as in the former, the mercury became less fluid and amalgamatized, as it appeared, with the earth on which the experiment was performed. By distillation, a part of the mercury was driven off, while the metal was left behind: but it did not seem possible entirely to separate it from the mercury, so as to be able to examine it in a state of perfect purity.

Alumine and silex were not decomposible by the same process which had been applied to the alkaline earths: but, by a different arrangement, the object was at last partially obtained. They were fused with potash, and then negatively electrified; and in this state they were touched by a positive wire, when a kind of explosive effect was produced, and the wire became coated with brilliant metallic scales, which seemed to be the metallic basis of the earth.- Respecting the earths in general, although the proofs of their composition. cannot be deemed quite so clearly made out as that of the alkalies, yet we see no reasonable cause for doubting the justice of Mr. Davy's conclusions regarding them.

ASTRONOMY and HYDRAULICS.

Observations of a Comet, made with a View to investigate its Magnitude and the Nature of its Illumination. To which is added, an Account of a new Irregularity lately perceived in the apparent Figure of the Planet Saturn. By William Herschel, LL.D. F.R.S.-This paper contains no observations relative. to the motion of the comet, but is entirely devoted to the subjects specified in the title. Dr. Herschel pursues his antient mode of journalizing, and on this occasion we are not disposed to complain of it; since several persons, who viewed the remarkable comet of 1807, will thus have an opportunity of comparing their observations with those of Dr. H., though no very important conclusions can be expected to follow from such comparison.

A principal object with Dr. H., and an object not easily fulfilled, was to ascertain the magnitude of the nucleus of the comet; the nucleus being, according to his definition, that part of the head which appears, to be a condensed or solid body, and in which none of the very bright coma is included.' By two methods, the magnitude was ascertained; the first consisting in a comparison of the disk with small sealing-wax globules, placed on a post 2422 inches from the object mirror of Dr. H.'s ten-feet-reflector; a mode which is liable to uncertainty and objection, because the observed magnitude of the disk was compared with the recollected magnitude of the globules. In the second method, a direct comparison was

made of the disk of the comet with the disk of one of Jupiter's Satellites; and the telescopes employed for the 6

purpose

purpose of making this comparison had, generally, a power a little above 200. From a due consideration of the observations, the circumstances attending them, and some slight necessary computation, Dr. H. concludes that the real diameter is 538 miles. With regard to the illumination, he says:

Having thus investigated the magnitude of our comet, we may in the next place also apply calculation to its illumination. The observations relating to the light of the comet were made, from the 4th of October to the 19th. In all which time the comet uniformly preserved the appearance of a planetary disk fully enlightened by the sun it was every where equally bright, round, and well defined on its borders. Now as that part of the disk which was then visible to us, could not possibly have a full illumination from the sun, I have calculated the phases of the comet for the 4th and for the 19th, the result of which is, that on the 4th the illumination was I 19° 45' 9", and that on the 19th it had gradually increased to 124° 22' 40". Both phases appear to me sufficiently defalcated, to prove that the comet did not shine by light reflected from the sun only: for had this been the case, the deficiency I think would have been perceived, notwithstanding the smallness of the object. Those who are acquainted with my experiments on small silver globules, will easily admit, that the same telescope, which could shew the spherical form of balls, which subtended only a few tenths of a second in diameter, would surely not have represented a cometary disk as circular, if it had been as deficient as are the figures which give the calculated appearances.

'If these remarks are well founded, we are authorised to conclude, that the body of the comet on its surface is self-luminous, from whatever cause this quality may be derived. The vivacity of the light of the comet also, had a much greater resemblance to the radiance of the stars, than to the mild reflection of the sun's beams from the moon, which is an additional support of our former inference.

The changes in the brightness of the small stars, when they are successively immerged in the tail or coma of the comet, or cleared from them, prove evidently, that they are sufficiently dense to obstruct the free passage of star light. Indeed if the tail or coma were composed of particles that reflect the light of the sun, to make them visible we ought rather to expect, that the number of solid reflecting particles, required for this purpose, would entirely prevent our seeing any stars through them. But the brightness of the head, coma, and tail alone, will sufficiently account for the observed changes, if we admit that they shine not by reflection, but by their own radiance; for a faint object projected on a bright ground, or seen through it, will certainly appear somewhat fainter, although its rays should meet with no obstruction in coming to the eye. Now, as in this case, we are sure of the bright interposition of the parts of the comet, but have no knowledge of floating particles, we ought certainly, not to

See Phil. Trans. for 1805, page 38, the 5th experiment.'
T 3

ascribe

ascribe an effect to an hypothetical cause, when the existence of one, quite sufficient to explain the phenomena, is evident.

If we admit that the observed full illumination of the disk of the comet cannot be accounted for from reflection, we may draw the same conclusion, with respect to the brightness of the head, coma, and tail, from the following consideration. The observation of the 2d of February mentions that not only the head and coma were still very bright, but that also the faint remains of the tail were still visible; but the distance of the comet from the earth, at the time of observation, was nearly 240 millions of miles*, which proves, [ think, that no light reflected from floating particles could possibly have reached the eye, without supposing the number, extent, and density of these particles, far greater than what can be admitted.

