of doubling images. On the contrary, if the principal sections of the crystal be perpendicular to the plane of reflection, the reflected ray will be refracted entire, according to the extraordinary law. In all intermediate positions, it will be divided into two pencils, according to the same law, and in the same proportion, as if it had acquired its new character from the double refraction. Hence the ray reflected from the fluid surface at an angle of 52° 45', has all the characters of an ordinary ray formed by a crystal, whose principal section is perpendicular to the plane of reflec


The angle of incidence at which light experiences this remarkable mo. dification, when reflected from the surface of transparent bodies, is not the same in all; but, in general, it increases with their refractive power. At angles different from this particular angle, a part of the ray is more or less modified, and in a manner analogous to what takes place between two crystals whose principal sections are not parallel or perpendicular.

A pencil of light undergoes the same modification, but at a d fferent angle, when reflected in the interior of bodies at the surface of emergence; and the sine of the first angle is to the sine of this angle, as the sine of incidence is to the sine of refraction.

Rays that are reflected interiorly at the second surface of double refracting crystals, exhibit peculiar phenomena, which depend both upon the refractive power and upon the new property of reflected light.

When a pencil of rays has been divided into two parts at the first surface of Iceland crystal, these two rays emerge from the second surface in two pencils parallel to the incident ray. But this is not the case with

reflected light. Though the ray refracted ordinarily at the first surface is refracted ordinarily at the second, yet it is reflected at this surface in two pencils, one ordinary and the other extraordinary. In like manner, the ray refracted extraordinarily is reflected in two others; so that there are four reflected rays, and only two emergent ones. When these four rays return to the first face of the crystal, they issue out in four parallel pencils, which make, with this face, the same angle as the incident ray, but in a contrary direction, and are parallel to the plane of incidence.

In examining the light which proceeds from the partial reflection of opaque bodies, as black marble, ebony, &c., M. Malus also found an angle at which this light obtains the properties of that which has suffered a double refraction. Polished metals, however, were not capable of producing this phenomenon, but they did not alter this disposition in the rays when they had already acquired it from an. other substance.

When a luminous ray was divided into an ordinary and extraordinary portion by double refraction, M. Malus received the two pencils on a surface of water at an angle of 52° 45'. The ordinary ray was partly refracted and partly reflected, like any other pencil of direct light; but the extraordinary ray penetrated the fluid entire, and none of its particles escaped refraction. On the other hand, when the principal section of the crystal was perpendicular to the plane of incidence, the extraordinary ray produ ced alone a partial reflection, while the ordinary ray was refracted entire.

If two glasses are inclined to each other at an angle of 70° 22′, and if we conceive between these two glasses a line making with each an angle of

35° 25', every ray reflected by one of the glasses parallel to this line will not be reflected anew by the second, but will penetrate it entirely, without having a single particle reflected.


Most of our readers are acquainted with the celebrated set of observations made by Dr Maskelyne, to ascertain the attraction of Schehallien, a mountain in Perthshire, in order to determine the density of the earth; and with the elaborate calculations made by Dr Hutton, from which he deduced that the density of the earth was 4.481. One of the fundamental points of this calculation depended upon the density of the mountain Schehallien itself, which Dr Hutton estimated at 2.5. Some

time ago Mr Playfair made a careful survey of this mountain, in order to determine the nature and density of the minerals of which it is composed. It consists of granular quartz, mica slate, and limestone. The specific gravity of the quartz is 2.639876, and the mean specific gravity of the mica slate and limestone is 2.81039; both higher than the specific gravity taken by Dr Hutton as the foundation of his calculation. Mr Playfair has on that account gone over the calculation again, substituting the real density of the mountain for the supposed density employed by Dr Hutton. If the granular quartz go to the bottom of the mountain, the density of the earth is 4.55886. But if, as is most probable, the whole bottom of the mountain be composed of

limestone and mica slate, then the density of the earth is 4.866997. Mr Cavendish made the density of the earth by his experiment 5.48. It is not improbable that it will turn out about 5.


No branch of science has received of late years greater or more important additions than botany; and Great Britain, from her great maritime power, and from her connection with various countries at a great distance from Europe, and abounding in new and unknown plants, has had it in her power to make many and splendid additions to the catalogue of plants. We have at present to notice a very valuable work on botany, published by Mr Robert Brown, giving an account of a great number of plants, chiefly new, collected by him in New Holland and New Zealand. He has in his Prodromus arranged them according to the method of Jussieu. The skill, the accuracy, and the clearness of his generic distinctions, are entitled to the greatest praise, and place him in the very first rank of botanical writers. It would be improper to pass by unnoticed a most valuable dissertation, by the same author, on the Asclepiadeæ, a natural order of plants, separated from the Apocineæ of Jussieu, published in the first volume of the Memoirs of the Wernerian Society. This dissertation is replete with the most important information, and exhibits the sagacity of the author in the most favourable point of view.

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In the History of the Useful Arts for 1809, we inserted a brief notice of the new method of dividing astronomical instruments, invented by the celebrated Mr Edward Troughton. The great inconvenience which attended the common method of dividing, by means of compasses, arose from the danger of enlarging, displacing, or deforming the points or divisions, by putting the point of the compasses into them; and from the difficulty of placing that point midway between two points very near each other, without its slipping towards one of them. In order to remedy this inconvenience in the old method, Henry Cavendish, Esq. F. R. S. has proposed to employ a pair of beam compasses with only one point, and a microscope instead of the other, and he has suggested a method of using this instrument, in which there is never any occasion of setting the point of the compasses into a division. Al

though this suggestion of Mr Cavendish is certainly an improvement upon the old method, yet we do not think that it will ever be adopted in preference to the very ingenious me thod of Mr Troughton, which has already been employed with so much success in the finest astronomical instruments which are now in use. The

opinion entertained by the Royal Society of London of Mr Troughton's method has been very unequivocally expressed, by their adjudg ing to him the Copleyan medal for 1809.

