of incidence, and becomes ultimately (rr—1)"

We cannot help

thinking ourselves justified in looking forwards to a perfect coincidence between this formula and the promised experiments of Mr. Biot on substances placed in these circumstances. We understand that Dr. Brewster has lately made some observations of a nature nearly similar; but we doubt whether he has determined the refractive powers of his crystals with sufficient accuracy to allow of the application of our calculations with perfect precision.

A singular confirmation of the mode of explaining the colours of thin plates, which we have adopted, is afforded by the experiments of Mr. Arago, who found that the light forming the transmitted rings appeared to be polarised in the same direction with the reflected light, while the rest of the transmitted light was polarised in a contrary direction. It is a necessary assumption in the theory of periodical colours, that the rings seen by transmission actually depend on light twice reflected within the plate, and which must therefore be polarised like the rest of the reflected light; although, without these experiments of Mr. Arago, it would have been difficult to obtain so direct a demonstration of the fact.

The colours exhibited by thick pieces of rock crystal, cut, as in Mr. Biot's unpublished experiments, perpendicularly to the axis, might be expected to afford some explanation of those which Dr. Seebeck has observed in large cubes or cylinders of glass, placed between two oblique reflecting surfaces, or between two piles composed of thirty pieces of glass each, w which produced the effect of complete polarisation on light transmitted at the appropriate angle. If, however, Dr. Seebeck's observations are correct, the analogy can be only superficial; for the effects of these pieces of glass seem to depend on their entire magnitude and outward form, without any particular relation to an axis of extraordinary refraction. Thus in the perpendicular transmission of the polarised light through any points in the diagonals of the surfaces of the cubes, or in the diameters parallel to their sides, the rays of different colours appeared to be dif ferently affected according to the part of the glass on which they fell, and to exhibit one or the other only of the two images, which would have been visible through a piece of doubling spar, if the glass had not been interposed; so that when the whole cube was viewed at once under these circumstances, it afforded an appearance of diversified colours, arranged in very singular forms, which Dr. Seebeck compares to the figures assumed by sand on vibrating pieces of glass, and discovered some time since by Professor Chladni; but which appear to have a still nearer resemblance to those which Comparetti has described, as produced by the ad

:

mission of a beam of light into a dark room, through apertures of different forms; and we are much inclined to suspect that they depend on the twofold transmission of the light to the eye, perhaps after repeated internal reflections, from the different points in the lateral surfaces of the substances employed. The effects were most conveniently observed in cubes of 12 inch, and better in white than in yellowish glass: in cubes of an inch only, they were indistinct nor were they produced by fluor spar, rock salt, or by any kind of liquids: they were modified, and sometimes inverted, by the interposition of a plate of mica and ice acted in a similar manner in depolarising the light transmitted through it. We find in these researches a full confirmation of the experiments which Mr. Malus had made some time before his death, to show, that the polarised light, which falls on a transparent medium at such an angle, as not to be reflected, is transmitted, with no material diminution of its intensity. Dr. Seebeck's language is a little enveloped in the mysticism of the school to which, by some singular caprice of fancy, he has thought proper to attach himself: but we cannot hesitate to believe, that as he continues his examination of the phenomena of nature, he will by degrees be persuaded of the futility of the objections which Mr. von Goethe has advanced against the Newtonian doctrine of the composition of white light, and of the inaccuracy of the assertions on which some of those objections are grounded.

While the optical philosophers of France and Germany have been engaged in these researches, Dr. Brewster has been very laudably employed, in this country, in experimental investigations relating to the same interesting department of physical science. He has found that the agate, cut by a plane perpendicular to its laminae, transmits one only of the polarised portions of light: that the polarity of light may be destroyed by transmitting it in a certain direction through almost all mineral substances, and through horn, tortoise-shell, and gum-arabic; while in certain other directions its properties rema in unaltered, whence he has distinguished, in these substances, different depolarising and neutral axes; and that the light reflected from the oxydated surface of polished steel is so modified, as to prove, in his opinion, that the oxyd is a thin transparent substance. His observations on the colours, sometimes exhibited by crystals of Iceland spar, seem to be identical with those of Martin and Malus..

Dr. Brewster has very ingeniously exercised his inventive powers in the contrivance of a variety of micrometers, goniometers, microscopes, and telescopes, several of which may very possibly be found useful in particular circumstances, although to others there appear to us to be many material objections: but, without referring to the test of experience, it would be of little

utility for us to discuss their particular. merits. Some detached remarks, however, we shall take the liberty of submitting to our readers, on passages of the work which appear to require correc tion. The advantage which Dr. Brewster attributes to the use of a transparent fibre for a micrometer, (p. 71,) is merely imaginary; since, although it is true that the central rays suffer no inflexion,' this circumstance affords us no assistance whatever in judging when the rays are actually central;' and the light transmitted by such a fibre, whenever the luminous object is in its neighbourhood, could only create confusion. In speaking of a telescope for the measurement of angular positions, Dr. Brewster observes that 'the line, which joins any two stars, forms every possible angle with the horizon in the course of 23 hours and 56 minutes;' (p. 128,) but this is obviously a mistake; for at the poles of the earth the angle would not vary; and in other latitudes only within certain limits. The table of the variation of the focal length of a telescope, (p. 218) is wholly erroneous, from the employment of linear feet and square inches in different parts of the same formula. Dr. Brewster has misunderstood Professor Robison and Mr. Wilson, where they observe, that the focal length of an achromatic telescope must be lengthened, when it is directed to a star towards which the earth is moving, (p. 221): it was not from the different distances of the stars, but from the difference of the relative velocities of light, that they argued, according to the general opinions respecting light, the necessity of the occurrence of such a minute variation. In p. 424-5, the magnifying power is miscalculated, and we must read 4.9 for 5.6.

