The fubject of this extenfive mathematical paper is expreffed in the commencement of it, which we fubjoin.

"Having," the author fays, "fome years back, when reading the learned Mr. Landen's fifth memoir, discovered the manner of applying a method of differences to the fpecies of feries whofe fums are obtained by the help of impoffible quantities, and having fince extended that application, I now venture to offer it to the confideration of others.

"The practice of this method, in moft cafes, appears to me ex. tremely fimple; and on that account, I am almoft induced to imagine, that they have already been confidered by mathemati cians; indeed fince the greatest part of this paper was written, I met with Euler's Inftitutiones calculi integralis; two simple series are in that work fummed by multiplications fimilar to those employed in the investigation of the principal theorems contained in this paper; but whether that learned mathematician has farther purfued the method, in that or in any other work, I have not as yet been able to ascertain.

"I have purposely confidered some of the series fummed by Mr. Landen, to afford an opportunity of comparing both the refults and methods; and because the series may have particular cafes in which both Mr. Landen's means and my own fail, I have added, towards the end, a general fcholium concerning the caufe, circumstances, and confequences of fuch failure in my me. thod." P. 147.

This author expreffes his method of fumming feries in feven theorems, which almost entirely depend upon three well-known lemmas. The ftatement of those theorems, together with the three lemmas which precede them, and a general fcholium, form the contents of this paper; of which it is impracticable to give a more particular account in a few lines.

VIII. An Account of a small Lobe of the human proftate Gland, which has not before been taken Notice of by Anatomifts. By Everard Home, Efq. F.R.S.

Having had occafion to examine the proftate gland of an elderly perfon, who had died in confequence of that part having been difeased, this author's attention was attracted by a little protuberance, which (probably in confequence of its being generally very finall,) does not appear to have been noticed by any other anatomift; upon further examination of the fame part in other fubjects, and in different states, he found that this protuberance is not always of the fame fize, nor has it always exactly the fame appearance; fo that Nn 2

in

in certain cafes of difeafe, the enlargement of it may be productive of a ferious obftruction. The ufual appearance and fituation of this newly-discovered part is shown in a plate which follows the paper.

IX. On the Quantity and Velocity of the Solar Motion. By William Herschell, LL. D. F.R.Ś.

In another paper which is inferted in the Ipreceding volume of the Philofophical Tranfactions, Dr. H. endeavoured to ascertain the direction of the folar motion in the immenfe fpace of the univerfe. In the prefent he endea vours to investigate the velocity of that motion. For this purpose his firft ftep is to examine the real motions of thofe ftars, which have been found to have an apparent motion;

"For," he obferves, " as it would not be proper to affign a motion to the fun, either much greater or much less than any real motion which may be found to exist in fome star or other, it follows that a general review of proper motions ought to be made before we can impartially fix on the folar velocity; but as trials with a number of ftars would be attended with confiderable inconvenience, I fhall ufe only our former fix in laying down the method that will be followed with all the reft." P. 206.

Dr. H. deduces the proportional diftances of thofe ftars from their apparent proportional brightnefs; which indeed, as he obferves, is at prefent the only rule we have to ge by. Those proportional distances are ftated thus:

In page 209, Dr. H. gives a table, which is calculated with a view to fhow that an increase or decrease of the folar motion will have a contrary effect upon the required real motions of different stars.

This table is followed by a variety of remarks concerning the effects, or the appearances that muft naturally take place amongst certain ftars, in confequence of their movements. Next to this Dr. H. treats of the calculations neceffary for drawing figures that will reprefent the obferved motions of the ftars, and not only gives a table of the refults of those calculations, but alfo exemplifies the use of it by means of fix plates which accompany the paper.

The other sections of this paper bear the following titles: "Remarks on the fidereal motions as they are reprefented from obfervation.

of

"The folar motion and its direction affigned in the first part this paper, are confirmed by the phenomena attending the observed motions of the 36 stars.

"Trial of the method to obtain the quantity of the folar motion by its rank among the fidereal velocities.

"Calculations for investigating the confequences arifing from any propofed quantity of folar motion, and for delineating them by proper figures."

The refult of thofe calculations is ftated in another table.

"Remarks that lead to a neceffary examination of the cause of the fidereal motions.

"Confiderations of the attractive power required for a fufficient velocity of the fidereal motions.

"Determination of the quantity of the folar motion. "Concluding remarks and inferences."

From those conclufions we fhall transcribe the following paragraphs, which will give our reader foine idea of this fublime fubject, as well as of Dr. Herschel's extensive views, and of the paths which he has opened to the industry of spe culative aftronomers.

"I muft," he fays, "now obferve, that the refult of calcu lations founded upon facts, fuch as we must admit the proper motions of the stars to be, fhould give us fome ufeful information, either to fatisfy the inquifitive mind, or to lead us into new dif coveries. The establishment of the folar motion anfwers both thefe ends. We have already feen that it refolves many diffi culties relating to the proper motions of the ftars, and reconciles apparent contradictions; but our inquiries fhould not terminate here. We are now in the poffeffion of many concealed motions, and to bring them ftill more to light, and to add new ones by future obfervations, fhould become the conftant aim of every aftronomer.

