ANNALS

OF

PHILOSOPHY.

JANUARY, 1816.

ARTICLE I.

Account of the Improvements in Physical Science during the Year 1815. By Thomas Thomson, M.D. F. R.S.

THE following account will be much less complete than I could have wished; but I was prevented by illness from commencing it till within three weeks of the period at which it was to be sent to the press. I was unable, in consequence, to peruse the vast number of papers and books which it was requisite to read (above 200 in number) with that attention which would have been necessary in order to give a complete account of their contents. I have, however, endeavoured to do as much justice to the subject as the shortness of the time would allow.

I. MATHEMATICS.

The observations of Professor Christison on the nature of fluxions (Annals of Philosophy, vol. v. p. 328, vol. vi. p. 178, 420,) will be read with interest by all those who wish to understand the metaphysics of this branch of mathematics, and to be satisfied of the accuracy of the calculus.

Only one mathematical paper has been published in the Philosophical Transactions for 1815, namely, an Essay towards the Calculus of Functions, by C. Babbage, Esq. The term function has long been used in analysis for the purpose of denoting the result of every operation that can be performed on quantity. The author of this curious and important paper first explains the notation which he makes use of, and the various orders of functions which may occur. He then solves 20 different problems, and shows their application to the solution of various interesting questions.

II. ASTRONOMY.

Three astronomical papers have been published in the Philosophical Transactions for 1815.

1. A memoir by Dr. Herschel on the Satellites of the Georgian Planet. It contains an immense collection of observations, continued from 1787 to 1810. The existence of two satellites has been established completely; the first of which performs a synodical revolution about the planet in 8d 16h 56′ 5.2"; the second, in 13d 11h 8' 59". He has rendered it probable that there exists a satellite nearer the planet than either of these two, and that there are likewise several exterior satellites. But the extreme remoteness of this planet renders the determination of these points exceedingly difficult.

2. A Memoir on the Dispersive Power of the Atmosphere, and its Effect on Astronomical Observations, by Mr. Stephen Lee. The author observes that stars of different colours must be differently refracted, and that the apparent altitude of the sun must vary according to the colour of the dark glass through which he is viewed. That the fixed stars differ from each other in respect to the composition of their light is evident to the naked eye; but this difference becomes still more perceptible when they are viewed through a prism properly adapted to the eye-piece of a reflecting telescope. The planets also differ much from each other in this respect. These considerations inducing Mr. Lee to suspect that the dispersive power of the atmosphere must be sufficient in many cases to produce considerable effect on astronomical observations, he made a set of observations on the diameter of the planet Mars while in opposition in 1813. From a great number of observations, he found that the deviation of the extreme rays of light was between and part of the total refraction. Mr. Lee conceives that the disagreement between the latitude of a place deduced from observations of circumpolar stars, and from observations of the sun, may be traced to the use of dark glasses. To a similar cause he ascribes some other discordances in astronomical observations.

3. Determination of the North Polar Distances, and proper Motions of 30 fixed Stars, by the Astronomer Royal. The table of the north polar distances of these stars laid before the Royal Society in 1813 was so accurate, that Mr. Pond found no occasion, from his subsequent observations, to make a greater alteration in any of them than of a second. By comparing his own catalogue with that of Dr. Bradley in 1756, he has ascertained the proper motions of these stars during a period of 58 years. The annual proper motion of the Pole Star is 0.057"; that of ẞ Ursa Minoris, +0.1".

III. ACOUSTICS.

Some objections to Dalton's theory of gases have been started in Germany. The most important of these is, that if the gases are not elastic to each other, every sound ought to be repeated four times,

as we live in an atmosphere composed of four elastic fluids; or supposing the effect of the carbonic acid gas and the vapour of water to be insensible, still every sound ought to be repeated at least twice by the azotic and oxygen atmospheres. As this never happens, it is concluded that these two gases are elastic to each other. This objection having been considered long ago, it is needless to resume the subject here.

The distance at which sounds may be heard is much greater than is generally imagined. Dr. Derham informs us, on the authority of S. Averrani, that at the siege of Messina the report of the guns was heard at Augusta and Syracuse, almost 100 Italian miles distant; and he states upon his own authority that in the naval engagement between the English and Dutch which took place in 1672 the report of their guns was heard upwards of 200 miles off, as far as Shrewsbury and Wales. (Phil. Trans. vol. xxvi. p. 2. 1708.) Humboldt mentions the reports of volcanoes in South America heard at the distance of 300 miles; and Mr. Monro, a British planter in Demerara, informed a friend of mine, on whose statement I can rely, that the loud explosions which took place from the volcano in St. Vincent's were heard distinctly at Demerara. this is a distance which must considerably exceed 300 miles.

