tuous to lay any great stress upon the stability of the present order of things; and many hitherto unaccountable varieties that happen in our seasons, such as a general severity or mildness of uncommon winters or burning summers, may possibly meet with an easy solution in the real inequality of the sun's rays.'

The catalogue subjoined to this paper comprehends nine constellations, which are arranged in alphabetical order, viz. Aquarius, Aquila, Capricornus, Cygnus, Delphinus, Equuleus, Hercules, Pegasus, Sagitta.

Having explained the general principle on which this catalogue is formed, we must refer the reader to the author's own account for its particular arrangement, and for the explanatory notes annexed to it. We are informed that the rest of the constellations will be given in successive small catalogues, as soon as time will permit the completion of them."

On the Periodical Star a Herculis; with Remarks tending to establish the rotatory Motion of the Stars on their Axes. To which is added a second Catalogue of the comparative Brightness of the Stars. By Dr. Herschel.

The utility of Dr. H.'s method of estimating the comparative brightness of the stars is now verified by experience. In the notes to his catalogue, in the preceding paper, he mentioned a Herculis as a periodical star. By a series of observations on this star, compared with Ophiuchi, which was most conve◄ niently situated for his purpose, he has been able not only to confirm this opinion, but to ascertain its period. His observations are arranged in a table, by means of which he determines that this star has gone through four successive changes in an interval of 241 days; and therefore the duration of its period must be about 60 days and a quarter. This fact concurs with other circumstances in evincing the rotatory motion of the stars on their axes. · Dark spots, or large portions of the surface, less luminous than the rest, turned alternately in certain directions, either towards or from us, will account for all the phænomena of periodical changes in the lustre of the stars, so satisfactorily, that we certainly need not look out for any other cause.' If it be alleged that the periods in the change of lustre of some stars, such as Algol, 6 Lyræ, & Cephei, and Antinoi, are short, being only 3, 5, 6, and 7 days respectively; while those of o Ceti, of the changeable star in Hydra, and that in the neck of the Swan, are long, amounting to 331, 394, and 497 days; and that we cannot ascribe phænomena so different in their duration to the same cause; it may be answered to this objection, that the force of it is founded on our

limited

fimited acquaintance with the state of the heavens. To the 7 stars, the periodical changes of which were before known, we may now add a Herculis, which performs a revolution of its changes in 60 days.

The step from the rotation of a Herculis to that of Ceti is far less considerable than that from the period of Algol to the rotation of Hercuils; and thus a link in the chain is now supplied, which removes the objection that arose from the vacancy.'-The rotation of the fifth satellite of Saturn is proved by the change observable in its light; and this variation of light, owing to the alternate exposition of a more or less bright hemisphere of this periodical satellite, plainly indicates that the similar phenomenon of a changeable star arises from the various lustre of the different parts of its surface, successively turned to us by its rotatory motion.'

Besides, we perceive a greater similarity between the sun and the stars, by means of the spots that must be admitted to exist on their surfaces, as well as on that of the sun.

Dr. H. farther observes that the stars, besides a rotatory motion on their axes, may have other movements; • such as nutations or changes in the inclination of their axes; which, added to bodies much flattened by quick rotatory motions, or surrounded by rings like Saturn, will easily account for many new phænomena that may then offer themselves to our extended views.'

The catalogue annexed to this paper comprehends the constellations Aries, Canis major, Canis minor, Cassiopea, Cetus, Corvus, Eridanus, Gemini, and Leo. To the catalogue are subjoined several notes, which are the result of constant and indefatigable attention, and which will serve to assist future. astronomers in extending their acquaintance with the coelestial bodies.

PHILOSOPHICAL and MATHEMATICAL PAPERS. Experiments and Observations on the Inflection, Reflection, and Colours of Light. By Henry Brougham jun. Esq.

If we advert to the analogy of Nature, and avail ourselves of principles already established by experiment and universally allowed, it is not unreasonable to imagine that there may be a disposition in the parts of light, with respect to inflection and reflection, similar to their different refrangibility. Whether this be the case, or not, is a curious subject of inquiry; and it is that which the ingenious author of this paper proposes to investigate and ascertain. Having laid down some general principles that pertain to the flexion of light, he proceeds to recite the experiments which led him to conclude that all the parts of which light consists, have not the same disposition to be influenced by bodies which inflect and deflect them. In the first experiment,

experiment, he darkened his chamber in the usual way, and let a beam of the sun's light into it through the hole of a metal plate fixed in the shutter of the window, th of an inch in diameter. At the hole within the room, he placed a prism of glass, of which the refracting angle was 45 degrees, and which was every where covered with black paper, except a small part on each side; and through this part the light was refracted so as to form a distinct spectrum on a chart at 6 feet distance from the window. In the rays, at 2 feet from the prism, he placed a black unpolished pin, of which the diameter was th of an inch, parallel to the chart, and in a vertical position. The shadow of the pin was found in the spectrum; and this shadow had a considerable penumbra, which was broadest and most distinct in the violet part, narrowest and most confused in the red, and of an intermediate thickness and distinctness in the intermediate colours. The penumbra was bounded by curvilinear sides, convex towards the axis to which they approached as to an asymptote, so as to be nearest to it in the place of the least refrangible rays. By moving the prism on its axis, and causing the colours to ascend and descend on any bodies that were used instead of the pin, the red, wherever they fell, made the least and the violet the greatest shadow.

