he was the ableft teacher. Of fuch a man the moft trivial anecdotes acquire a dignity; but those in particular deserve a diligent difcuffion, which are connected with his fpeculative opinions.'. . . The question however. is of fuch a nature as to demand great caution in those who would refolve it, fince either to cut the knot entirely, by difcrediting the whole narration, or to elude the preffure of it by forced explanation and unfatisfactory refinement, is alike to fhake the very pillars of hiftorical evidence, and confound every rule of criticifm and interpretation.' The opinions of the learned on this curious queftion may be reduced to these two general heads: 1. The firft is that of those who are inclined to give implicit credit to the hiftory as commonly understood, and to allow that Socrates was actually attended by a familiar demon; an opinion founded upon the words of Plato, fupported upon the principles of his philofophy by the fuperftition of his followers, and too eafily admitted afterwards by the Platonizing Chriftians, whofe notions of demons were nearly coincident with thofe of the Academic. 2. The fecond, and of late years, for evident reafons, the most in fashion, is that of those who endeavour to explain away the meaning of the word demon; who would perfuade themfelves and others, that the reason, penetration, or wisdom of the philofopher, with a certain felicity of conjecturing contingent events, is all the expreffion implies. Mr. Nares, previous to the particular difcuffion of his own hypothefis, lays down two propofitions which must be admitted as data, and which are too plain to occafion the flightest hefitation. 1. That for the determination of any queftion concerning Socrates, whether it relate to his hiftory or to his opinions, the authority of Xenophon is preferable to that of Plato. 2. That a fingle inftance of error, or of fuperftition, is by no means incompatible with the character even of the greateft and best of men. The folution which the learned and ingenious author of this effay propofes to give of this famous queftion is founded on a fact often denied; and that too on the very principles against which the latter of the above propofitions is aimed-viz. "That Socrates believed in the gods of his country, and was not free from the fuperftitions connected with that belief; particularly those refpecting omens and divinations."- His education furnished him with the names and offices of numerous deities whofe exiftence, though he could not, nor ever tried to prove, he never once prefumed to difpute. Such enquiries he thought prefumptuous, and had no good opinion of their utility. The idle fables related of them he probably rejected as the fig 5 ments ments of inventive brains; but these might be falfe without af fecting the existence of thofe beings, of whofe interpofition in the conduct of human affairs, he seems not to have entertained the fmalleft doubt. This evidently appears from every hiftory of his life, and every regifter of his opinions. Such being his eftablished principles, he was naturally led from thence to the belief in omens, dreams, oracles, and divinations of every name and fpecies; a belief, which as he took it up without any rigorous examination, did doubtlefs, according to the invariable nature of fuch ideas, grow habitual and inveterate in his mind: In the ift chapter of the Memoirs written by Xenophon, the creed of Socrates is very exactly stated: in it, not the words, but the opinions of the fage are delivered; and I think it hardly poffible to read it through with attention, without being convinced that he had at least as much faith in the religion of Athens as in this effay is attributed to him.' All the previous reafonings of the learned Author lead to this conclufion (which may be confidered as the chief object of the prefent attempt), "THAT SOCRATES, BY THE EXPRESSIONS USUALLY UNDERSTOOD TO REFER TO HIS DEMON, ALLUDED ONLY TO SOME SPECIES OF DIVINATION PERFECTLY ANALAGOUS TO THE OMENS OF HIS AGE AND COUNTRY." This conjecture is fupported by the exprefs teftimony of Xenophon; and is illuftrated by a remarkable paffage in the elegant treatife of Plutarch upon the genius of Socrates. The former puts the following expreffions into the mouth of Socrates: How is it that I am guilty of introducing new deities, in that I fay, that the voice of the Divinity gives me notice what I fhall do All men, as well as myfelf, are of opinion, that the Deity forefces the future, and to whom he pleases