Nothing (fays he) can warrant refiftarce to any established government, but an attack upon thofe principles of liberty, civil or religious, which, if once deftroyed, muft neceflarily destroy all liberty, and overturn the very foundations of all free and lawful vernment. In fuch a cafe, to refift is highly virtuous and praiseworthy, and will moft affuredly be crowned with the approbation of God.'

go.

In his conclufion of this fenfible and ufeful difcourfe, Mr. Evans justly remarks,

It is no fmall part of the happiness of this day to recollect it as one principal blefling of the Revolution we commemorate, that to it we are indebted for the prefent reigning Monarch and his illuftrious family, under whofe aufpicious influence we may fafely fay we have every thing to hope for, and nothing to fear. Our divifions about the late unhappy war, concerning which the best of men entertained different ideas, are at an end; and, bleffed be God, we are once more (and what good man but must exult in it?) an united and happy people, with a King fo virtuous and good, laws fo juft and upright, and a conftitution fo free, fo firm, and fo excellent, what remains for us but to provoke one another to love and good works.' V. At St. Margaret's Weftminster, before a Society of Noblemen and Gentlemen, Friends to the Conftitution, Nov. 5, 1788; being the hundredth Anniversary, &c. By Colin Milne, LL. D. Rector of North Chapel, in Suffex. 4to. Is. 6d. Elmsley. The text is from Pfalm lxxv. 5, 7. The Doctor informs us that the two fignal deliverances which are annually commemorated on this day fuggefted the words of the text, as afferting the doctrine of a Divine fuperintendence of states and nations that this was very remarkable in the occurrences of the Jewish ftate; and ftill more fo in the propagation of the Gospel. He then obferves that the doctrine of the text receives farther confirmation from the annals of every nation and people, and of none more than of our own. Here he inftances the Reformation, the deftruction of the invincible Armada, the Popish gun-powder confpiracy, and the glorious Revolution. The reflections which Dr Milne makes on the last mentioned happy event, are very juft. His notions of civil liberty agree very well with ours; but we cannot entirely acquiefce in his ideas of religious freedom, which, he tells us, is exceedingly different from that innovating temper which would overleap every mound, and destroying the bulwarks of national eftablishments, leave Scripture open to the wild interpretation of every enthufiaftic vifionary.' We had hopes that nothing which we could queflion, would have occurred in this otherwife fenfible and pertinent difcourfe. But we think it incumbent on us to remark, that, according to the Scriptures, we are not to call any man malter upon earth (i. e. in matters of confcience and religion) and that we are to judge for ourselves. "No! (fay our SPIRITUAL GUIDES) out of love to your fouls, we will judge for you." This is very kind! But when THEY fay one thing, and REVELATION and REASON fay another; our Readers will eafily determine WHICH it is fafeft for us to follow.-We agree with Doctor M. that the pattern of excellence held forth to us from the throne

is tranfcendantly bright; and we heartily pray that the good wifhes with which he very properly concludes his fermon may be fully realized.

VI. An Oration delivered at the London Tavern, on the 4th of Nov. 1788, on occafion of the Commemoration of the Revolution, and the Completion of a Century from that great Event. By Jofeph Towers, LL. D. 8vo. is. Dilly.

This very fenfible addrefs is well calculated to excite a laudable zeal for maintaining the important privileges fecured to us by the happy event here commemorated. Having exprefied his good wishes, that in every age, this country may continue to enjoy the honour and the felicity of public freedom, Doctor Towers adds, in a note,

I alfo fincerely with fuccefs to all the efforts of the French nation, for the recovery of their liberties; and I fhould rejoice to fee them poffeffed of a conftitution fimilar to that of England; and that two nations, fo eminently diftinguished in arms and in literature, instead of exhaufting themfelves in fanguinary wars for no valuable purpose, may unite together in communicating the advantages of freedom, fcience, and the arts, to the moft remote regions of the earth.'

In this generous and praife-worthy fentiment, we heartily and cordially join; hoping that, from this time, we fhall hear no more of that illiberal and fenfelefs abuse of our neighbours, whom it bas been common for us, in the frenzy of national prejudice, to ftigmatize, as the NATURAL enemies of our country!

CORRESPONDENCE.

** In answer to our Correfpondent, Y. Z. who thinks that in p. 226. of our Review for September, we have mifquoted Matthew Paris, or rather miftaken the meaning of his words, let it be obferved, that the word argentum does not correfpond exactly either to a fhilling, or to a penny. In a matter fo uncertain as the value of ancient coins, and their precife proportion to labour and the neceffaries of life, compared with that of the currency of the prefent day, antiquaries vary much in opinion. The fenfe in which we explained the paffage is confirmed, or at leaft corroborated, by the authority of Mr. Gibbon. See his Roman Hiftory, vol. vi. p. 303.

From the very great prefs of temporary bufinefs, we must poft. pone our answers to other correfpondents; they will he found in our Appendix, which will be publifhed with the Review for next month.

Particular Omiffion in our laft.

·

P. 461. Art. 29. in the title, after by W. Withering, M. D.' add, including a new set of references to figures. By Jonathan Stokes, M. D. Phyfician at Kidderminster. See alío the note at p. 544

APPENDIX

TO THE

SEVENTY-NINTH VOLUME

OF THE

MONTHLY REVIEW.

