242 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



observation. The first experiment of this series cannot therefore 

 properly be used as a test of our equations. Similar considerations 

 apply with somewhat less force to the last experiment. By compar- 

 ing the temperatures and pressures of the three last experiments 

 with the observed relative densities, the reader may easily convince 

 himself that if we admit the substantial accuracy of the determina- 

 tions in the two first of these experiments (the second and third of 

 the series, which have the greatest weight), the last determination of 

 relative density 2.588 must be too small. In fact, it should evidently 

 be greater than the number in the preceditig experiment 2.645. 



If we confine our attention to the second and third expei'iments of 

 the series, the agreement is as good as could be desired. Nor will 

 the admission of errors of .152 and .120 (certainly not large in deter- 

 minations of this kind) in the first and fourth experiments involve 

 any serious doubt of the substantial accuracy of the second and third, 

 when the difference of weight of the determinations is considered. 

 Yet it is much to be desired that the relation expressed by (336), or 

 with more generality by (334), should be tested by more numerous 

 experiments. 



It should be stated that the numbers in the column of pressures are 

 not quite accurate. In the experiments of Deville and Troost 

 the gas was subject to the actual atmospheric pressure at the time of 

 the experiment. This A^aried from 747 to 764 millimeters of mercury. 

 The precise pressure for each experiment is not given. In the ex- 

 periments of Playfair and Wanklyn the mixture of nitrogen and 

 peroxide of nitrogen was subject to the actual atmospheric pressure 

 at the time of the experiment. The numbers in the column of pres- 

 sures express the fraction of the whole pressure wliich remains after 

 substracting the part due to the free nitrogen. But no indication is 

 given in the published account of the experiinents in regard to the 

 height of the barometer. Now it may easily be shown that a varia- 

 tion of j^^xs ill t.he value of p can in no case cause a variation of more 

 than .005 in the value of D as calculated by equation (336). In any 

 of the experiments of Playfair and Wanklyn a variation of more 

 than 30""" in the height of the barometer would be necessary to 

 produce a variation of .01 in the value of D. The errors due to this 

 source cannot therefore be very serious. They might have been 

 avoided altogether in the discussion of the experiments of Deville 

 and Troost by using instead of (336) a formula expressing the 

 relation between the relative density, the temperature, and the actual 

 density, as the reciprocal of the latter quantity is given for each ex- 