The most useful part of the whole work appears to be the series of experiments on the refractive powers of fluid and soft substances performed by interposing them between the object glass of a microscope, and a plane glass nearly in contact with it, and then measuring the joint focal length of the combination. The comparative distances, thus obtained, are exhibited in several extensive tables: but we cannot help feeling some surprize, that the author has not attempted to deduce, from any one of his numbers, the direct refractive power of the substance concerned, as he certainly would have done if he had been aware how easily it might have been accomplished, after a preparatory investigation, dependent on the common laws of dioptrics. From such an investigation we have obtained formulae for each of the two series of experiments; for the first (pp. 258, 268, 270,) f being the focal length expressed by the number in the table, and the index of refraction, ? 1.887 and for the second, (p. 264) r = 2.31.sf' f Thus we obtain for phosphorus 2.125, sulfur 2.008, aloes 1.643,

1

3.31.

balsam of Tolu 1.636, oil of cassia 1.625, guaiacum 1.609, and pitch 1.589. Dr. Wollaston's Table gives for phosphorus 1.579, and for pitch 1.53; and there can be no doubt that the accidental presence of some phosphoric acid, and some oil of turpentine, on the surfaces of these substances occasioned an error, in these instances, in Dr. Wollaston's determinations, however excellent his method may be in other cases; for we cannot agree with Dr. Brewster, in thinking that the acknowledged exhibition of the index appropriate to the extreme red ray is an objection to the method. It is remarkable, as our author has justly observed, that the assignment of so high a refractive density to phosphorus restores the inference of Newton, respecting the relation between refractive powers and inflammability, to its original universality and importance.

Dr. Brewster's mode of ascertaining the refractive powers of solids, by immersing them in a mixture of fluids of equal refrace density, is perfectly unobjectionable; and he observes that is easy to discover, in this manner, the internal flaws and other irregularities of gems, without the labour of polishing any part of their surface. He does not, however, appear to have followed this method in determining the indices of refraction which are contained in his table, (p. 283,) having employed for this purpose 'the same prisms in which the dispersion was corrected,' and probably in the same manner: hence, from an erroneous mode of computation, his numbers are almost uniformly too large thus we have phosphorus 2.224, sulfur 2.115, carbonate of lime 1.665 and 1.519, oil of cassia 1.641, and guaiacum 1.619, all of which exceed the more accurate determinations which we have already mentioned. In the same manner we find for diamond 2.487 to 2.470, instead of 2.439, the density assigned by Newton; and it is probable that the chromate of lead and realgar, both of which Dr. Brewster finds more dense than the diamond, are also rated somewhat too high at 2.974.. 2.503, and 2.549: the former appears to have a double refraction more distinct than any other known substance.

For a similar reason, we can place no dependence whatever on the table of dispersive powers, which is calculated according to a coarse approximation, wholly inapplicable to the circumstances of the experiments. The mode of inclining a prism of a greater density, until it caused the image of a right line, viewed through it and in conjunction with a prism of smaller density, to be colourless, would be a very good one, provided that the apparatus were so arranged, that the rays should be perpendicular to the common surface of the prisms; but even then Dr. Brewster's mode of calculation would be only applicable to prisms with very small

refracting angles. In the only experiment which is related with precision (p. 306,) the result implies an impossibility; for if we trace a ray of light through its intricate progress from the water to the glass, the angle of incidence upon the last surface will come out 41° 5', while the utmost obliquity, at which it could have been transmitted is 38° 14', consequently the index of refraction assigned to the prism, 1.616, must be extremely erroneous, if the angular measurements were correct. And since various errors of this kind may have affected the different results in different degrees, we cannot depend on the tables, even for the order of the different dispersive powers.

a

Dr. Brewster appears, however, to have been more successful in confirming and extending the observations of Dr. Blair on the different proportions in which the prismatic spectrum is divided, according to the diversity of the substances which afford it. He has shown very clearly, both from theory and by experiment, that the violet rays must be proportionally more expanded by prism with a large angle than by a smaller one of the same substance; while he has found, on the other hand, that a smaller prism of a more dispersive substance almost always expands the violet rays more than a larger prism of a less dispersive substance; and that when two such prisms are combined, they exhibit a green fringe in the usual place of the red, and a wine coloured' fringe in that of the violet. The substances most expansive of the violet are oil of cassia and sulfur; the least expansive, sulfuric acid and water, although water has not quite so low a disperpower as fluor It spar. seems to follow from Dr. Brewster's estimate, that the proportions of 2 red, 3 green, 4 blue, and 3 violet, which are nearly those of Dr. Wollaston's determination, are changed, when sulfuric acid is employed, at least as much as to 4 red, 3 green, 3 blue, and 2 violet; but we feel great difficulty in believing that so great a variation as this could have escaped the notice of any attentive observer. We have no doubt, however, that if Dr. Brewster continues to pursue his ingenious investigations, he will by degrees acquire a habit of introducing greater accuracy into his measurements, and what is of still more importance, more mathematical neatness into his calculations; and, with these improvements, we doubt not that his future labours may be productive of material benefit to those departments of physical science which have engaged his attention.

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