temperature and pressure at which the colours disappeared noted on cooling. The mercury-thermometer is scarcely sensitive enough for such observations, and the temperatures of the diagram are probably too high. I have therefore lumped all my observations between Feb. 10 and 23, 1893, in this chart, seeing that the phenomenon as a whole is well represented.

7. In the following work, however, the apparatus, Plate V. fig. 1, was used, with the phosphorus-tube closed up and the phosphorus removed. Great care was taken to wait for stationary temperatures, and about five (or more) steps between 10° C. and 40° C. were selected for observation.

The first set of experiments was made on Feb. 23, the chart, fig. 3, curve A being obtained in the morning, and fig. 4 in the afternoon. The day was cold, with snow covering the ground. The blue-opaque curve, A, fig. 3, virtually reproduces fig. 2; but the curve, fig. 4, differs from it inasmuch as the tangential angles in the latter case are steeper, so that the locus is less curved and rises higher than in figs. 2 or 3. In all cases yellow-opaque lies above blue-opaque. I was at first inclined to refer this to differences of the vanishing standard, believing the two curves to contain consistent observations, but differing from each other for reasons purely subjective. Whether or not this is the case can only be found by comparison with succeeding series of observations, as will presently be seen. Taking the observations at their face value, the indication is less dust for the afternoon than for the morning. The curve P found for artificially dusty air will be described below (§ 11).

8. The next series of observations were made on Feb. 27 (cloudy), 28 (rain), and on March 2 (clear). There was but little difference in the respective loci of the data except that on the latter day the asymptote was somewhat below the position for the other days (see chart, Plate V. fig. 5). The common asymptote takes a mean position (pressure, p=43 cm.) between the corresponding values of figs. 2 and 3 (p=42 cm.) and fig. 4 (p=48 cm.).

9. On March 3, however, the asymptote rose again to the value p=46 cm. The weather was cloudy, antedating the storm of March 4, 1893. Two series of observations were made.

Finally, the results of March 6, 8, 10 agree in character with fig. 5; while during the intermediate date, March 7, the asymptote fell to the lower position p=42 cm. These

* The observations FF in fig. 3 refer to filtered air and will be described in § 14.

figures, as a whole, give some evidence in favour of an oscillation of the asymptote with the dust-contents of atmospheric air. The observed interval of oscillation is within about 8 cm. of mercury pressure, but usually much below this.

10. General character of the Loci.-Resuming the remarks of §6, it is seen that when the asymptotes are high, the loci as a whole show less curvature and the points between 200 and 30° C. tend to fall below the corresponding points for low asymptotes. I have endeavoured to bring the whole phenomenon into a convenient equation, in which temperature and dust-contents might appear as two variables by which the contours (pressure) of the margin of the opaque field (figs. 2 et seq.) are conditioned. The invention of a single form in which both the blue-opaque and the yellow-opaque margins are contained is more difficult than the fitting of a separate form for each curve, and I have not been fully successful in any case. Cumbersome equations, or such as lead to involved computations, are of little interest for the present purposes, where the object sought is merely a terse and convenient epitome of the very large number of isolated observations which go to make up each of the curves in question.

Let p be the steam-pressure actuating the jet, and t the temperature of the air into which the jet is discharged, and let A, B, C, n be constants to be presently discussed. Then

The quantity (p-B) in (1) is always to be taken as a numeric, i. e. positively; otherwise imaginary results are encountered. Suppose now this equation is tested by the data of fig. 5, as these fairly represent a mean case. Then p=0, t=A=9, by observation ;

p=B, t=∞, or B=43, the height of the asymptote above the abscissa;

p = ∞, t=∞.

Hence the yellow-opaque margin, lying quite above p=B =43, corresponds directly to equation (1); whereas the blueopaque margin, lying quite below p=B=43, corresponds to (1) with (p-B) replaced by (B-p). Furthermore, while in the yellow-opaque branch p increases from 43 cm. to ∞, t passes through a minimum value. It is, therefore, necessary to inquire the position and character of this uncalled for singular point. Let equation (1) be differentiated, remembering that t=0 corresponds to p=-, and therefore does not

enter the present problem, and that B=p has already been Then the pressure pm, corresponding to the

disposed of.

minimum temperature tm in question, is found to be

and the somewhat more involved expression of tm is found from equation (1).

With these preliminaries, the remaining constants C and n are then easily enough, though somewhat tediously, obtained from the observations making up fig. 5, by trial. The results are as follows:

:

A=9; C=0·013; n=0.35; B=43. Steam-pressures, p, in cm. of mercury; air-temperatures, t,

Blue-opaque. * Minimum. Yellow-opaque.

This curve, equation (1), has been inscribed in fig. 5, to show the grouping of the observations around it. The minimum is marked at a (tm=17.4° C., pm=66.2 cm.). Throughout the extent of the figure, it unites two sufficiently flat curves to fairly represent the observations; for this part of the margin, from its exceedingly steep ascent, cannot be traced with precision.

