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tions which are required to be remarkably correct "We have only to measure the arc which has been determined by the observation, against the whole circle, or against the multiple of it, which approaches nearest to the circle, and from thence to deduce its value in the manner explained above, and we shall either have entirely excluded the error which we apprehended, or have rendered it too small to be of any importance." p. 242.

Mr. L. thinks this expedient possesses all the advantages of the French circle of repetition, without its inconveniences, and that it is capable of a higher degree of accuracy. XV. On the Identity of Columbimn and Tantalum. By

William Hyde Wollaston, M. D. Sec. R. S. Read June

8, 1809.

Some degree of suspicion has been entertained, that ths two metals discovered about the same time by Mr. Hatchett and M. Ekeberg were in fact the same metal; and Dr. W» in the paper before us appears to have removed all remaining doubt on the subject. Haying obtained specimens of the. Swedish minerals tantalite, and yttrotantalite, he procured a small supply of the oxide of colutnbium from Mr. Hatchett, and a tew small fragments of the mineral analysed by Mr. H. from the trustees of the British Museum. The external appearance of the two minerals is so much the same, that no difference can be discovered. The external surface, the colour, lustre, and fracture are precisely the same ; but columbite breaks rather more easily under a blow, and the fracture is less uniform. When the two minerals are rubbed against each other, they appear to have the same degree of hardness, and the colour of the scratch in both has the same dark brown tint. Each of the minerals, when analysed, is found to consist of a white oxide, combined with iron and manganese.—Five grains of columbite gave of white oxide 4 grains, oxide of iron i of a grain, oxide of manganese £ of a grain. Five grains of tantalite, treated in the same manner, gave of oxide 4 $■ grains, oxide of iron \ a grain, oxide of manganese TV of a grain. The white oxide o't the minerals is. remarkably insoluble in the muriatic, nitric, and sulphuric acids, but very readily soluble in potash whether pure or saturated with carbonic acid, and in soda, though much less completely; they are each precipitated from the alkaline solution by the addition of an acid, but are not re-dissolved by an excess of the sulphuric, nitric, muriatic, succinic or acetic acids ; they are each perfectly soluble in the oxalic, tartaric, and citric acids, and the solution with each is subject to the same limitations, for if the oxide has been dried after precipitation, it can scarcely be re-dissolved, until it has been again fused with potash. Prussiat and hydrosulphuret

ofpota-sh occasion no precipitation from the alkaline solution} the infusion of galls throws down an orange-coloured powder, but to produce this effect it is necessary that sufficient acid should be added to neutralize any excess of alkali which might happen to be present, and there should be no excess present of the oxalic, tartaric, or citric acids. Dr. W. considers the infusion of galls as the characteristic precipitanf>of this metal. From this perfect agreement in the chemical properties of the two oxides, there can be no reasonable doubt of their identity; but there J9 a remarkable dif-» ference in the specific gravity of the two minerals from which they are obtained. The specific gravity of columbite as determined by Mr. Hatchett is 5.918, that of tantalite as ascertained by Mr. Ekeberg 7-953 ; results which Dr. W. considers from his own trials sufficiently correct. Whether this discrepancy arises from a difference in the state of oxidation of the metal, or from the state of aggregatiou, is uncertain.

XVI. Description of a reflective Goniometer. By William Hyde Wdlaston, M. J). Sec. li. S. Read June a, 1809. This is an ingenious instrument, but a description of it could

not be very intelligible without a reference to the engraving annexed to the paper. It is intended to measure the inclination of the surfaces of crystals by means of the rays of light reflected from them, and from the principles of its 'construction, it would appear to admit of very considerable accuracy. Dr. W. finds it possible by means of it to determine the position of surfaces of ^ of an inch in breadth, with as much precision as those of much larger crystals ; and he thinks it will supply the means of correcting many of the errors of former observations.

XVII. Continuation of Experiments for investigating the Cause of coloured concentric Rings, and other Appearances of a similar Nature. By William Herschel, LL. D. F. K. S. Read, March 3'A, 1809.

This paper is a continuation of a disquisition which we have already noticed (Vol. V. p. 128,) in reviewing the second part of the Philosophical Transactions, for 1807. In that communication, Dr. Herschel pointed out a variety of .methods that will produce coloured concentric rings between two glasses of a proper figure applied to each other; and it was attempted to be proved that only two surfaces, namely, those that are in contact with each other, are essential to the formation of such rin^;. The Doctor now enlarges the field of prismatie phainom&na, shews that the appearance in the shape of rings has been owing to the exclusive use of spherical curves, and intends from the whole to establish a more satisfactory theory than the Newtonian one of fits of easy reflection and transmission.

In the paper before us, the first section, numbered in continuation 35, affirms that' cylindrical curves produce streaks.' One surface of a plate of glass being ground to a cylindrical form, it exhibited, when in contact with a plane surface, streaks of colour which ' differed in no respect from rings, except in their linear, instead of circular arrangement.'

The next two sections inform us, that' cylindrical and spherical surfaces combined produce coloured elliptical rings;* and that 'irregular curves produce irregular figures.' All this contains nothing new. In the two succeeding sections, it is attempted to prove that curved surfaces are necessary to the production of the coloured appearances under consideration ; and that such appearances cannot be produced between the plane surfaces of two parallel pieces of glass: yet the author adds that 'when the incumbent plane is not of a parallel tliicknessj1 as he strangely expresses it, c coloured pbaenomena may be rendered visible between two perfectly plane surfaces;' while in the same page he asserts, that no more than two surfaces are essential to the formation of coloured rings. Such contradictions it is- not our business to reconcile. Here, too, the Doctor's explanation of the disappearance of the colours between two pieces of glass separated at one end by a slip of platina, is extremely forced, arbitrary, and inadmissible; unless he can shew that the same colours are not produced by a pressure, immediately upon the places in contact. In this part, also, when speaking of the mutual repulsion of the glasses, he has been anticipated by Newton himself, by the late Professor Robison, and by Dr. Thomas Young.

