OF ARTS AND SCIENCES. 27 



the stem before closing the open ends. The theory of the instrument 

 is the same in either case, but in our description we will assume that 

 the index has been set for measuring high temperatures, as shown in 

 our figure. 



As the instrument is a differential thermometer, its accuracy de- 

 pends on keeping the stem at a constant and known temperature ; 

 and from this constant temperature the observed temperatures are 

 deduced. AVhen the thermometer is held in a horizontal position, and 

 the stem can be protected from the neighboring sources of heat, it is 

 sufficient to place a standard mercury thermometer at the side of the 

 stem ; but it is alwa)'s better, and generally necessary, when the stem 

 is in a vertical position over the source of heat, to surround the stem 

 with a jacket, through which circulates a stream of water of known 

 temperature. This temperature we will call the temperature of refer- 

 ence, and represent by T°. In order now to determine the value in 

 centigrade degrees of the division of the instrument, we place it in the 

 position in which we propose to use it ; and when the two ends are at 

 the same temperature, we observe the position of the two ends of the 

 index on the graduate scale. AVe can now easily find from the weights 

 obtained before closing the instrument, first the weight of mercury 

 which would fill the bulb and stem up to the index, which we call W ; 

 and, secondly, the small weight of mercury which would fill one 

 division of the stem which we will call w. "We have also, by obser- 

 vation, the number of division on the stem above the index. This 

 number, which we count from the closed end of the stem, we will 

 represent by N'. 



Assume now that the bulb and stem up to the index is immersed 

 in a medium which has the temperature, T'. The index moves, and 

 in its new position let N' represent the number of division on the stem 

 above the index. We can now easily deduce the following values : — 



rrhrr = the ratio of the tension of the confined air at T'° and T°. 



N' 



^ — N' = the number of division through which the index moved. 



W + (N N') IV 



— — = the ratio of the volumes of the air in the bulb at 



T° and T'°, independent of the expansion of the glass. 

 W+(N—N')w ^j _^ j-yT_ -yT,-j ^^ _ g^j^g j.^^Jq^ allowing for 



expansion of glass. 



Then, as we can easily deduce from the laws of Mariotte and 

 Charles : — 



