VAPOR-DENSITIES. 385 



of the total and the partial pressures. The numbers here given 

 are obtained by setting the total pressure, which was that of the 

 atmosphere at the time of the experiment, equal to 760 mm . The 

 effect of this inaccuracy upon the calculated densities would be 

 small. Two of these observations agree closely with the formula; 

 and two show considerable divergence, but in opposite directions, 

 and these are the two in which the quantities of peroxide of nitrogen 

 were the smallest. The differences appear to be attributable rather 

 to the difficulty of a precise determination of the quantities of 

 nitrogen and of vapor, than to any effect of the one upon the 

 other. 



Special interest attaches to experiments at the same or nearly the 

 same temperature but different pressures. For with experiments at 

 the same temperature, the constants of the formula which are deter- 

 mined by observation are reduced to one, so that the verification of 

 the formula by experiment cannot possibly be regarded as a case 

 of interpolation. It is not necessary that the temperatures should 

 be exactly the same, for it will be conceded that the formula 

 represents the actual function well enough to answer for adjusting 

 slight differences of temperature ; but it is necessary that the 

 range of pressures should be considerable in order that the differ- 

 ences of density should be large in proportion to the probable 

 errors of observation. But the pressures must not be so low that 

 accurate determinations become impossible. 



In the experiments of Naumann we see some fair correspondences 

 with the formula in respect to the influence of pressure, especially 

 in the first four experiments of the list, where, if we average the 

 results of the third and fourth experiments, as is evidently allowable, 

 the observed values follow very closely the fluctuations of the cal- 

 culated, extending from 2*26 to 2*41. In other cases the agreement 

 is less satisfactory. The circumstance that the experiments at the 

 two highest pressures (301 and 279 mm ) give results exceeding the 

 calculated values considerably more than any other experiments at 

 adjacent temperatures may seem to indicate that the densities increase 

 with the pressures more rapidly than the formula allows; but the 

 differences are not too large to be ascribed to errors of observation, 

 and the experiment at the lowest pressure (84 mm ) also shows a large 

 excess of observed density. 



A much more critical test may be found in the comparison of 

 Naumann's experiments with those of Deville and Troost, notwith- 

 standing the interval of about 4 of temperature. The formula 

 requires that a diminution of pressure from 760 to 101 millimeters 

 shall reduce the density from 2'676 at 26'7 to 2'26 at 22'5, not- 

 withstanding the effect of the change of temperature. Experiment 

 G. i. 2 B 