My last observation of the comet, on the 21st of February, gives additional support to what has been said, for at the time of this ob servation, the comet was almost 2,9 times the mean distance of the Sun from the earth. It was also nearly 2,7 from the sun. What chance then could rays going to the comet from the sun, at such a distance, have to be seen after reflection, by an eye placed at more than 275 millions of miles § from the comet? And yet the instant the comet made its appearance in the telescope, it struck the eye as a very conspicuous object.'

The latter part of this memoir relates to a subject which has for some years occupied Dr. H.'s attention, namely the figure of the planet Saturn. The astronomical world was astonished, when it was first announced to them by the Doctor that the equatorial parts of Saturn did not bulge out, but were flattened; and the phænomenon is so contrary to that which might be expected to happen from the effect of rotation, and from the attraction of the planet's ring, that, without incurring the charge of obstinate and blameable incredulity, we may venture to doubt the existence of the fact stated, till it has been verified by more numerous observations. Dr. H. will no doubt multiply his examinations; and indeed he was, for the very purpose of ascertaining the phænomenon, observing Saturn when he remarked the new phænomenon of a difference in its two polar regions. On June 16, 1807, he perceived that the southern regions were more curved, or bulged outwards." For this phenomenon, however, Dr. H. does not seem inclined to account on any principles of material attraction, since he calls it an illusion; and it is properly an illusion, if the cause which he suggests be the true cause. The rays of

1

* 239894939.'

+ The sun's mean distance being 1, that of the comet was

2,89797-2

The comet's distance from the sun was 2,683,195.' § 275077889.'

light from the southern regions of the planet to the spectator's eye pass very closely to the edge of the ring; and they may be inflected by the edge, or refracted by its surrounding atmosphere. The last is imagined by Dr. H. to be the case; and he thinks that his supposition is somewhat confirmed by one of his former observations, (see Phil. Trans. 1790, p. 7.). when the smallest satellites of Saturn were seen (as it were) bisected, by the narrow luminous line under which the ring appeared when the earth was nearly in the plane of it.

Hydraulic Investigations, subservient to an intended Croonian Lecture on the Motion of the Blood. By Thomas Young, M.D. For. Sec. R. S. These discussions relate to the mechanical principles of the circulation of the blood; and accordingly the author has found it necessary to investigate the motion of fluids in pipes as affected by friction, the laws of the propagation of an impulse through the fluid contained in an elastic tube, the magnitude of pulsation in various parts of a conical vessel, and the effect of a contraction advancing through the length of a given canal. The mathematical part of this discussion is con tained in the present paper, and the physiological is reserved for a future occasion.

In the Encyclopedia Britannica, we find an extensive and ine teresting article on Rivers, written (as it is acknowleged to have been) by the late Professor Robison: in which the chief aim of the writer is to explain and confirm the theory of M. Buat, as it is delivered in his Hydraulique; and indeed from this article all our knowlege of M. du Buat's labours is derived, because we possess not his work. It would lead us very far beyond our boundaries to explain the plan and construction of M. Buat's system: but we are persuaded that we shall do a kind office by recommending to our mathematical readers a perusal of the article Rivers. It will be difficult to point out such another specimen of a cautious, refined, and dextrous application of the language of Mathematics to Physics..

Among the important formule given by M. Buat, one expresses the velocity of water flowing in a pipe. If V be the mean velocity, d the mean hydraulic depth, s the slope of the pipe, g12 × 82 inches, n a number determined from expe riment and 243.7, then

To this formula of computation Dr. Young objects, because it is not very convenient for practice; and because, which is more material, in extreme cases, (that is, when the tube is either extremely narrow or extremely long,) it is completely

T F 4

erroneous:

erroneous: another formula is therefore substituted, which is thus obtained: - if we denote by f the height necessary to overcome friction, by d and the diameter and length of a pipe, and assume a and c as arbitrary quantities, then

Dr. Y. states that he was justified in assuming this formula, because, from certain experiments, (which, however, he does 'not relate,) he found that the friction could not be expressed by any single power of the velocity, but appeared to consist of two parts, the one varying simply as the velocity, the other as its square.

a

are

The parts of the coefficients of v2 and ʊ, that is, -—-—-, rightly assumed, because the friction will vary as the length of the pipe and inversely as its diameter: the other parts, a and c, are numerically exhibited in this paper, and determined, we suppose, from experiment. These being ascertained, the whole height of water, composed (according to the ingenious principle of M. Buat) of two heights, one due to the friction, resistance, &c., the other necessary for producing the actual velocity with which the water flows, is equal to

=f+

or, according to Dr. Young, more nearly =

f+

550

དུ° 4783

Hence,

if we call b the height, and put for f its value, we have

If this quadratic be solved, and if b be put for

d

al +.00182.d

which is the form that Dr. Y. regards as more convenient for practice than that of M. Buat, and, with the determination of his arbitrary quantities, more nearly agreeing with the results. of experiments.

In order to compare his formula with that of Buat, Dr. Young gives at page 168, &c. a tabular view of both; and he then adds:

I

It appears from this comparison, that in the forty experiments. extracted from the collection, which served as a basis for Dubuat's calculations, the mean error of his formula is of the whole velocity, and that of mine only; but if we omit the four experiments, in which the superficial velocity only of a river was observed, and in