nies into Arabia. Tab. 14. Genealogy of Saul king of Ifrael. Tab. 15. Kings of Syria and Damafcus. Tab. 16. The Genealogy of king David, from Judah to Rehoboam. Tab. 17. Kings of Judah. Tab. 18. Kings of Ifrael. Tab. 19. Judges of Ifrael. Tab. 20. The Genealogy of Jefus Christ, according to St. Luke. Tab. 21. According to St. Matthew. Tab. 22. Chrift's kindred. Tab. 23. High Priests from Aaron to the Captivity. Tab. 24. High Pricfts from the Captivity to Judas Maccabæus. Tab. 25. High Priefts after Herod got Ariftobulus drowned, till the City was destroyed by Titus Vefpafian. Tab. 26. Afmonean, or Maccabean Princes and Priefts. Tab. 27. Idumæan Kings of Judæa. Tab. 28. Kings of Affyria, according to Eufebius and Syncellus. Tab. 29. Kings of Affyria, according to Scripture, and according to Univerfal History. Tab. 30. Kings of Babylon, according to Eufebius, and to Syncellus. Tab. 31. Kings of Babylon, according to Ptolemy's Canon, and according to Syncellus. Tab. 32. Six laft Kings of Babylon. Tab. 33. Kings of Medes. Tab. 34. Kings of Medes, according to Herodotus, and Diodorus Siculus, Eufebius and Syncellus. Tab. 35. Kings of Perfia to Alexander the Great, according to Mirkhond. Tab. 36. Kings of Perfia, according to other Oriental writers.

We cannot purfue this throughout; but the reader will, from this fpecimen, perceive in what manner the work is digefted. We should obferve, that the titles we have printed in Italics, have nothing correfponding to them in Anderson's tables. The difference in the whole number of tables is indeed one hundred and feventy-fix, and the real difference is much greater than the apparent, for of the tables in Anderfon's work, a great number are completely chronological. Mr. Betham has therefore a prodigious number of genealogics, for which we look in vain in the publication of his precurfor. Such are many of the Oriental families, and thofe of remote countries in general, which are either given here alone, or with much more extent and exactness. Such alfo are many of the family genealogies of the nobility of Great Britain, who deduce their lines from fovereigns; a very flattering and attractive part of the work to perfons fo related. We are glad to fee a production of fo very laborious as well as ufeful a kind, encouraged by a confiderable number of fubfcribers; and we doubt not that, as the book shall become more known, the author will find it in demand, by all who feek to stock their libraries with books of general reference. A work of this kind, though apparently barren and uninterefting to the cafual infpector, will often furnifh a key which could in no other

R 2

way'

way be obtained, for unlocking the obfcurities of history, and giving, in a clear and diftinct view, that which narrative usually delivers with more or lefs of confufion.· ́

ART. II. Philofophical Transactions for 1795. Part II.

(Concluded from our laft, Page 136.)

XV. On welding caft Steel.

Bart, F. R. S.

By Sir Thomas Frankland, pp. 296 and 7.

CAST fteel, in a welding heat, fays Bishop Watfon, Chem.

Efs. iv. 148, runs away under the hammer like fand. Sir Thomas Frankland has difcovered that, in order to unite it perfectly with iron, it is only neceffary to apply it, in a lower degree of heat: the caft fteel being in a white heat, while the iron is in a welding heat. For this purpose they must, of courfe, be heated feparately. He is uncertain whether the Sheffield artists may not also have discovered this process, but as he finds it unknown to other cutlers and fmiths, he here publishes it for the general benefit of fuch artificers.

XVI. The Binomial Theorem demonftrated by the Principles of Multiplication. By the Reverend Abraham Robertson, A. M. of Chrift Church, Oxford, F. R. S. In a Letter to the Reverend Dr. Mafkelyne, F. R. S. and Aftronomer Royal. Read May 21, 1795. P. 298-322.

The Binomial Theorem, which was invented by Sir Ifaac Newton, about the year 1665, was not communicated to the world till many years after, and then appeared without a demonftration. The extenfive utility of this Theorem has induced feveral eminent mathematicians, and particularly thofe of late years, to give demonftrations of it; which, till now, have been effected by one or other of the following methods. By induction; by the properties of the figurate numbers; by the method of increments; by the method of fluxions; or by the refidual analyfis. But, in the paper now before us, Mr. Robertfon has produced a demonftration of this celebrated

* This was the invention of the late very able mathematician, Mr. John Landen.

Theorem,

Theorem, by the principles of multiplication; which, as he obferves, is a more direct way to the eftablishment of it.

This paper confifts of two-principal parts; the first contains an investigation of the Theorem in the fimpleft cafe, or when the index, 2, is a whole number; the fecond contains a demonstration of it when the index,, is any fraction, which is the most general cafe: and here the co-efficients of the terms in the feries are not affumed, but determined by the preceding investigation.

In examining this paper, we found a very ingenious fubftitution, by which the fubfequent operations are extended to more terms, and yet are contained in lefs room, and are more clear and diftinct, than they could have been in the ufual notation. We had the fatisfaction alfo to obferve, not only that the notation is neat and ingenious, but that the whole procefs is conducted in a correct and masterly manner.

XVII. Experiments and Obfervations to investigate the Nature of a Kind of Steel manufactured at Bombay, and there called Wootz: with Remarks on the Properties and Compofition of the different States of Iron. By George Pearfon, M. D. F. R. S. P. 222-346.