fignifies it: but the difference between us is this; they name the birds, the omens, &c. as the foretellers of what is to come. I call the fame thing the Divinity (or the Deity); and I think that in fo faying, I fpeak more truly and more refpectfully than thofe who attribute to birds the power which belongs to the Gods." And fo far, fays Mr. Nares, was this writer from annexing to the words in difpute any idea of a demon, that, in the very next paragraph, he fubftitutes for them a God, and the Gods, as expreffions perfectly equivalent.' The paffage in Plutarch, on the Genius of Socrates, which the ingenious Effayift hath produced to corroborate his hypothefis, is the following: "I turn (fays Galaxidorus, one of the chief perfonages in the Dialogue) to you, Polymnis, who exprefs a wonder that Socrates, a man whofe peculiar merit it was, that, by unoftentatious fimplicity, he accommodated philofophy to the ufes of human life, fhould not have called this fign a Sneeze, or a Sound, if fuch it were—but, in a ftyle of tragic pomp, the Deity. On the contrary, I ra ther ther should have wondered, if a man fo perfect as Socrates in the art of speaking, and in the true application of proper terms, had faid that the Sneeze gave him the intimation, instead of attributing it to the Deity. As if any one should fay, that he was wounded by a dart, rather than with a dart by the perfon who threw it or that the weight of any thing is eftimated by the scales, instead of saying, that it is performed with the fcales by the man who weighs them. For a work is not properly to be ascribed to an inftrument, but to him who poffeffes the inftrument, and applies it to its proper office; and the fign in the prefent queftion, is the inftrument which that power employs from whom the intimation proceeds." "What is this but the diftinction infifted on by Xenophon-that other perfons, though they believed the divination to proceed from the Gods, commonly mentioned the birds, &c. as the authors of it, confounding the inftrument of divination with the real agents in it; whereas Socrates was careful to maintain the dignity of the Gods, even in his expreffions, by afcribing the whole to them.' Mr. Nares hath illuftrated his hypothefis by a variety of curious and learned notes. We were, however, fomewhat furprised to see a writer of his penetration and erudition referring to the Fragment of a Letter from Xenophon to Efchines, as a genuine relique of the illuftrious ancient, whofe name it hath been made to bear. We know, indeed, that the learned Pearfon admitted it as authentic; but Dr. Bentley rejected it, for reasons which we have never seen refuted. In addition to the arguments of that great Critic, another has fuggefted itself to us, which poffibly may not be unworthy of attention. Towards the conclufion of the fragment the Author, speaking of the murderers of Socrates (Anytus and Melytus), fays, * οι δε κλεινανίες της μετάνοιας αποκαθαρσιν εκ ευρον. Now the purgation of repentance appears to us to be purely a Chriftian idea: and, what is ftill more, the expreffion itself seems to have been borrowed from Heb. xii. 17, μετανοιας γαρ τοπον εκ ευρε. Upon the whole, we confider this Effay as a very ingenious attempt to illuftrate a difficult problem in the hiftory of Socrates; and we recommend it, with the fincereft opinion of its merit, to the attention of the learned. *Raphelius confeffes that he doth not understand this paffage, and leaves it to be decided by the learned. We fee no difficulty in it; for, whether the Fragment be genuine or fpurious, it is eafy to underftand the paffage of the hatred which purfued Socrates's accufers, till growing intolerable they banged themfelves, απήξαιο μη φεροίας το μισος, as Plutarch fays. ART. ART. VII. PHILOSOPHICAL TRANSACTIONS, Vol. LXXI. For 1781. Part II. Concluded. See Review for Auguft last, p. 130. ASTRONOMICAL' and MATHEMATICAL PAPERS. Article 20. Aftronomical Obfervations made by Nathaniel Pigot, Efq. F. R. S. Foreign Member of the Academies of Bruffels and Caen, and Correfpondent of the Academy of Sciences at Paris. HESE Obfervations were made with the Inftruments defcribed in the Philofophical Tranfactions, Vol. LXVI. and LXVIII. Part II. They are defigned to fhew the latitudes and longitudes of fome particular places. Mr. P. fays, that the rocks on the Welch coaft, which run obliquely flanting into the Bristol Channel, render the navigation fo dangerous, that each year affords the horrid fpectacle of fhips wrecked: And here I