As a whole, therefore, equation (1) has reproduced the complete phenomenon surprisingly well, both as regards the blue-opaque (AB) and the yellow-opaque (BC) margin of the opaque field. No doubt, better agreement could be had on further trial, particularly by varying the point of intersection with the abscissa, t=A. I shall not, however, do this, since in the present paper the chief datum is the height of the common asymptote (p=B) above the abscissa. It is this parameter which expresses the dust-contents of the air, and which fortunately may be obtained without computation by the direct observations presently to be more fully specified.

11. Artificially Dusty Atmospheres.-To interpret the above data it is necessary to increase the dust-contents of the normal

atmosphere artificially, utilizing the tube F, fig. 1, containing phosphorus. The results for this case are not without complexity, but the character of the effect produced is obvious at once it takes but a trace of the phosphorus-tainted air to make the field permanently opaque at all pressures and temperatures not unreasonably high. In other words, the tendency is to drop the blue-opaque curve of the above figures into coincidence with the abscissa. One would surmise that at least the asymptotic portion of the yellow-opaque curve would likewise drop to the abscissa, and this is actually the case, as will be shown presently. By allowing the discharge from F to take place into E through a glass tube only a few millimetres in diameter, while the air-tube C is fully two inches in diameter, I was able to dust the air sufficiently to obtain at least the approximate contours of the corresponding relation of steam-pressure and air-temperature. The data are inscribed in fig. 4, and together they make up the curve P near the axis of temperature. Thus the striking potency of even traces of dust is well exhibited.

Clearly the rudimentary curve P is a member of the same family to which AB belongs, and it is therefore obvious that the whole field between B and the abscissa is a region of temperature and pressure loci *, each of which corresponds to a particular value of dust-contents. Since, therefore, the accuracy with which the point can be located at any (mean) temperature is about 1 cm., the apparatus ought to register about 40 degrees of dust-contents between normal atmospheric air and the artificial mixture stated. On this scale the variation of the dust-contents of normal air † lies in the interval between 40 cm. and 50 cm. of mercury, remembering that the height of the asymptote (virtually reached at 28° to 30°) is taken for registry.

12. To bring out the conditions more fully, however, it is necessary to make supplementary tests both with phosphorus and with filtered air.

If the basket of phosphorus is placed in the tube E (fig. 1)

* Probably the best method of actually mapping out these curves will consist in using nozzles of different degrees of smoothness. By mere haphazard drilling and polishing of such nozzles, I obtained curves between asymptote 20 cm. and asymptote 50 cm. That these curves will be identical with the corresponding dust-curves is made probable by $16

below.

+ Supposing that the possible errors have been correctly apprehended. In experiments made throughout the entire month I was surprised that an apparatus so sensitive to artificial dust should show such slight mean variations of the dust-contents of atmospheric air from day to day. Witness the above curves.

near its mouth d, where the air-temperature (in winter) is near the freezing-point, no effect is produced. Thus at 21°-22° the blue-opaque margin was at 41-42 cm., showing that the oxidation of phosphorus at zero is relatively negligible in spite of the current of air.

If, however, the same phosphorus be placed in the tube EC at i, somewhere between the point of confluence and the colourtube, and where the temperature is say 20°, then it is actually possible to obtain the yellow of the first order at steam-pressures less than 1 cm. Thus at 19°, the yellow-opaque margin was at 1.2 cm., and the colour persisted with increasing brilliancy at all pressures above this.

For temperatures greater than 20°, the tube is yellow at all pressures until eventually above 35° all colour vanishes for want of supersaturation.

For temperatures below 20°, the tendency is to produce opaque fields. Thus at 15° the tube is opaque at all pressures above a few millimetres.

The explanation of this somewhat puzzling behaviour is this at any given admissible temperature, the effect of phosphorus dust is a change of the colour of the field in the direction from blue through opaque to yellow in proportion as more dust of the given kind is added. Again, the dustcontents of the air passing over a given lump of phosphorus decreases both with the rapidity of the current and with the degree of cold. Hence at higher temperatures than 20° brilliant brown-yellow fields are the usual occurrence when the phosphorus lies in the air-tube i C. If withdrawn from the air-tube and so circumstanced that its exhalation is diluted with much air (tube F, fig. 1), then any colour may be produced, depending on the degree of dilution. On the other hand, below 20° the oxidation takes place more and more slowly, so that only very gentle currents of air can carry off enough dust to produce a yellow field. For strong currents in C there is a double source of dilution, and opaque fields are the rule. In other words, the air now approaches the state AB in fig. 4, so far as dust-contents are concerned.

I have entered into this subject at length because of its important theoretical bearing, seeing that it is necessary to disentangle a series of involved relations.

13. In fig. 6 (diagram), the pair of curves ABC indicates the margin of the opaque field for unusually pure atmospheric air. Above the horizontal asymptote through B there is a symmetrical disposition of browns, oranges, and yellows, the order of colours decreasing upward. Below B the colours are blues, greens, and hues of higher orders. The whole field to