservoir. 



In fact the new thermometer may practically be regarded as 

 a reservoir of air of invariable capacity. In such a reservoir the 

 variations in the pressure are proportional to the variations in 

 the temperature. Let V be the volume of the gas at 0° and 

 under an initial pressure H . If, now, the temperature is t, the 

 pressure becomes H + h } and we have 



V =V (l + «/) 



and then , , h 1 



1-f tt =l+at; 



H + A' 

 H, 



L o 



