rays reflected in a directly opposite course. In this spectrum, the blue rays are nearest to the common image, and the colour is so great that it requires a prism of flint-glass with a refracting angle of 65° to correct it: a large secondary spectrum being left, having the uncorrected green towards the vertex of the prism. If the candle be now left in its position, and the plate of mother-of-pearl be turned round on its centre 180°, so as to bring that end of it nearest to the candle which was before most remote, the coloured image will be found to have a motion of rotation about the natural image, and will in this position be at the same distance from it as before, only as much above it as it was then below. If now the ends of the plate be still made to preserve the new direction, but the other surface of the plate be exposed to the candle, the extraordinary image will be found again at the same distance below the natural image; and, if the plate be again turned about its centre, the same rotation of the coloured spectrum will be observed, and its position again be found above that of the natural reflected image. Hence it follows that the two surfaces of mother-of-pearl have always their poles of extraordinary reflection in opposite directions; except in specimens in which a change of structure takes place, a case which is not intended to be considered in this memoir, those which are here introduced being regularly formed, and nearly colourless in day-light.

That the reader may better comprehend the results in the following extract, we will observe that the line joining the two extremities of the plate, which we have supposed to be alternately presented to the candle, is called the axis of extraordinary reflection; the angle formed between a perpendicular to the surface and the coloured ray, the angle of extraordinary reflection; and the angle formed by the ordinary and extraordinary reflected rays, the angle of aberration. These circumstances being premised, the nature of the results comprehended in the subsequent table will be readily understood:

The first column contains the angle of incidence; the second, the complement of that angle; the third, the angle of aberration as determined by experiment; and the fourth, formed by adding the second and third columns, contains the complement of the angle of extraordinary reflection.

Angle

RrC SrCA SrB=RrA x=sr S | A + x = srB

If we now compare the angles of aberration in the third column with the angles of extraordinary reflection in the fourth column, and make

‹ A=RrA=SrB the complement of the angle of incidence or ordinary reflection,

x=srS the angle of aberration,

A+xsrB the complement of the angle of extraordinary reflection, it will be found that

sin. x: sin. x ́=sin. A ́+x': sin. A+x

That is, the sines of the angles of aberration are to one another in versely, as the sines of the complements of the angles of extraordinary reflection.'

If the plate be now turned so as to present its opposite surface to the candle, then similar observations will be found to give similar results: viz. sin. x : sin. x' :: sin. A'—x ́ : sin. A-x, which indicates the same relation as before, except that here we have the differences instead of the sums; arising from the change in the relative position of the two images, as before stated.

We cannot enter farther on this part of the present memoir, but must proceed to the second head, in which the author details his experiments relative to the communication of the pro perties of mother-of-pearl to other bodies.

In order to measure the angles contained in the preceding tables, I had occasion to fix the mother-of-pearl to a goniometer by a hard cement. Upon removing it from the cement, the plate left a clean impression of its own surface, and I was surprised to observe that the cement had by this means received the property of producing the colours which were exhibited by the mother-of-pearl. This strange result I at first attributed to a thin film detached from the plate, but subsequent experiments soon convinced me that this was a mistake, and that the mother-of-pearl really communicated to the cement the properties which it possessed.

I have also succeeded in imparting the same faculty of producing colour to black and red wax, balsam of Tolu, gum Arabic, gold leaf placed upon wax, tinfoil, the fusible metal composed of bismuth and mercury, and to lead by hard pressure, or by the blow of a hammer. When the impression is first made upon the fusible metal, the play of colours is singularly fine, but the action of the air corrodes the metal, and speedily destroys the configuration, as well as the polish of its surface. The same effect was produced when the metal was immersed in oil.'

This power of communicating its properties to other bodies is, as far as we know at present, peculiar to mother-of-pearl, and is perhaps one of the most remarkable facts relating to optical phænomena that has yet been discoverd.

With regard to the Causes of the Phænomena of Mother-ofPearl, which form the third part of the present memoir, the author observes;

From a careful examination of the preceding facts, we must how be prepared to infer, that all the peculiar phenomena of mother-ofpearl, as seen by reflection and transmission, are owing to a particular configuration of surface; that the communication of these properties to other bodies is the necessary consequence of the communication of its superficial structure; and that none of the light, which is concerned in the production of these phenomena, has penetrated the surface of the mother-of-pearl.

