84 PROCEEDINGS OF THE AMERICAN ACADEMY 



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

 weight thermometers have been used by some of the best experi- 

 menters, 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 

 thermometer with the mercurial. 



For the expansion of mercury and of glass the following formulae 

 must bold : — 



For mercury, V = V (1 -f- a t -f b f- + &c.) ; 

 « glass, V = V' (1 -f a t -f jS t 2 + &c). 



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



where V' and F 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 



T = 100 £Z^L £» = 100 -p , 



Pioo 



where P , P„ &c. are the weights of mercury in the bulb at 0° C, 

 t° C, &c. 



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



.-. §>= 1 + At + Bt*+ &c, 



seeing that V is constant. 



A t + B t n - + &c. 



T= 100 



100 4 + (100) 2 £ + &c. 



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

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

 to 0°, variable. As the volume of the glass V' n 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. 



... r=ioo ( ^- ( ^ = ioo<^' 



(Kg, 



