BRIDGMAN. — A SECONDARY MERCURY RESISTANCE GAUGE. 237 



under increasing and decreasing pressure, to determine freedom from 

 hysteresis, are given in Table II. Here the displacements of the slider 

 in cm. are tabulated against pressure, calculated from the corrected 

 dimensions of the absolute gauge as described in the first part. The 

 displacements under increasing or decreasing pressure agree within 

 the limits of error of reading the position of the slider. Another com- 

 parison of R 9 against the same absolute gauge, as also a comparison 

 against another absolute gauge, led to the same result. These com- 

 parisons were taken to afford sufficient proof of freedom from hyste- 

 resis of the mercury resistance in the soft Jena glass capillary within 

 errors of yV per cent. 



Having established the reproducibility and freedom from hysteresis 

 of the mercury, we pass to the more important results to be obtained 

 from the comparison with the absolute gauge, namely the final transla- 

 tion of the indications of the mercury gauge into kgm. per cm. The 

 data used for this were those obtained from the two comparisons of 

 R 9 against absolute gauge No. 1, and the one comparison against 

 gauge No. 2. The results of these comparisons have already been 

 given in Part I of this paper, where it appears that the two absolute 

 gauges do not differ on the average so much as ^ per cent from the 

 mean. The average of these two comparisons is taken as the true 

 value and is used in the following computations. 



If the change of resistance is to be used as a practical standard of 

 pressure, some empirical formula is desirable connecting the change 

 of proportional resistance with the pressure. In the following, two 

 formulas will be given, the first expressing the change of resistance 

 in terms of the pressure, and the second, which will be more useful 

 in practice, expressing pressure in terms of observed change of 



A R 

 resistance. -=— will be abbreviated by p, where A R is the ob- 

 H 



served change of the resistance in the soft envelope of Jena glass 

 No. 3880 a, and R Q the initial resistance measured in this envelope. 

 Then p is some function of the pressure, approximately linear. A 

 number of forms of this function were tried, it being desirable for 

 convenience in computation to choose such a form that the number of 

 empirically determined constants is small. It was at once obvious 

 that the ordinary power series representation of the relationship was 

 totally inadequate, at least five and probably more arbitrary con- 

 stants being necessary to obtain tV per cent agreement over the 

 entire range. Several other forms of power series tried, with frac- 

 tional instead of integral exponents, were better, but not sufficiently 

 approximate. Several exponential forms of the type p = ap 10 p , 



