he determines the parallaxes and the apparent places of two stars, referred to the equator or the ecliptic. It is then only that he endeavours to find the apparent distance, and he obtains it by two lineary formulas of the most simple kind, as well as all those through which he has successively passed. M. Lagrange, on the other hand, attacks the difficulty at once, and without supposing any thing, except what he takes directly from the astronomical tables, he expresses the tangent of the apparent distance of the centres. But this expression is embarrassed by radicles; the quantities under the sign represent values very long and very complicated. The author to no purpose exhausts all the resources of his art and his genius to eradicate from these formulas all the terms, the absence of which will produce scarcely any change in the degree of precision. To no purpose has he contrived tables of an ingenious construction, in order to diminish the length of the calculation; even these tables, and the artifices of the calculus, are tacit acknowledgements that the problem surpasses the force of analysis, and a disguised imitation of the practice of astronomers. These tables, in fact, are formulas of the parallaxes from which the nonagesimal and its height are eliminated, which only makes the use of them more troublesome. It is this task, so great and so difficult, that M. Henri has accomplished by means quite different. M. Lagrange expressed by rectangular co-ordinates the true and apparent positions of two stars and those of the observer in space. M. Henri draws the same expressions from trigonometry, either plane or spherical. By this means he obtains all the formulas of Lagrange; so that the solution has gained nothing on the side of facility. To abbreviate, he restores the nonagesimal eliminated by Lagrange. Without using the name parallax, he introduces what is equivalent, and reduces it to tables; but notwithstanding all these efforts, he acknowledges himself that the method is still very troublesome. He does not believe that any professed astronomer will ever prefer it; but if the method is long and troublesome, this is the only fault with which it can be charged. It is neither less precise nor less proper to give exactly the difference of longitude between two places where the same eclipse shall have been observed. And the new point of view, under which M. Henri has presented it, cannot but augment the number of its partisans, by increasing the number of calculators capable of appreciating it. The methods employed by M. Henri deserve to be generally known. Opportunities perhaps of applying them more advantageously will occur. And the Class, as well as the commissioners, were of opinion, that at at a time when the original memoir of Lagrange is printed in the Connoissance des Temps for 1817, of which only a German translation had appeared in the Ephemerides of Berlin, astronomers would see with pleasure the same formulas demonstrated in a manner quite different, which is neither less rigorous nor less easy.

Annals of Mathematics, pure and mixed; a periodical Work, edited by M. I. D. Gergonne, Professor of transcendental Maihe

matics in the Lyceum of Nimes, Secretary and Supplemental Professor of Philosophy of the Faculty of Letters of the Academies of Gard, Nancy, and Turin. Nimes, Madame Veuve Belle; & Paris, Madame Veuve Courcier.

The physical and mathematical works presented to the Class are always enumerated in the accounts of the meetings, faithfully and honourably placed in the library, letters of thanks are sent to the authors, and complete lists of all these presents are printed in several of our volumes. But these lists can only contain the titles of the works, the names of the authors, and the time of their reception. There are, however, productions, and especially collections, which would deserve a more particular notice, either on account of their importance, or of the names of their editors. Such in particular are the Annals of Mathematics, the idea of which has been conceived, and the execution followed up, with a perseverance worthy of praise, by two distinguished members of the University of France, MM. Gergonne and Lavernede, powerfully and usefully seconded by several of their worthy colleagues or other professors of celebrity, such as MM. Kramp, Français, brothers Encontre, Du Bourguet and Servois; and likewise by several correspondents of the Institute, among whom we may mention MM. Tedenat, Flaugergues, and Lallemand.

These Annals are chiefly devoted to pure mathematics, and especially to researches having for their object to perfect and simplify the method of teaching the science. Nothing is excluded which may give an opportunity of applying them to the different branches of the exact sciences. Articles occur which will interest the mechanical philosopher in general, and likewise on optics, acoustics, astronomy, geography, fortification, seamanship.