rays

In the next experiment, a screen was substituted in the place of the pin; and this screen had a large hole on which was a brass plate, pierced with a small holed of an inch in diameter. While an assistant moved the prism slowly on its axis, the author observed the round image made by the different rays passing through the hole to the chart; that made by the red was greatest, that of the violet least, and that of each intermediate was of an intermediate size. When the sharp blade of a knife was held at the back of the hole, so as to produce the fringes mentioned by Grimaldo and Newton, these fringes in the red were broadest and most moved inwards to the shadow, and most dilated when the knife was moved over the hole; and the hole itself on the chart was more dilated during the motion when illuminated by the red than when illuminated by any other of the rays, and least of all when illuminated by the violet.' From these two experiments, the author infers that the rays of the sun's light differ in degree of flexibility, and that those which are least refrangible are most inflexible.' From other experiments, he concludes that the most inflexible rays are also most deflexible. In the sequel of his paper, he ascertains the proportion which the angle of inflection bears to that of deflection at equal incidences, and the proportion which the different flexibilities of the different rays bear to one another.

The next object to which our author directs his attention is the effect of that force by which rays are reflected on the different parts of light; and this force he apprehends to be exerted in a different degree in this case as well as in refraction, inflexion, and deflexion. In determining this point, he pursues a series of experiments, of which no abstract nor abridgment, that would not far exceed our limits, would either do justice to the author or give satisfaction to our readers. They are, however, ingeniously devised; and admitting the accuracy with which they were conducted, and that of the results deduced from them, (of which there seems no sufficient reason to doubt,) they warrant the conclusion that the sun's light consists of parts different in reflexibility; and that those which are least refrangible are most reflexible,' or most disposed to be reflected nearer to the perpendicular than others. He next proceeds to inquire, what are the different degrees of reflexibility belonging to each ray, and what are the sines of reflection of the different rays, when all of them have the same sine of incidence. From the experiment subservient to this investigation, he infers that the spectrum by reflection is divided exactly as the spectrum by refraction, only that the former is inverted, and the different rays have reflexibilities that are inversely as their refrangibilities.'--The next object of the author's inquiry is the absolute reflexibility of the extreme colours, from which he would be able to deduce the angle of reflection of all the different rays at a given angle of incidence. The result of his experiment for this purpose is, that, if the sine of incidence be 50° 48', the angles of reflection will be as follow; viz. of the extreme red 50o 21'; of the orange 50° 27′; of the yellow 50° 32'; of the green 50° 39′; of the blue 50° 48′; of the indigo 50° 57′; of the violet 51° 3'; and of the extreme violet 51° 15".

Having, by a train of argument and calculation, founded on these results, investigated the physical cause of reflexibility, Mr. B. does not hesitate to ascribe it to the different sizes of the various parts of light; so that the force exerted for producing this effect on the red being to that exerted on the violet as the size of the red to the size of the violet, the red particles will be to the violet as 1275 to 1253. By similar calculations, this deduction may be extended to all the other colours, their sizes being between 1275 and 1253, which are the extreme red and extreme violet; thus the red will be from 1275 to 1272; the orange from 12721 to 1270; the yellow from 1270 to 1267; the green from 1267 to 1264; the blue from 1264 to 1260; the indigo from 1260 to 1258; and the violet from 1258 to 1253.

He

He closes this discussion with replying to two objections, which he conceives may be urged against that reasoning which ascribes the intensity of the particles of light to their size.

Having endeavoured to unfold the property of flexibility, as varied in inflexion, deflexion, and reflection, and also the physical cause of this property, Mr. B. proceeds to explain several phænomena of vision by means of the principles which he has advanced; and he applies his idea of reflexibility to the doctrine of colours, which he supposes to depend, not on the size, but on the position of the particles that compose them; or at least on the size merely so far as it influences their position. As we cannot pursue his reasoning on this subject, we shall close this article with observing that the experiments, and many of the reflections, contained in this paper, are original and interesting; and that they claim the attention of persons conversant with disquisitions of this nature. Some errors, which had escaped the author in this paper, are corrected in the second part of the Transactions.

The Construction and Analysis of Geometrical Propositions, determining the Positions assumed by Homogeneal Bodies which float freely, and at rest, on a Fluid's Surface; also determining the Stability of Ships, and of other floating Bodies. By George Atwood, Esq. F. R. S.

In order to determine the positions of floating bodies in the circumstances here supposed, it is necessary to state the principles on which they depend. A floating body is pressed down-. wards by its own weight in a vertical line that passes through its centre of gravity; and it is sustained by the upward pressure of a fluid, acting in a vertical line that passes through the centre of gravity of the immersed part; and unless these two lines be coincident, so that the two centres of gravity may be in the same vertical line, the solid will revolve on an axis, till it gains a position in which the equilibrium of floating will be permanent. Hence it appears that it is necessary, in the first place, to ascertain the proportion of the part immersed to the whole; for which purpose, the specific gravity of the floating. body must be known; and then it must be determined by geometrical or analytical methods, in what positions the solid can be placed on the surface of the fluid, so that the two centres of gravity already mentioned may be in the same vertical line, when a given part of the solid is immersed under the surface of the fluid. When these preliminaries are settled, something still remains to be done. Positions may be assumed, in which the circumstances just recited concur, and yet the solid will assume some other position in which it will perma

nently