IV. OPTICS.

Now

The various experiments that have been made by different philosophers to determine the relative quantities of light which proceed from luminous bodies are known, I presume, to most of my readers. The curious results obtained by Bouguer and Lambert, the photometer of Count Rumford, and of Professor Leslie, deserve to be studied and understood by all who are interested in such pursuits. Lampadius has lately proposed a new photometer, and he informs us that he has succeeded in making his instruments agree with each other as accurately as different thermometers do. His photometer consists essentially in a tube a foot long, through which he looks at the luminous object. At the extremity of the tube furthest from the eye he places thin shavings of horn till he can no longer distinguish the luminous object. At first he reckoned the degree of light given out by the luminous body by the number of shavings of horn necessary to intercept it; but as instruments constructed on such a plan could not be comparable with each other, he fell upon the following method to graduate his photometer. He burns phosphorus in oxygen gas, and ascertains the thickness of horn shavings necessary to intercept the light; and he contrives, by means of a screw and a ring, to pack these shavings always so that they shall occupy nearly the same space. This space he divides into 100 degrees. The instrument, thus graduated, serves to measure the light emitted by other luminous bodies. The defects of such an instrument must be apparent to every person. The difference in the transparency and thickness of the horn shavings, and the difficulty of packing them so that they shall always occupy the same space, must render

the instrument difficult of execution. Nor is it impossible that the polarization or non-polarization of the luminous rays according to the nature of the surface from which they proceed may have considerable influence upon the quantity of light capable of reaching the eye through the horn, upon which the value of the instrument as, a photometer totally depends. Lampadius has given various tables of the light emitted by different bodies as measured by his instrument. I shall transcribe one, by way of specimen. It exhibits the light emitted by the sky in a clear morning on the 16th of February at Freyberg. The photometer was directed to the south-east at the height of 45° above the horizon.

From this table we see that the twilight began an hour and a half before sun-rise.

But the greatest additions that have been made to the science of optics during the course of the year consist in the investigations respecting the properties of different bodies as far as the polarization of light is concerned. The principal experimenters on this subject have been Dr. Brewster and M. Biot. Dr. Brewster has been most indefatigable, and has published, during the course of 1815, no less than six different memoirs on the subject; five in the Philosophical Transactions of London, and one in the Philosophical Transactions of Edinburgh. I shall first notice such of the memoirs of Biot as have come to my knowledge, and then I shall give an account of Dr. Brewster's discoveries.

1. M. Biot discovered that the tourmaline, when very thin, refracts doubly, like calcareous spar; but when in thick plates, it refracts only singly. From this it is evident that in this mineral there exist two distinct causes of polarization; one belonging to the crystalline molecules of the tourmaline, the other depending on the plates of which the crystal is composed. The first acts sensibly only when the mineral is very thin; the second, when it has a certain degree of thickness.

M. Biot ascertained likewise that, when the agate is very thin, it transmits light in every direction, and possesses the properties of a doubly refracting body. The laws observed by Dr. Brewster respecting the agate hold only when it possesses a certain degree of thickness.

2. After Malus had discovered the polarization of light, when

reflected from the surface of diaphanous bodies, he examined the metals, and found that polarization was not produced by reflection from them, at least in the same manner as from diaphanous bodies. But Dr. Brewster afterwards discovered that, when a ray of light already polarized is reflected several times from the surface of plates of silver or gold, it is modified in such a way that, when analyzed by means of a prism of Iceland spar, it divides itself into two differently coloured pencils. Biot, on repeating the experiment, observed that the colours of the pencils were precisely the same with the coloured rings observed by Newton. These observations did not coincide with those of Dr. Brewster; but upon mentioning the subject to M. Arago, that Gentleman stated that he had obtained results similar to those of Dr. Brewster, and furnished Biot with a plate of silver by means of which that philosopher was enabled to observe similar results. Surprised at this difference, he investigated the subject with care, and found that the phenomena depended on the way in which the metallic plate had been polished. There are two ways of polishing metallic plates; by hammering and by friction. When the former mode is followed, the phenomena observed by Biot are obtained; when the latter, the phenomena observed by Dr. Brewster. Biot at last ascertained that a metallic surface polished by friction produces two distinct effects upon light. It gives to a part of the incident light what he calls moveable polarization, the same which is produced by a thin crystallized plate. This occasions the series of coloured rings of Newton. It gives also to the white incident light a fixed polarization in the plane of incidence, the same as is produced by a thick crystalline plate. The first of these polarizations is only sensible in particular positions when the metallic plate is polished by friction. Hence the reason why it was not observed by Dr. Brewster; but it is strong when the plate is polished by hammering, and accordingly it was observed by Biot.

3. M. Biot showed long ago that when light traverses certain crystals, the repulsive force which produces the extraordinary polarization acts with more intensity on the violet molecules than on the blue, more on the blue than on the green, and so on, acting with least intensity upon the red ray. It is natural to conclude that the extraordinary refraction acts in the same manner on the molecules of light, since it is intimately connected with polarization. In a memoir published in the Annales de Chimie for June last (vol. xciv. p. 281,) he has shown that this law holds with respect to Iceland crystal, and indeed all crystals in general.

I shall now give a short account of the discoveries on this subject published by Dr. Brewster during the year 1815.

1. He found that the glass tears formed by dropping melted glass into water, and commonly called Prince Rupert's drops, have the property of depolarizing light like crystallized bodies. He observed cleavages in these glass drops, as in crystals. When sufficiently heated, and allowed to cool slowly, they lose the property of depo