Each number gives one or more theorems to be demonstrated, one or more problems to be resolved. Likewise a list of the new mathematical books, both foreign and domestic.

To the memoirs which they insert and the solutions that are sent them, the editors often add their own reflections and interesting researches. A part containing 32 pages appears each month. Two years form a large quarto volume, and the work is now in its fifth year. Among the great variety of objects discussed in this work, and among which it would be difficult to make a choice, we shall satisfy ourselves with pointing out for the meditations of mathematicians, the memoir of M. Servois on the different systems explaining the principles of the differential calculus, and several memoirs in which M. Kramp gives new alytical solutions of the most important problems of astronomy. What he proposes for the comets or planets newly perceived has this in particular, that it informs us whether the orbit be elliptical, parabolic, or hyperbolic. The author applies these formulas to the comet of 1781, calculated in the parabola by the method of Laplace, and he obtains very different results. These orbits conduct him to a hyperbolic orbit. The distances of the aphelia and perihelia are 1,633934, and

1,048364. This last in the parabola had been found 0.9609951, less of consequence by 0.087367. This is about of the great semiaxis of the earth's orbit. The longitude of the node is 13° 56′ 43′′ greater than in the parabola. The inclination is also greater in the hyperbola, but only 36 minutes. It would have been curious to have found at the end of the calculations the comparison of the two orbits with the observations. Mechain had made 12, and Pingré assures us, that the errors of the parabola did not exceed a minute and a half. M. Kramp has only employed three; the total interval is only eight days. By another combination the interval is reduced to five days. Perhaps so small an arc is not sufficient to warrant the conclusion that the orbit is really hyperbolic. But whether parabolic or hyperbolic, we can have no hopes of seeing the comet again, and therefore the question will always remain undecided. Astronomers will learn with interest that M. Kramp announces a sequel to this third memoir.

At the last meeting of the year, on the 26th of December, M. Desmarets read a Memoir on the Tides in the English Channel. From the soundings given in the French Neptune, and the charts of Dr. Halley, the author begins by giving a general plan of the basin. He determines the different depths of the waters of the sea, both towards the two coasts and in the middle of the channel. From these data, from the situation of the coasts of America, and the effects of the luni-solar attraction, combined with the general motion of the waters of the sea, M. Desmarets derives an explanation of the considerable tides observed on the coast of Eritanny. We want room for a more exact analysis, and therefore refer to the memoir itself.

M. Biot at the same meeting presented to the Class new researches on the phenomena and laws of polarisation.

M. Burckhardt has communicated new calculations respecting the comet of 1786. This comet could only be twice observed, which, as is well known, is not sufficient for determining its orbit. As a substitute for the third observation, M. Burckhardt makes the most probable suppositions for the distance of the comet from the earth. These different hypotheses conduct him to four orbits, the difference between which are sufficiently small to induce us to hope that the comet might be recognised in case it should return. The author of this memoir, who has much practice in these calculations, regarded generally as very troublesome, and which he is better able to abridge than any other person, endeavours to draw every advantage from this facility. He does not wish to allow any thing to be lost, and endeavours to supply what is wanting to us. In this view he has examined what was the greatest distance which could be supposed between the earth and the comet. He has found that it could not exceed 0,942. In that case indeed the elements would undergo pretty remarkable alterations; but this extreme case is very little probable. His worthy associate M. Buache, entering into his views, and seconding him with equal zeal, is consulting the journals

of navigators at that period. A third observation will perhaps be found, which, though not very precise, will be sufficient at least to reduce the uncertainty within much narrower limits; an uncertainty which is to be apprehended from two observations separated from each other only by an interval of two days.

ARTICLE XIV.

SCIENTIFIC INTELLIGENCE; AND NOTICES OF SUBJECTS
CONNECTED WITH SCIENCE.