Wootz is faid, by Dr. Scott of Bombay, in a letter to the Prefident of the Royal Society, to be a kind of fteel, in high esteem among the Indians. It admits of a harder temper than any thing known in that part of India; is employed for covering the part of gun-locks which is ftruck by the flint; for cutting iron on a lathe, or stones; for chizzels, files, faws, and wherever exceffive hardness is required. But, as it will not bear any thing beyond a flight red heat; after which a part of it feems to run, and the whole is loft, as if it confifted of metals of different degrees of fufibility, it is inconvenient to manage, and can only be joined with iron, by fcrews and other mechanical aids. Dr. Pearfon having obtained fome fpecimens of this fubftance, in the form of round cakes, undertook to investigate its properties, and gives, in this paper, an exact account; 1. of its most obvious properties, and its fpecific gravity, compared with that of other kinds of fteel, and iron 2. of the effects produced upon it by fire, with refpect to malleability, fufibility, induration, &c. 3. of the effect of fire united with oxygen gas, nitrous, and other acids: and, laftly, of the properties of its oxide or calx.

:

The refult of thefe experiments is, that Wootz is manifeftly a fpecies of iron and Mr. Stodart, who forged a penknife of it for the Prefident, was of opinion, that, notwithstanding the

difficulty

difficulty and labour in forging, "it is fuperior, for many purpofes, to any feel ufed in this country. He thought it would carry a finer, ftronger, and more durable point; and might, therefore, be particularly valuable for lancets, and other chirurgical inftruments." It appears that it is not malleable when cold, nor eafily forged when ignited; the ftate of ignition requifite for that purpose being confined within a very few degrees of heat: that it may be tempered and diftempered, but this alfo not within a confiderable range of heat; that the degree of heat at which it is forged, is lefs than that, at which it is tempered, the former being red in the dark, the latter red in the light: that it will receive a polish equal to the finest steel: that its fufion requires a higher degree of heat than that of crude iron that it is not easily reduced into filings, even after annealing; is not fo brittle as raw iron or even steel; and on folution in fulphuric acid and water, affords about the fame quantity of carbone, and rather iefs of hydrogene gas than fteel.

In order to afcertain the clafs of this metal, among the fpecies of ferrugineous fubftances, Dr. Pearfon enumerates the fpecifical properties of all the kinds of iron now known, and decides that Wootz approaches nearer to the state of steel than of either raw or forged iron; and that, with regard to the kind of fteel to which it is to be referred, it is not that variety in which there is either an excefs or deficiency of carbone; but that it contains undoubtedly fome other ingredient, which he conceives to be oxygen. This curious investigation is carried on with great fkill and accuracy, and promifes to lead to fome ufeful application of the fubftance in queftion in this country.

XVIII. Defcription of a Forty-Feet reflecting Telescope. By William Herfchel, LL. D. F. R. S. 19 Plates. P. 347

409.

The defcription here given is full, perfpicuous, and illuf trated by forty-feven figures. From the introductory part of. the paper it appears, that Dr. Herfchel was indefatigable in his attention to aftronomical inftruments before he was generally known in the literary world, as ardently engaged in the purfuit of science.

"When I refided at Bath," he fays, "I had long been acquainted with the theory of optics and mechanics, and wanted only that experience which is fo neceffary in the practical part of thefe fciences. This I acquired, by degrees, at that place, where, in my leisure hours, by way of amufement, I made for myfelf feveral 2-feet, 5-feet, 7-feet, 10-feet, and 20-feet Newtonian telescopes; befides others of the Gregorian form, of 8 inches, 12 inches, 18 inches, 2 feet, 3 feet, 5 feet,

and

and 10 feet focal length. My way of doing these inftruments, at that time, when the direct method of giving the figure of any of the conic fections to fpecula was ftill unknown to me, was, to have many mirrors of each sort cast, and to finish them all as well as I could; then to felect, by trial, the beft of them, which I preferved; the reft were put by, to be repolifhed. In this manner I made not less than two hundred 7-feet, one hundred and fifty 10-feet, and about eighty 20-feet mirrors; not to mention those of the Gregorian form, or of the conftruction of Dr. Smith's reflecting microscope, of which I alfo made a great number."

Such ftrenuous endeavours in the fabrication of inftruments, and a fimilar perfeverance in their application, juftly deferved patronage, and, fortunately for the caufe of aftronomy, it was granted. Succefs had emboldened Dr. Herfchel to conceive ftill greater projects for difcovery, and "the Prefident of our Roval Society," he fays, "who is always ready to pronote ufeful undertakings, had the goodness to lay my defign before the king. His Majefty was graciously pleafed to approve of it, and, with his ufual liberality, to fupport it with his royal bounty. In confequence of this arrangement, I began to conftruct the 40-feet telescope, which is the subject of this paper, about the latter end of the year 1785.

After mentioning fome interruptions and accidents relating to the construction of the inftrument, he concludes the introduction with the following fentence.

Auguft, the 28th, 1789. Having brought the telescope to the parallel of Saturn, I difcovered a fixth fatellite of that planet; and alfo faw the fpots upon Saturn, better than I had ever feen them before, fo that I may date the finishing of the forty feet telescope from that time."

A moment's reflection will convince our intelligent readers that any attempt, without figures, to convey a clear idea of Dr. Herfchel's inftrument and apparatus, defcribed in the paper before us; must end in difappointment. We, therefore, refer them to the paper itfelf. From a review of Dr. H.'s difcoveries, and a confideration of other circumftances, we fear that his forty-feet reflector does not anfwer the expectations. at first entertained from it; but it would be extremely unfair, on this account, to derogate either from the defign or execution, as throughout both, an uncommon degree of ingenuity appears to have been exerted.

XIX. Abftract of a Register of the Barometer, Thermometer, and Rain, at Lyndon, in Rutland, 1794. By Thomas Barker, Efq. Communicated by Thomas White, Efq. F. R. S. Read, June 18, 1795. P. 410-413.

The nature of Mr. Barker's annual regifter is well known to those who have been accuftomed to perufe the Philofophical Tranfactions