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r=t-> (* + 106
perature of the air t, and u the maximum at the temperature m of the moist bulb; also tm being=d, we have w=u- -ca.
But if the temperature , at which w grains would saturate the original volume, be wanted, it may be found from the thermometers only, without the aid of any tables, by the following approximate formula, which, however, comes very close to the foregoing, between the temperatures of 25° and 90° Fahrenheit. Put k for the temperature at which the variation in the weight of moisture in the given volume for a change of 1° is c grain, then the temperature sought will be
t-0(*2*). If the volume be a cubic foot, and if, as appears from a mean of various experiments, c=.15, then k= 53° Fahr., and
106). If the centigrade thermometer be used, c = 27, and both k and m must be increased about 18. Hence
m + 18° The maximum forces of vapour for different temperatures follow a law very similar, and nearly related, to the law of the density. So that the actual force of vapour in the air may be represented by f=F-gd; where F = maximum force at the temperature m, and g a constant, which will=.0125 or so when c=.15. Hence the temperature at which aqueous vapour having the force f, would be in a state of saturation, and which temperature is usually called the dewing point, will be
D=t-> (+999). The number substituted for k in this case being 49o.5 Fahr. the temperature at which the variation of force for 1° is .0125. By means of this formula, the point of deposition, or dewing point, may be readily obtained without the aid of tables. With the centigrade thermometer,
16") These formulæ are adapted to the ordinary pressure, and are by much the simplest I have ever seen for the purpose. .
The dewing point, or point of deposition, is the temperatur of saturation under the original pressure. The temperature
the point of saturation under the original volume. The want of attention to this distinction frequently leads to important
My object in the preceding pages, has been rather to state what appeared to be matter of fact, than to throw out a mass of random hypotheses. But this paper, having been drawn up
before the article on the air-thermometer in the last Number of this Journal, is more conformable to the common theory of that instrument. It is only the formulæ near the end that could be affected by this circumstance; and within the limited range of atmospheric temperatures, the difference on these formulæ would not be material. At any rate, till the weight of moisture which can exist in the air at different temperatures be better determined, it is impossible to construct either rules or formulæ which can be depended on with perfect confidence.
On Coloured Shadows. By Messrs Zschokke and TRESCHSEL
THERE appeared at Arau, at the commencement of the present year, a memoir upon coloured shadows, read by Mr Zschokke to the Society of Natural Sciences of that city. It was received with the interest which attaches to all the productions of its author, productions so númerous and so varied that one can scarcely believe them to proceed from the same pen. Nor was this the first time that Mr Zschokke, the historian, politician, economist, novelist, &c. bestowed some moments upon the Sciences properly so called; several scientific memoirs form partof the collection of his works, and bear testimony in favour of the general nature of his acquirements.
The opinion entertained by Mr Zschokke on the subject of coloured shadows, was destined to meet with opposition. Mr Treschsel, son of the learned professor of Berne, to whom we owe the triangulation of a portion of our territory, and several other
* Extract of a Memoir of M. Zschokke, entitled, “ Die farbigen Schatten, &c. Arau 1826 ;" and of a refutation of that memoir, by Mr F. Treschsel jun.
valuable performances, has charged himself with this task in a memoir which he has latterly communicated to us. The subject is delicate and contestible.
We shall give in succession the explanations of the phenomenon in question given by the two authors, announcing at the same time that we do no hesitate to adopt, at least in its fundamental parts, the opinion of Mr Trechsel.
M. Zschokke, at the beginning of his memoir, gives an account of the authors who have observed coloured shadows, and attempted to explain them. It will not be uninteresting to go over this ground. Shadows coloured in blue are those which have been most frequently remarked, because in fact nature presents them oftenest to us. Priestley, in his History of Optics, states that this phenomenon was for the first time observed and described, about the middle of the seventeenth century, by Otto Guerick, the celebrated inventor of the air-pump; but he is wrong, for Leonardo da Vinci speaks of it in his Treatise on Painting, written in the fifteenth century. This able artist sought to discover, with all the interest excited' by a subject of so much importance to his art, to what was owing the colouring of shadows in blue. He only såw in it a reflection of the colour of the sky, or rather of the atmosphere, having recourse for this phenomenon to the same explanation as for the purple tints, which colour rocks and buildings, before the rising and after the setting of the sun, or for the greenish reflection which diffuses itself upon the sides of a vessel, or upon the piles of a bridge above a deep and limpid body of water. Bouguer, in his Optics (1729), Buffon, in his Memoirs of the Academie des Sciences for 1743; Begnelin in those of the Berlin Academy for 1767; Monge in 1789, and other natural philosophers, have more or less adopted the opinion of the celebrated painter.
