BRIDGMAN. — A DETERMINATION OF COMPRESSIBILITIES. 277 



The compressibility of the steel envelope has already been deter- 

 mined, and hence the proportional change of volume of the mercury 

 can be corrected and the true compressibility found. It was assumed 

 that 



■— - = a + bp + cp 2 , 



and the constants were calculated by least squares. The results are 

 shown in Table V. The constant a has the same significance as in 

 the case of the steel and aluminum rods, the constants b and c alone 

 having significance for the mercury itself. The values found were 



a = 0.001252, 



b = 3.699 X 10- 8 , 



c = -1.985 X 10"". 



The compressibility at low pressures is b, 3.70 X 10~ fl compared with 

 3.80 X 10 -6 , found by Amagat, de Metz, and Richards, and 3.7 X 10 -6 

 found by Carnazzi. It is to be remarked, however, that the purpose of 

 this investigation was not to find the compressibility at low pressures, 

 only two observations being made at less than 800 kgm. Both the di- 

 mensions of the piezometer and the temperature changes make the low 

 pressure values of this determination doubtful. There is, moreover, 

 obvious on inspection of the table a tendency for the low pressure 

 values to lie below the values given by the formula. This would in- 

 crease the initial compressibility. The experimental error is sufficient, 

 however, to make illusory a more accurate determination of the initial 

 b by passing a curve of the above type through the lower values only. 

 The probable error of a single observation, discarding the first, is 

 J per cent at the highest pressure. The probable percentage error 

 of values determined by the formula is 0.25 per cent, discarding the 

 lowest value, or 0.18 per cent, discarding the lowest two. 



The departure of the compressibility from constancy is shown by the 

 constant c, which is very small, in fact much smaller than has been 

 found by either Carnazzi or Richards. It may be found from the above 

 formula that the instantaneous compressibility at 2700 kgm. has de- 

 creased to 3.58 X 10 - * from its initial value of 3.70 X 10 -6 . Carnazzi 

 finds the average compressibility between 2500 and 3000 to be 

 3.3 X 10- 6 against 3.7 X 10 -6 between and 500. Richards finds a 

 decrease of compressibility from 3.80 X 10 -6 to 3.64 X 10 -6 over a 

 pressure range of 500 kgm. However, Richards himself recognized 

 the possibility that his pressure unit might be in error at the higher 



