352 HENRY A. EOWLAND 



t * 

 (c.) Relation of the Mercurial and Air Thermometers ,J* 



' ' & 

 1. GENERAL AND HISTORICAL REMARKS 



* .-* 

 Since the time of Dulong and Petit, many experiments Have been 



made on the difference between the mercurial and the air thermometer, 

 but unfortunately most of them have been at high temperatures. As 

 weight thermometers have been used by some of the best experimenters, 

 I shall commence by proving that the weight thermometer and stem 

 thermometer give the same temperature; at the same time, however, 

 obtaining a convenient formula for the comparison of the air ther- 

 mometer with the mercurial. 



For the expansion of mercury and of glass the following formulae 

 must hold : 



For mercury, V V (I + at +~W + &c.} ; 

 " glass. V = V\ (1 + at + /3f + tic.} ; 



In both the weight and stem thermometers we must have V = V. 



'0 "i ! 7 ! /vTo ! ~p ' V -^ L*~V I X> ~P O6, ). 



1 + at + pt + <XC. 



where V and V are the volumes of the glass and of the mercury 

 reduced to zero, and t is the temperature on the air thermometer. 

 The temperature by the weight thermometer is 



P -1 



P7 



where P , P , &c., are the weights of mercury in the bulb at C., 

 t C., &c. 



Now these weights are directly as the volumes of the mercury at 0. 



/. -p = 1 + At + Bt* + &c., 

 seeing that V is constant. 



... 7'=100 ra ^ +B/ ' + * <; - 



+ &c.' 



In the stem thermometers we have V , the volume of mercury at 0, 

 constant, and the volume of the glass that the mercury fills, reduced 

 to 0, variable. As the volume of the glass T' is the volume reduced 

 to 0, it will be proportional to the volume of bulb plus the volume of 

 the tube as read off on the scale which should be on the tube. 