Pursuing these reflections, Dr. Brewster was led to examine the surface of the mother-of-pearl with a microscope; and, though he anticipated no assistance from this source, yet with powers of from 200 to 400 he discovered a peculiarity in the structure of its surface, to which we may doubtless attribute all the phænomena above stated. We learn that he found, in almost every specimen of mother-of-pearl, an elementary grooved surface, which no polishing can either remove or modify, resembling the delicate texture at the end of an infant's finger; or those fine lines parallel to the coast on a map, by which the engraver marks the limit of the sea and the land. This peculiarity of superficial structure Dr. Brewster very naturally considers as the cause of the various phænomena detailed in this interesting

ΙΟ

interesting memoir; the remainder of which is occupied in investigating the laws before discovered by observation. Our limits will not, however, allow us to accompany him any farther into his new world of lights and shades.

An improved Method of dividing Astronomical Circles and other Instruments. By Captain Henry Kater. Any remains of inaccuracy in astronomical observations cannot but be considered as a matter of important interest to astronomers, and deserving of their utmost and unwearied attention. Astronomy, as it is the noblest, is also the most perfect of any of the philosophical sciences, and displays the mental powers and persevering genius of man in the highest and most favourable point of view. Yet some trifling defects and inaccuracies still occur in observations, which it would be well if we could avoid : but which, as they may arise from different causes, it is extremely difficult to obviate, or even to estimate with due precision. Among others, we must in course include every trifling aberration in the division of instruments; which operation has therefore always been deemed one of great importance, and has consequently stimulated the exertions of the most eminent artists. The method of division, which until very lately was in general use, was that which was practised so successfully by the late Mr. Bird: but the laborious and delicate operation by the scale and beam-compasses has recently been superseded by the invention of Mr. Troughton, of the excellency of which the mural circle at the Royal Observatory at Greenwich affords a noble proof. This method, however, Captain Kater thinks, still admits of improvement with regard to simplicity and facility of operation; the manner of effecting which forms the subject of the present memoir. Without the aid of the necessary figures and diagrams, we cannot undertake to explain the principles on which the paper rests: but we must observe that it has all the appearance of answering the intended purpose, though to give a decided opinion on the subject requires a greater practical knowlege of the divisional operations than we possess.

Results of some recent Experiments on the Properties impressed upon Light by the Action of Glass raised to different Temperatures, and cooled under different Circumstances. By David Brewster, LL.D., &c.We have here a few other facts connected with the subject of the polarization of light; the result of which is that glass brought to a certain temperature forms two images, and polarizes them in an opposite manner, like all double refracting crystals, the one image being coincident with the

other.'

Consideration of various Points of Analysis. By John F. W. Herschel, Esq. F.R.S.-We could have wished to have given

our readers an intelligible abstract of this ingenious memoir : but, when we inform them that the first three or four pages of it are occupied in defending and illustrating the notation employed in the subsequent part, they will readily perceive that within our limits such an abstract is wholy impossible. The object of the paper is to shew the application of the theory of generating functions to several curious and interesting results, derived originally from other principles, but which the author manifests to flow with the utmost facility from the first elements of this calculus. Mr. Herschel seems to think that analysis in its present state is already adequate to every purpose to which we can reasonably hope to see it applied; and that all which we can now expect is a generalization of it, and a reduction of it to one universal and comprehensive principle: but we much question whether the first article of the author's analytical creed will be readily subscribed by mathematicians in general. Analysis has certainly, within the last half-century, been in a state of successive and continual improvement, and has been employed in the solution of problems that Newton himself perhaps considered as totally beyond its powers. These improvements were proceeding till the last days of Lagrange, of which his "Theory of the Variation of the Elements of the Planets," one of his latest productions, is a sufficient proof; and, though the sciences have lost this able master, we have still a Laplace, a Legendre, a Poisson, and an Ivory. Let us not, therefore, suppose that analysis has yet reached its ne plus ultra of perfection, or that nothing is now left to effect but generali

zation.

ART. IV. The Lord of the Isles, a Poem. By Walter Scott, Esq. 4to. 21. 28. Boards. Constable and Co., Edinburgh. Longman and Co., London. 1815.

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N order to avoid needless and tiresome repetition, we must refer the reader to our former critiques on the poems of Mr. Scott, for all preliminary observation on the character and costume of his well-known compositions, and at once enter into an account of the story, the beauties, and the defects, of The Lord of the Isles.'

The materials of this tale are very simple. Its time is the commencement of the 14th century. Lord Ronald, the Lord of the Isles, is betrothed to Edith, daughter of the Earl of Lorn but his real affections are fixed on Isabel, sister of "The Bruce." Preparations for his nuptials with Edith are made in the first canto; and the approach of Lord Ronald's fleet, streamer'd with silk,' is descried by Edith and Moray (her foster-mother, a tie most sacred in the Highlands,) from Artornish

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