Buffon had the merit of contributing powerfully to direct the attention of observers toward the coloured shadows that form in the solar light. . “ I observed,” says he, “ during the summer of the year 1743, more than thirty sun risings and as many set: tings. All the shadows that fell upon white, as upon a white wall, were sometimes green, but most commonly blue, and of a blue, as lively as the most beautiful azure. I shewed the phenomenon to several persons, who were as much surprised as my
self. Difference of season has no effect upon it, for there are not eight hours (15th November 1743) since I have seen blue shadows; and whoever will give himself the trouble of looking to the shadow of his fingers at sun-rise and sun-set, upon a bit of white paper, will see like me this blue shadow," &c. The illustrious naturalist also cites a letter of the Abbe Millot, in which he announces to him that at noon, with a cloudy sky, in which some openings were seen here and there in the clouds, he had observed shadows of a beautiful blue upon white paper ; and further, that, under certain particular circumstances, he had remarked green, violet, or yellowish shadows, or shadows surrounded with a coloured margin of these different tints. Buffon, recapitulating these various observations made in 1743, adds in 1773: “ This blue colour of shadows is nothing else than the colour of the air itself *.”
M. de Schrank, in the Memoirs of the Academy of Munich for 1812, brought forward again the opinion proposed in 1783 by Opoix, a French naturalist little known, supporting it by new arguments. The blue shadows, according to him, come from the inflection of the rays' tangent to the edges of the solid, from which the shadow proceeds. As the blue
rays are very
refrangible, they are more strongly attracted than the others by bodies, and thus come to colour the interior of their shadows. 0poix, as well as M. de Schrank, knew well that the violet rays are more refrangible than the blue rays; and they reply to the objection which arises from this circumstance, the one that, in the shadows of thin bodies, the violet rays are sufficiently deflected to pass beyond the opposite edge of the shadow, and enter into the open light; the other, that, in the case where the body has a sufficient breadth to prevent the application of such an explanation, the rays fall, it is true, into the interior of the shadow, but that the tint which they carry there is too obscure to be perceived
Rumford observed not only the coloured shadows formed in the pure solar light, but also the various shadows resulting from several sorts of coloured lights combined with each other and with the solar light; and thinking that he had remarked that,
* Buffon, Hist. Nat. d’Min., Memoire viii.
when seen through a tube, which excluded all comparison of one shadow with another, all these shadows appeared black, he concluded from thence that all these effects are mere optical deceptions *.
M. de Grotthuss arrived at nearly the same conclusion, but by a different process t. He knew the phenomenon of the blue and yellow shadows, which are produced by the concurrence of the light of a candle and that of the twilight; he also knew the impression which the long continued observation of coloured plates produces upon the retina; an impression which afterwards reproduces in the organ spots tinged with colours exactly complementary, in the scale of the spectrum, to those on which the
has been fixed; and he in like manner considers the phenomenon of coloured shadows as a physiological deception, as the result of the fatigue caused by an effort of the organ in the same direction, and of the disturbance of an equilibrium of sensibility in it.
After giving this historical narration, Mr Zschokke remarks, that none of the hypotheses explains all the cases in which shadows appear coloured, and he proceeds to the exposition of a new theory. Let us first give an account of the fundamental phenomena, the causes of which form the subject of inquiry.
Coloured shadows are produced in the solar light, when it is refracted by the vapours of the lower strata of the atmosphere, or reflected by the clouds. Thus, 1st, the colouring is perceptible chiefly at sunrise and sunset, when the sun is not higher than from ten to twenty degrees above the horizon. 2d, In winter, the shadows are sometimes coloured at noon,
because at that season in our latitude the sun scarcely rises to the height of twenty degrees. In summer, they are only coloured in full day when the sky is overcast, and the clouds reflect a strongly coloured light. 3d, The more deeply the rays penetrate into the lower strata, the more strongly are the shadows coloured,
See Philosophical Transactions 1794 ; or in the Biblioth. Britann. vol. i. p. 339, an extract of Count Rumford's paper, terminated by a note (p. 372) upon coloured shadows, and the authors who have treated of them.
+ See in Schweigger's Beytrag. zur Chemie und Physik, vol. ii. p. 148. an abridgment of M. de Grotthus's Paper on the Accidental Colours of Shadows, and on Newton's Theory of Colours.