I. Lectures.

Dr. Merriman's Lectures on Midwifery, at the Middlesex Hospital, will recommence on Thursday, Feb. 8, at half past 10 o'clock. Medical School of St. Thomas's and Guy's Hospitals.-The Spring Courses of Lectures at these adjoining Hospitals will commence the beginning of February, viz.:

At St. Thomas's.-Anatomy and the Operations of Surgery; by Mr. Astley Cooper and Mr. Henry Cline.-Principles and Practice of Surgery; by Mr. Astley Cooper and Mr. Henry Cline.

At Guy's.-Practice of Medicine; by Dr. Babington and Dr. Curry.-Chemistry; by Dr. Babington, Dr. Marcet, and Mr. Allen.-Experimental Philosophy; by Mr. Allen.-Theory of Medicine, and Materia Medica; by Dr. Curry and Dr. Cholmeley -Midwifery, and Diseases of Women and Children; by Dr. Haighton.-Physiology, or Laws of the Animal Economy; by Dr. Haighton.-Structure and Diseases of the Teeth; by Mr. Fox.

N. B. These several lectures are so arranged, that no two of them interfere in the hours of attendance; and the whole is calculated to form a complete Course of Medical and Chirurgical Instruction.

Russell Institution.-A Course of Lectures on Electrical Philosophy, with its application to the improvement of Chemical Science, and the explanation of Natural Phenomena, will be commenced at this Institution by Mr. Singer, on Monday, Feb. 5, at eight o'clock in the evening.

These Lectures will be continued on the succeeding Mondays at the same hour. They will embrace the most important features of this interesting branch of Natural Philosophy, with occasional observations on the Sciences with which it is most immediately connected.

II. Coal Gas.

The Coal Gas Company in London have lately very much increased the gaseous product yielded by coal, by distilling a second time the tar which is obtained during the first distillation. This second product of gas they consider as purer and better than the first product. Many years ago I made various experiments on

the quantity of gas yielded by coals. I found that the tar could be almost completely converted into gas during the first distillation, by making the whole pass through a red-hot tube. I conceive this. method might be economically adopted by the Coal Gas Company. They would probably be able by means of it to obtain by the first distillation double the quantity of gas which they procure at present, and thus save a considerable sum, which they must at present waste on a second distillation.

1

III. Condensation of Water on Glass. By Dr. Wells.

SIP,

(To Dr. Thomson.)

London, Jan. 5, 1816. I think it very probable that glass may attract moisture from the atmosphere through some special quality, originating, perhaps, in the alkali which forms a part of it, and that this circumstance occasioned the plate of your electrical machine, as mentioned by you in the last number of your Journal, to be wet, while other bodies, though similarly situated, were dry. The quantity of moisture, however, which you found upon the plate, I would denominate Sinall, notwithstanding that it is called by yourself considerable. For you said, if I recollect rightly, when you related this circumstance to me in conversation several weeks ago, that the moisture on the plate was uniformly diffused over it, which appearance I regard as only the commencement of the formation of dew, agreeably to what I have remarked in the eighth page of my essay. I am of opinion, therefore, that although it should be established by further observations, that glass can attract moisture from the atmosphere, in some way unconnected with its greater cold, still the quantity hence arising will always be very trifling, when compared with what it receives in consequence of its lower temperature.

I am, Sir, your most obedient humble servant,

WILLIAM CHARLES WELLS.

IV. Royal Society.

As the writer of the excellent letter which constitutes the first article of the present number does not appear to be sufficiently aware of the nature and constitution of the Royal Society, it may be proper to say a few words on the subject. The Royal Society consists of an association of Gentlemen for the express purpose of promoting the cultivation of the natural sciences. The expense of the association, which is considerable (for Government, so far from supporting the association, as is done in other countries, charges it with taxes which amount to several hundreds a year), is defrayed by the annual contributions of the members. This circumstance prevents the possibility of conferring the title of Fellow upon any person, however celebrated, unless he petition for it. Such a title would be, in fact, imposing on him a tax of 27. 12s. a year, which the Royal Society has no right to do. If, therefore, the mathema

8