"This leads me to a fubject, which though not new in itself, will henceforth affume a new and promifing afpect. An elegant outline of it has long ago been laid before the public in a most valuable paper on general gravitation, under the form of Thoughts on the fubject (See the note to Phil. Tranf. for 1783, p. 283.); but I believe, from what has been faid in this paper, it will now be found that we are within the reach of a link of the chain which connects the principles of the folar and fidereal motions with thofe that are the caufe of orbitual ones.

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"A discovery of fo many hitherto concealed motions, prefents us with an interefting view of the conftruction of that part of the heavens which is immediately around us. The fimilarity of the directions of the fidereal motions is a ftrong indication that the ftars, having fuch motions, as well as the fun, are acted upon by fome connecting caufe, which can only be attraction; and as it has been proved that attraction will not explain the obferved phenomena without the existence of projectile motions, it must be allowed to be a neceffary inference, that the motions of the ftars we have examined are governed by the fame two ruling principles which regulate the orbitual motions of the bodies of the folar fyftem. It will alfo be admitted, that we may justly invert the inference, and from the operation of thefe caufes in our fyftem, conclude that their influence upon the fidereal mo. tions will tend to produce a fimilar effect; by which means the probable motion of the fun, and of the ftars in orbits, becomes a fubject that may receive the affiftance of arguments fupported by obfervation." P.235.

The meteorological journal, kept at the apartments of the Royal Society, occupies the laft pages of this part of the Philofophical Tranfactions.-It confifts, as ufual, of eleven columns, in which are ftated the following particulars; viz. 1. the days of each month throughout the year 1805, commencing with the 1st of January, and ending with the 81ft of December; 2. Six's thermometer, least and greatest heat; 3. Time of making the obfervation, which was done twice in the course of every 24 hours; 4. Thermometer without; 5. Thermometer within; 6. Barometer; 7. Hygrometer; 8. Rain; 9. Winds; 10. Strength of ditto; 11. Weather.

From the regifter of thofe obfervations it appears, that the leaft height of the thermometer (when it came down to 23°,) was obferved on the 2d of February; the greateft height, viz. 79°, took place at various times in July, in Auguft, and even in September. The leaft height of the barometer, viz. 28,81 inches, was obferved on the 22d of December; the greateft, viz. 30,68 inches, on the 15th and 16th of November. The quantity of rain that fell in the course of the year amounts to 20,4 inches.

At the end of the journal there is one ftatement of the declination of the magnetic needle for the year 1805, which makes it 24°, 7,8 W. And one for the dip of the fame, which is 70°, 21′.

ART.

ART. VIII. Etchings reprefenting the best Examples of ancient ornamental Architecture; drawn from the Originals in Rome and other Parts of Italy, during the Years 1794, 1795, and 1796. By Charles Heathcote Tatham, Architect, Member of the Academy of St. Luke at Rome, and of the Inftitute at Bologna. Imper, folia, 72 Plates, 34. 15s. Gardinen, Princes-ftreet, Cavendifh-square. 1799.

WE E break through all our ordinary rules of time, to notice not a work of literature, but of art, and one which, in fact, is no older now than when it first appeared, fince it profeffed from the first to reprefent only antiques.

A short preface, full however of found remark, is all the letter prefs that accompanies the work. The obfervations of Mr. Tatham on the labours of Piranefi, Le Roy, Stuart and Rivett, and Le Potre, are fuch as fufficiently prove his difcriminating taste and judgment To Piranefi, in particu lar, he gives both the praises and the cenfures which every enlightened student in art knows to belong to him,

The fingular fertility of his inventive powers, his intimate acquaintance with picturefque effect, and above all, his masterly boldness of execution, have obtained him a reputation, which will last as long as tafte for the productions of genius in the libe ral arts fhall exift among mankind.

"The warmeft panegyrifts of this great artist muft, however, acknowledge that even his works are not without defect. Fired with a genius which bade defiance to controul, and rejected with difdain the restraints of minute obfervation, he has fometimes facrificed accuracy, to what he conceived the richer productions of a more fertile and exuberant mind. This has betrayed him into much incorrectnefs of delineation; and his exceffive fondness for the antique has alfo led him to introduce many specimens of fculpture, of a vitiated, as well as of a more correct taste. So that one would fometimes imagine him to be influenced by the common, but erroneous opinion, that all the productions of antiquity are perfect and worthy of imitation; a notion, which is fo far from being true, that it will not hold with regard to several performances, even of the beft æras."

P. 3.

Of his own work, he fays, that he does not "offer it to the public as a complete and regular fyftem, but only as a mifcellaneous collection, defigned to prefent the admirers of compofition in ornament, and artifts efpecially, with materials, upon which their genius may employ itself with advantage; that by ftoring their minds with the ideas of the ancients, and becoming tho roughly acquainted with them, they may learn to conceive their own fubjects in the fame manner." P. 5.