EXPANSION OF LIQUIDS. 



81 



and A,, or the expansion of unit volume at for a rise of t can be 

 found from H and H . 



As there were several details in this method open to criticism, 

 Regnault, in making a redetermination, introduced some modifications 

 in the apparatus. He carried out a very extensive series of experiments, 

 which have till recently been the standard ones on this subject. 



He arranged the apparatus in two forms. 



The general principle of one arrangement may be understood from 

 Fig. 22. The two vertical tubes AB, A'B', are united by the hori- 

 zontal crosspiece AA' with a small hole at 0, so that at that level 

 the mercury is exposed to 

 the atmospheric pressure. 

 The lower crosspiece is 

 broken in the middle by 

 the insertion of the in- 

 verted U tube BCD', 

 connected with the re- 

 servoir M, of compressed 

 air, the pressure being 

 adjusted so that the 

 mercury rises to the 

 levels 00' in the two 

 arms of the U. The 

 temperature of A'B' is 

 kept constant throughout 

 by surrounding it with 

 water running from the 

 mains, while that of AB 

 may be raised to any 

 desiredpoint by surround- 

 ing it with a bath of oil 

 heated by a furnace. The 

 temperature of AB is 

 given by an air thermo- 



FIG. 22. Diagram of Regnault's First Apparatus 

 for finding the Expansion of Mercury. 



meter. The heights AB, 



A'B', CD, and C'D' are 



all measured at each 



temperature by a cathetometer, and from these the expansion may be 



found as follows : 



The pressure at A is equal to that at A', both being equal to the 

 atmospheric pressure through the communication with the atmosphere at 

 o. Also the pressure at is equal to that at 0', both being equal to the 

 air-pressure in the reservoir M. 



Then, pressure at - pressure at A = pressure at C' 



pressure at A' (1) 



Expressing these differences by the usual hydrostatic formula, we 

 obtain an equation giving the expansion of the mercury. For, let H, H' 

 be the heights of AB, A'B', let h, h' be the heights CD, C'D', and let 

 T, T' be the temperatures of AB, A'B' ; and let us, to simplify matters, 

 suppose the temperature of CD, C'D', to be T'. Let p, p be the densities 



