52 HEAT. 



Let us suppose that at first the whole instrument is placed in melt- 

 ing ice at temperature 6 , M being filled with mercury and the pressure 

 being so adjusted that the levels in G are the same. Now let the 

 temperature of Vj rise to 0, M and V 2 being still at . Run out 

 mercury from M till the equality of pressures in G is restored. The 

 volume of air expelled into M is determined by the volume M of the 

 mercury run out. Let the initial pressure be P, the final pressure be 

 P'. The two are nearly equal, so that the constancy of mass of the 

 gas is expressed by 



PV 



2-z- = constant. 

 V 



Let Vj expand to Vj', v l and v% to v^ and v 2 ', and let - be the 



t> 



mean of the reciprocals of the temperatures of Vj', v 2 '. We have for the 

 bulb and manometer 



FV,' F< FM PV, Pv, 



!_ 4. . L j ij 1 



e t e " e + e 



and for the other system Y 2 and v 2 , 



FV PV PV. 



e~ ' t 



Now making V 2 = Vj, v 2 = v lt and v% Vj', we may equate the two 

 left-hand members, and P' divides out so that 



or 



The thermometer is easily handled and gives exceedingly accurate 

 and consistent determinations of temperature. One advantage of the 

 automatic compensation is that the connecting tube may be of consider- 

 able length and of flexible material. 