am forry to add, that the barbarous custom of plundering thofe unfortunate veffels ftill fubfifts in all its inhumanity, notwithstanding all that the gentlemen of the country can do to prevent it.' Correct maps of this Channel are therefore extremely neceffary; yet, at a part where the univerfal opinion of the country gave 20 or 21 miles for the breadth of the Channel, an actual geometrical admeasurement gave not 20, but little more than 13 miles. Upon the whole, Mr. Pigot wifhes, that aftronomical obfervations, fufficiently correct, were made on the Somersetshire fide, which might be compared with thofe he has made on the oppofite fhore. It may poffibly be found, that the towns on the English coaft are placed in the maps too much fouth, and those in Wales too much north; and hence, perhaps, the too great breadth of the Bristol Channel. Article 27. A general Theory for the Menfuration of the Angle fubtended by two Objects, of which one is obferved by Rays after two Reflections from plane Surfaces, and the other by Rays coming directly to the Spectator's Eye. By George Atwood, M. A. F. R. S. Sir Ifaac Newton, fo long fince as the year 1672 (when Dr. Halley fet about making the catalogue of the fixed ftars in the South Seas), invented an inftrument for taking the angular diftance of the moon from a fixed ftar, by making the image of the moon, feen after two reflections from fpeculums, perpendicular to the plane of the inftrument, touch the flar seen by direct rays, the fecond reflecting fpeculum making a conftant angle of 45°, with the axis of the telescope directed to the ftar, the two fpeculums being parallel when the index ftood at the beginning of the femi-graduated arch of the octant. This was improved, with fome additional contrivances, by Mr. Hadley and others afterwards, afterwards, fo as to correct the obfervations, by making them. double, by means of what is called the back obfervation and other inftruments of various forms have been made by Smith and others, all anfwering the fame intention. The theory here given by Mr. Atwood includes all these, and a number of other forms hitherto untried; his only limitation being, that the two reflectors must each make always the fame conftant angle with the plane of the inftrument, let that angle be what it will; this, and the inclination of the telescope admitting of unlimited variety. Mr. A. fays, that he was induced to confider the fubject, because a general theory to determine the angle obferved by two reflections from the data on which its magnitude depends, without limitation or restriction, feems applicable to feveral useful purposes in practical aftronomy. He has given the general conftruction and analyfis of the problem very ingeniously, and fhewn the practical application to Hadley's inftrument, and one or two other forms, for which we must refer to the paper itself, as they cannot be understood without the plates. But the approximations, efpecially thofe that are deduced from the fluxions of others, muft not by any means be depended upon. Article 30. Hints relating to the Ufe that may be made of the Tables of Natural and Logarithmic Sines, Tangents, &c. in the Numerical Refolution of adfected Equations. By William Wales, F. R. S. Mr. Wales fays, that the firft intimation that he has met with of the ufe of the tables of fines, tangents and fecants, in refolving adfected equations, is in the latter part of the fecond volume of Profeffor Saunderfon's Elements of Algebra, printed in 1741, after his decease. The Profeffor there fhews how to refolve two cafes of adfected cubic equations by means of the tables; but it appears from many circumftances, he was not aware that the third cafe could be refolved in the fame manner. All the three forms were, however, refolved by the late Mr. Anthony Thacker, a very ingenious man, who died in in the beginning of the year 1744, by the help of a set of tables of his own invention, different from, but in fome measure analogous to, the tables of fines and tangents. Thefe tables were finifhed and publifhed, together with feveral papers concerning them, after his death, by a Mr. Brown of Cleobury. In these papers, befide explaining fully the ufe of the tables in refolving cubic equations, Mr. Thacker fhews, that his method comprehends the refolution of all biquadratic equations, if they be first reduced to cubic ones, in the manner which has been explained * He was mathematical master of Birmingham free-school, though by trade a journeyman taylor. by |