HEAT. 



of mercury at T, T', AT, A^ the expansions of unit volume at 0, ou 

 raising the temperature respectively to T and T'. 



Then Hp - hp' = H>' - tip from ( 1 ) 



or Hp = (H.' + h-ti)p 



But if p is the density at 0, the volume of the same mass being 

 inversely as the density, we have 



P 1 P' 1 



Po 1+A T 



Then 



H 



1 + A T 



or 



H 



(2) 



Now Ajv is in practice only small, and we may take an approximate 



Hot 



H' 



fold 



FIG. 23. Regnault's Second Apparatus for the Expansion of Mercury. 



value for it without seriously affecting the value of A T . Then (2) gives 

 us Aj in terms of known and measurable quantities. 



Regnault also used a method very nearly the same as that of Dulong 

 and Petit, which will be understood from Fig. 23, the U tube in the 

 lower crosspiece being replaced by a flexible iron tube, so that the two 

 halves could expand independently. 



The great advantages over the arrangement of Dulong and Petit 

 consisted in the maintenance of known fixed temperatures in each 

 vertical part and in the greater accuracy of measurement of the vertical 

 heights, attained by bringing the two levels close together. 



It will be easily seen that in the arrangement of Fig. 23 

 H h H' + h' 



1+V 



or 



i+V 



H 



A T ,). 



