BRIDGMAN. — MERCUEY UNDER PRESSURE. 357 



lowing paper. In calculating the compressibility from these two sets 

 of data, one for the water and the other for mercury, the method of 

 successive approximations was applied. The compressibility of water 

 was first calculated, assuming the compressibility of the mercury to be 

 constant at its initial value at atmospheric pressure. A curve was 

 then plotted giving the volume of water against pressure. From this 

 curve for water, an improved curve for mercury was calculated, from 

 which again a better curve for water was found. In practice it was 

 not necessary to carry the steps further than this. 



The relations connecting the compressibility of the water and the 

 mercury with the observed weights of mercury, etc., are given below. 



Notation. 



V = initial volume of Piezometer, 

 Fh,o= " " "water, 



KHg = mercury. 



Then r=rH,o+rHg. 



At'H^o = shrinkage per initial unit vol. of water at pressure under 

 consideration. 



Ai'Hg = " " " " ■' " mercury " 



consideration. 



Ai'Fe = " " " " " " steel " 



consideration; 



and in addition : 



in the upright position 



A Fng — vol. at atmos. pressure of mercury forced in 

 by the pressure in question, 

 in the inverted position 



AT'Hg = voL of mercury forced out, etc. 



A Fng is the same thing as the volume of the water forced in. The 

 corrected volume of the piezometer at any pressure is evidently 

 V-V.ArFe- It is a simple matter to verify the following equations: 



Upright position 



HjO J .- > 



Ar _ ^ ^ Hg + >^-^^'Fe - ^\o ^?'H,0 



' Hg + "^ ' Hg 



