have been calculated as given along with the diffusion-coefficients in the following table :

(1/M1+1/M2)3/{(M‚ß1)3/2 + (M1⁄2ß2)1⁄2}aD

are nearly constant, though showing on the whole a tendency to increase with the number of atoms in the diffusing molecules, as we already noted in connexion with 103B/(1+1C2/T) for the original six pairs of gases.

The last table can be greatly extended, thanks to the experiments carried out by Winkelmann for determining diffusion-coefficients according to Stefan's evaporation method founded on his equation marked (5) in the present paper. He has determined the rates of evaporation of a number of esters from C3H6O2 to C9H1802, and ethyl oxide, carbon disulphide, and benzene in air, hydrogen, and carbon dioxide at different temperatures, and has calculated the corresponding coefficients of diffusion.

In order to obtain the values of D273 it is necessary to obtain approximate values of C2 for use in the equation

Data = (213) 1+1C2/273

Dr

T

These can be calculated from equation (9) if we know C1 and Mẞ for the esters. The values of C1 can be obtained in the following manner :-In the paper on the Viscosity of Gases and Molecular Force it is shown that for compounds

Mẞ1C1102=21M27/2,

where is the virial constant of molecular attraction in the characteristic equation of the substance; values of M2l for a large number of bodies being given in the Laws of Molecular Force (Phil. Mag., March 1893) along with methods of calculating them for any body. As regards MB for the esters, I have found by determining ẞ that for CH2O2,

:

MB=29+17.5 (n-1)

approximately thus all the data are to hand for calculating C2 for each of Winkelmann's diffusing pairs.

Winkelmann's determinations include a number of isomers, as, for instance, propyl formate, ethyl acetate, and methyl propionate of the composition C4H8O2; and in the diffusioncoefficients about to be given I have taken the mean of the isomers in each case, so that, for instance, the mean diffusioncoefficient of the bodies just mentioned is given as the value for C4H8O2. When the broad principles have been established it will be time enough to take account of minor differences in the diffusion-coefficients of isomers. The following table contains the mean diffusion-coefficients obtained from Winkelmann's determinations at the temperatures of his experiments, and the values at 0° C. calculated by the last formula and the values of C2 just given.

Phil. Mag. S. 5. Vol. 38. No. 230. July 1894.

C

With these values of D at 273 the values of

(1/M2+1/M2)3/{(M11)3/2 + (M2ß2)/2}2D

can now be calculated as for the gases, with the following results (treating air as N2):

It will be noticed that with hydrogen and air at the lower members of the ester series and (C2H5)2O and CS2, the values are near to the 2 which was about the mean value for the gases, but that they increase steadily as the series is ascended; so that the result for vapours joins on continuously with that for gases, but shows a decided departure from our empirical result for gases that for temperatures near 0° C. the diffusioncoefficients have nearly the same relative values as if the molecules were forceless. But it should be remembered that the results for vapours are all calculated on the assumption that they obey the gaseous laws, and therefore that care should be taken not to give much weight to them till it is ascertained, either theoretically or experimentally, what is the effect on the diffusion-coefficient of such departure from the gaseous laws as vapours show.

To carry the subject to the most suitable point at which to leave it at present, it seems best to take all the values of

(1/M2+1/M2)3/{(M1ß1)3/2 + (M1⁄2ß2) 3/2}2D273

which have been given in this paper and divide them by the corresponding values of 1+1C2/273, using only the theoretical values of C2, calculated according to equation (9). In this way, according to equation (10), we ought for attracting smooth perfectly restitutional spherical molecules to get the constant 1/B273a the same for all pairs of substances; and the amount of departure from constancy will furnish a good measure of the present degree of incompleteness of the kinetic theory of diffusion, the chief cause of incompleteness being, in my opinion, the assumption of perfect restitutionality in each

individual collision.

Values of

(1/M2+1/M2)3/{(M11)+/2+(M2ß2)/2}2D(1+1C2/273)=1/B273}.

Winkelmann's values of the diffusion-coefficients for the vapours of water, the alcohols, and fatty acids have not been discussed in the present communication on account of the exceptional nature of these substances, but they will doubtless be of value when the time is ripe for a full discussion of the physical reasons of their exceptional behaviour.

Melbourne, January 1894.

II. Coloured Cloudy Condensation, as Depending on the Temperature and the Dust-contents of the Air. By CARL BARUS *.

[Plate V.]

1. N the "koniscope" Mr. Aitkent has expressed the given sample of air, in terms of the colour, or of the intensity of colour, or of the amount of exhaustion necessary to produce a given colour, when the cloudy condensation is produced by sudden expansion of the gas in a suitable tube, containing enough moisture to saturate the air. The importance of temperature is pointed out, but not evaluated. Mr. Aitken prefers to make the

* I have availed myself of the permission of the Editors of this Magazine to reproduce here a condensed account of certain parts of a forthcoming Bulletin of the U.S. Weather Bureau, believing the subject to possess some general physical interest.

† Aitken, Proc. Roy. Soc. London, li. p. 425 et seq., 1892. For a review of the earlier history of the subject (for which there is no space here) the reader is referred to my papers in the American Meteorological Journal,' ix. p. 488, 1893; x. p. 12, 1893. On reviewing my résumé I find that the tribute there paid to the breadth and thoroughness of Mr. Aitken's researches (many of which I have since repeated) is inadequate, I therefore feel bound to make this acknowledgment.

estimation in terms of the colour-intensity of the blue, and the apparatus is graduated by comparing it with the direct dustcounter. Based as this apparatus is on colour discriminations, it is not adapted to give more than a few steps of dustcontents, and Mr. Aitken chiefly recommends it for qualitative purposes, such, for instance, as may present themselves in sanitary work.

2. During the course of my experiments on the thermal distribution in steam-jets, I had frequent occasion to note the actuating steam-pressure at which the intense blue-violet field of my colour-tube merges into opaque, eventually to reappear (pressure increasing) as an orange-brown field of the first order. It struck me that here was a sufficiently sharp criterion for fixing a value of pressure depending in the given apparatus only on the temperature and the dustcontents of the inflowing air. In other words, for a given kind of air, and at a given temperature, there are two welldefined pressures at which colour (blue and yellow) vanishes into blackness. If the kind of air remains the same while its temperature varies, the paired values of pressure will also vary markedly, so that the margins of the opaque field may be mapped out in a diagram in which pressure is expressed in its dependence on temperature. It is the chief purpose of the present paper to show the character of this diagram, and to indicate the manner in which the positions of the loci vary, when the dust-contents of the inflowing air are also varied. Incidentally I will endeavour to ascertain the more immediate cause of the opaque field, and to see whether the water molecules may not themselves become nuclei of condensation, §§ 15, 16.

3. Apparatus.-Full details of the necessary apparatus is given in Pl. V. fig. 1, where the colour-tube is shown at AA, and the method of varying the temperature and dustiness of the inflowing air is shown at E, D, F. The colour-tube is identical in form with the apparatus described in an earlier paper*. I need only call to mind here that the steam issues at the jet j, from a nozzle about 16 cm. in diameter, and that the tube AA is about 50 to 60 cm. long, and, in common with the air-hole C, about 5 cm. in diameter. The glass plates g and a are kept clear by moistening with a solution of caustic potash, and the mirror M reflects skylight through the tube. Mixed steam and air escape at B, and provision is made (not shown) for screening off extraneous light from g, the window through which the colour observations are made.

*Barus, Amer. Meteorolog. Journal, ix. p. 488 (1893).