The subject of dividing astronomical instruments has also attracted the attention of the Rev. William Lax, A. M. F.R. S. and Lowndes professor of astronomy in the university of Cambridge. This gentleman proceeds upon the principle, that every method of dividing circular instruments is liable to considerable errors; and he therefore proposes that every practical astronomer shall examine, by a particular method, the accuracy of each division; that the artist shall

merely set down a point at the end of every five or ten minutes, and that the observer, who will be the virtual divider of his own instrument, shall determine the distance of these points from zero, and enter them in his book, to be referred to when wanted. Mr Lax maintains, that the error of examination (which in a circle of two feet diameter will never exceed 9.63 seconds, and in one six feet diameter, 3.21 seconds) bears but a small proportion to the accumulated errors in the division of the instrument, and that the errors of examination may be diminished as much as we please by taking a mean of different examinations. In dividing the whole circle into arcs of 15° each, 44 measurements must be performed; and in examining every point in each arc of 15°, 161 measurements will be required, making in all 3908 measurements. By allowing a minute and a half for each measurement, the time necessary for completing the whole examinations will be 5862 minutes, or nearly 98 hours. Mr Lax considers the method which he proposes as not merely a security against the errors of division, but also against those which arise from bad centering, and from the imperfect figure of the circle. He conceives that it may be particularly useful in guarding against the effects of unequal expansion, or contraction, in the metal, and that it gives us all the advantages of the French circle of repetition, without the inconvenience of turning the instrument, and moving the telescope so many times in the course of the observation. It may be proper to remark, that Mr Lax's paper, though published in the same volume of the Philosophical Transactions with Mr Troughton's paper, was written before he was acquainted with the latter

method. His remarks, therefore, have a particular reference to the old methods of dividing, and had he been aware that Mr Troughton's plan was capable of such accuracy, it is probable that he would not have so much overrated the errors of division.

As this subject is at present under our notice, we cannot omit the opportunity of mentioning a particular construction of circular instruments which has often occurred to the writer of this article, as highly deserving of consideration. In every mural and transit circle, even if we conceive the limb to be divided with mathematical accuracy, there is a great risk of error, arising from a change of form, produced either by an inequality of temperature, or by any accidental injury which the instrument may suffer. When this change of form does take place, (which was the case with the great mural quadrant at Greenwich) the instrument may be considered as useless, since equal arches on the limb will not correspond with equal angles at the centre. We should propose, therefore, to separate the part of the instrument which contains the divisions, from the telescope and the part of it that is moveable, which may be done in two ways, either by placing the divisions on a fixed circular rim, while the telescope is moveable on a horizontal axis like a transit instrument, or, what is perhaps more advisable, by putting a scale of equal parts upon a rectilineal bar placed in a horizontal position on the floor of the observatory, and forming a tangent to the circle described by the telescope. Five or six microscopes should also be fixed along with the telescope, so that their axes may form equal angles with each other, for the purpose of reading off on the rectilineal scale the angle formed by the

telescope. By this means the divided part of the instrument is separated from the moveable part; the risk of a change of form, arising from inequal expansion, is removed; the load upon the axis of the instrument is diminished, and the whole of its construction is greatly simpl fied. The same method of construction might be applied to portable instruments.



The Rev. James Hall, of Walthamstow, has received the silver medal of the Society of Arts, for a communication on the preparation of a fibrous substance from bean stalks, which is applicable to the uses for which hemp is employed. According to its size, every bean plant contains from 20 to 35 filaments, or fibres, running up on the outside, under a thin membrane, from the root to the top all around, the filament at each of the four corners being rather thicker and stronger than the rest. After the plant has been steeped 10 or 12 days in water, and is in a state approaching to fermentation, the filaments may be easily separated from the strawy part, by beating, rubbing, and shaking. Washing and putting it through hackles, or iron combs, of different degrees of fineness, has been found by Mr Hall to be the easiest way of separating the filament from the thin membrane which surrounds it: He found also that there are at a medium about two hundred weight of these filaments in every acre, which he thinks may not only be employed in the manufacture of numerous articles where strength and durability are requisite, but may also, with a little preparation, be converted into paper

of all kinds, even that of the most delicate texture. Sir H. Davy, to whom a specimen of this hemp was sent for examination, remarks, that it seems to bear bleaching very well, and, as to chemical properties, differs very little from hemp." Mr Joseph Home, who also bleached a portion of it, observes, "that the texture and strength were not in the least degree impaired by bleaching, and that he did not find more difficulty in accomplishing the bleaching of this than of other vegetables." The wri ter of this article has in his possession specimens of this hemp, both in its bleached and unbleached state; but as far as he can judge, without any accurate experiments, the filaments do not appear to have that degree of strength which has been ascribed to them. Mr Hall's communication will be found in the Transactions of the Society for the Encouragement of Arts, Manufactures, and Commerce, for 1809, and in the Philosophical Magazine, vol. xxxv. p. 180.


A new method of performing the operation of cupping, without the assistance of a syringe, has been invented by Robert Healy, M. B., Dublin. The instrument consists of a hollow vessel with a stop cock, containing about half a pint of water, and made of thin sheet copper or tin, and of a cupping glass made in the usual way, and adapted to the stop cock with a coarse-threaded screw. The stop cock should extend half an inch within the first mentioned vessel. After unscrewing the cupping glass from the vessel, a little air is to be drawn from the latter by the mouth of the operator, and the cock is then

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