Sections 40, 41, 42, 43, relate to the production of co-' loured appearances, to the Newtonian prismatic blue and red bows, and the sudden change of colours of the bows; and are particularly objectionable; we can, however, specify only one thing here. The Doctor says, ' according to my accoitnt of the red bow it ought to be seen in the pris:n a little above, the blue one, and this is also farther confirmed by any one' of the experiments in which we have some part of each bow in view at the same time, for then the relative situation of the two bows will be visible.' Now this must all be a fallacy; for the red bow is merely tha supplement of the blue one, its breadth the same, and it must necessarily appear at the same elevation. To a careless observer, indeed, it might seem a little more elevated, on account of the slight difference of the upper edge of the blue bow from white light, and the consequent feeble marking, compared with the strong termi

nation of the red one. But had Dr. H. simply covered the opposite halves of two of the sides of a common prism with two pieces of paper, and looked up through the third towards the stay, he would have had a perfect view of both bows placed side by side, and equal in breadth: while, according to his calculations, the red bow ought to be not only • a little,' but entirely above the blue one.

The 44th section relates to the ' streaks and other phenomena produced from the prismatic blue and red bows.' Here, however, nothing occurs but what is perfectly conformable to Newton's rule for computing the effects of light falling obliquely upon thin plates. The 45th section contains descriptions of the different appearances of the prismatic bows, in prisms of different forms, and according to the different directions of the light Section 46, is designed to prove that 1 the first surface of a prism is not concerned in the formation of the blue bow, nor of the streaks that are produced by a $ lane glass applied to the efficient surface;' and section Viy that ' the streaks which may be seen in the blue bow contain, the colours of both the parts of the prismatic spectrum, by the critical separation of which the bow is formed.' The 48th section relates to the * formation of streaks.' This is accompanied by some immense figures, on a scale a thousand times magnified. It is intended to be proved, that' the principle of reflection is the cause of streaks;' but, notwithstanding the aid of the gigantic diagrams, we are by no means satisfied with the supposed demonstration. From the 49th section the reader may Jearn that * prismatic bows, when seen at a distance, are straight lines.' The 50th affirms, that 'the colours of the bow streaks owe their production to the principle of the critical separation of the different parts of the prismatic spectrum.' It must here be remarked, that the angles, at which the rays constituting the blue bow (sect. 41) are separated from the rest, are termed by Dr. H. critical, and tho effect a critical separation.

• Let a plain glass be laid under the base of a right angled prism; then, if the eye at first be placed very low, no streaks will be seen; but •when afterwards the eye is gradually elevated, till by the appearance of the blue bow we find that the principle of the critical separation of colours it exerted, the streaks will become visible, and not before ; nor will they remain in view when the eye is lifted higher than the situation in which, the effects of the critical separation are viable. It is therefore evident, not only that the colours are furnished by the same cause which produces the bow, hot also that they are modified into streaks by the plain surfac* Under the prism.' pp. 292, 293.

All this, notwithstanding, is perfectly consistent with the Newtonian theory ; and will admit of a ready explanation^ without adverting to Dr. H.'s new principle. • For the streaks cannot be seen when the eye is very low, because the reflection is then total; and they will usually disappear when the eye is much elevated, because either a great obliquity, or a very close contact, is required for producing them.

The 51st section is to prove that' a lens may be looked upon as a prism bent round in a circular form.' This proposition may be admitted withont any proof, provided the . angle of the supposed prism be always thought equal to that formed by the tangent planes to the lens at the point concerned in any individual experiment. Dr. H. details some experiments to establish this: and then says, 'a consequence of great importance may be drawn from' them:

•For since the cause of the coloured appearances, which have been called bows when seen in a prism, is now perfectly understood to be the critical separation of the colours of the incident light, it must be admitted that such a separation will certainly take place whenever a beam of light can find an entrance into glass, so as to make the required angles either with an interior or exterior surface, be it in the shape of a prism, lens, or solid of any kind, although the figure of the last transmitting surface should not permit such coloured-appearance-making-rays to reach the eye. A plano-convex lens will consequently by its construction separate die rays of light which enter at the convex surface in.such a manner, as by reflection to produce what, if it could be seen, would be called a blue bow, and by rays that come in at the plain side, separate them by intromission so as to produce a red one.

«To remove all doubt about the truth of this theory, I ground a small part of a plano-convex lens flat, that I might look into it, as it were, through a window, to see what pasted within. The flat made an angle •with the base of about thirty-four degrees, and I saw through it very plainly, in different directions of the illumination, a blue bow by light entering at the convex surface, and a red bow by light coming in at the plain one.' p. 297.

How egregiously may a very ingenious man deceive himself, to support a favourite theory! When Dr. Herschel 'ground a small part of a plano-convex lens //;/,' ;o mike 'a window' by which he might 'see what passed within/ 'tis pity he did not grind another window for hi:; understanding, through which he might have perceived that by this process he actually converts his lens into a prism. To convert a lens into a prism in order to see what takes place in a lens, is curious enough. We recollect only one experiment equally ingenious: that of the Irishman, who placed himself before a mirror and shut his eyes, in order to see how he looked when he was asleep.

In section 52, Dr. H. attempts to prove that 'the critical separation of the colours, which takes place at certain angles of incidence, is the primary cause of the Newtonian coloured Vol. VI. T

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