Page:Scientific Papers of Josiah Willard Gibbs.djvu/213

The determinations of MM. Deville and Troost are satisfactorily represented by the equation

$\log _{10}{\frac {(3.178-D)^{2}p_{at}}{2(D-1.589)}}=9.47056-{\frac {3118.6}{t_{c}+273}},$

(336)

which gives$D=3.178+\Theta -{\sqrt {\Theta (3.178+\Theta )}},$

where$\log _{10}\Theta =9.47056-{\frac {3118.6}{t_{c}+273}}-\log _{10}p_{at}.$

In the first part of the following table are given in successive columns the temperature and pressure of the gas in the several experiments of MM. Deville and Troost, the relative densities calculated from these numbers by equation (336), the relative densities as observed, and the difference of the observed and calculated relative densities. It will be observed that these differences are quite small, in no case reaching .03, and on the average scarcely exceeding .01. The significance of such correspondence in favour of the hypothesis by means of which equation (336) has been established is of course diminished, by the fact that two constants in the equation have been determined from these experiments. If the same equation can be shown to give correctly the relative densities at other pressures than that for which the constants have been determined, such correspondence will be much more decisive.

$t_{c}$	$p_{at}$	$D$ calculated by eq. (336).	$D$ observed.	diff.	Observers.
26.7	1	2.676	2.65	-.026	D. & T.
35.4	1	2.524	2.53	+.006	D. & T.
39.8	1	2.443	2.46	+.017	D. & T.
49.6	1	2.256	2.27	+.014	D. & T.
60.2	1	2.067	2.08	+.013	D. & T.
70.0	1	1.920	1.92	.000	D. & T.
80.6	1	1.801	1.80	-.001	D. & T.
90.0	1	1.728	1.72	-.002	D. & T.
100.1	1	1.676	1.68	-.008	D. & T.
111.3	1	1.641	1.65	+.004	D. & T.
121.5	1	1.622	1.62	-.002	D. & T.
135.0	1	1.607	1.60	-.007	D. & T.
154.0	1	1.597	1.58	-.017	D. & T.
183.2	1	1.592	1.57	-.022	D. & T.
97.5	1	1.687			P. & W.
97.5	${\tfrac {10450}{26397}}$	1.631	1.783	+.152	P. & W.
24.5	1	2.711			P. & W.
24.5	${\tfrac {18090}{42529}}$	2.524	2.52	-.004	P. & W.
11.3	1	2.891			P. & W.
11.3	${\tfrac {9265}{44205}}$	2.620	2.645	+.025	P. & W.
4.2	1	2.964			P. & W.
4.2	${\tfrac {6023}{35438}}$	2.708	2.588	-.120	P. & W.

Messrs. Playfair and Wanklyn have published^[1] four determinations of the relative density of peroxide of nitrogen at various temperatures

1. Transactions of the Royal Society of Edinburgh, vol. xxii. p. 441.