FOREIGN LITERATURE.

ART. I.

Hiftoire de l'Académie Řojale des Sciences, &c. i. e. History and Memoirs of the Royal Academy of Sciences at Paris, for the Year 1785. Concluded from our last Appendix, p. 630.

HAY

AVING promised a farther account of the laft volume of the memoirs of the academy of fciences at Paris, we resume the pleafing task of laying before our readers an account of the labours of this learned body; which has for many years been employed in making new difcoveries in various branches of natural philofophy, and confiderable improvements in the arts depending on it. Philofophers cannot, furely, be better employed, than in rendering their discoveries useful to mankind. For this end, an extenfive knowlege of facts is the chief requifite. The aftronomer who merely peeps at the planets through his telescopes for curiofity, or the naturalift who only admires the variegated wings of butterflies and moths, confer little benefit on fociety: but if the former, in confequence of his obfervations, fimplifies the art of navigation, or the latter, by attending to the economy of infects, directs the gardener and the farmer how to counteract or prevent the mischiefs which they occafion; their fpeculations are of pub lic utility and the more effectually to accomplish this end, no difcovery, though its ufe be not immediately apparent, ought to be concealed; for when known, it may ferve as the groundwork for future improvements.

The first paper which now demands our attention, belongs to the class of mathematics.

* Imported by Mr. Elmiley,

APP. Rev. Vol. LXXIX.

Pp

MATHE

MATHEMATICS.

On the Analysis of indeterminate Equations. By M. LE GENDRE. This memoir is divided into four parts. The firft treats of thofe indeterminate equations which admit of an infinite number of answers in whole numbers, and which may be represented

by the general form Ay ax + bx +cx &c. M. LE GENDRE confines his enquiries, chiefly, to the particular equation Ayx-B which affords many remarkable theorems.

The fecond part defcribes the ufes of the analysis of indeterminate equations in finding the divifors to equations. This is a curious as well as an ufeful part of the prefent abftrufe memoir; a direct method of finding the divifors has long been a defideratum in Algebra; but though M. LE GENDRE'S contrivances are truly ingenious, and will afford much fatisfaction to the fpeculative algebraift, it muft, nevertheless, be confeffed, that his direct method will in fome cases be more laborious than the common one by trial, or even than the folution by approximation, by means of infinite feries.

The third part contains a theorem for afcertaining the poffibility of indeterminate equations of the fecond degree.

The fourth is a collection of theorems on the properties of prime numbers. The immediate utility of contemplations on the properties of numbers may not perhaps be apparent to the fuperficial enquirer: they are, however, the basis of all arithmetical operations. They frequently afford concife methods for fimplifying complicated calculations; and, independently of the pleasure they afford, by opening an extenfive field where the human faculties may range at large in the purfuit of truth, thefe fpeculative enquiries have led the way to the nobleft and moft useful discoveries. Logarithms might be produced to confirm the affertion: they were difcovered by the fpeculative NAPIER, while he was inveftigating the curious properties of numbers in general, without any particular view for shortening the labours of trigonometrical or other computations to which they may be applied.

M. LE GENDRE regrets that M. FERMAT, who has cultivated the theory of numbers with fingular fuccefs, has not left the demonftrations of thofe theorems which he has given. Among thefe propofitions M. LE GENDRE particularly remarks the two following; every number is composed of three triangular number's at moft; and, every prime number of the form 8n —1, is of the form pq+2r2, or, what comes to the fame, its double is the Jum of three squares. He obferves, with regard to the last, that

it by no means characterizes thofe primes which are of the form 8n-1, for there is no uneven number, fimple or com. pounded, which may not be of the form p2 + q2+2r2, or which may not be, at the fame time, of the two forms p+q2+r2, and p2+q2+2r2, except only fuch numbers (whether primes or not) as are of the form 8x-1, which never can be of the form p2+q2+r2, but which are always of the form p2+q2+2r2. The demonftration of thefe propofitions is ingenious, and it is, on account of the many deductions that may be made from it, no less useful than curious.

The memoir clofes with four tables, containing the different divifors of the number t2 + au2, a being a prime, and of the form either 8n3, 8n +1, 8n + 3 or 8n1. In a minute description of thefe tables, M. LE GENDRE has introduced a variety of curious remarks on the properties of thofe prime numbers which come under the forms above specified; and the whole memoir, containing 94 pages, is replete with curious and interefting properties of different kinds of numbers.

ASTRONOMY, concluded.

Obfervation on the Moon at the Time of its Paffage over the Meridian, about two Hours before the Occultation of feveral Stars in the Pleiades, December 13, 1785. By M. JEAURAT.

From this obfervation, which feems to have been accurately made with good inftruments, it appears that on Dec. 13, 1785, at 9h 59′ 7′′ true time at the Paris obfervatory, there is an error in Mayer's tables of +39′′ in the moon's longitude, and of -10" in her latitude. In comparing MAYER's with DE LA CAILLE's folar tables, M. JEAURAT has found that these last give 3". 5 more than MAYER'S.

On the Conjunction of the Moon with the Pleiades, Dec. 13, 1785. By M. LE MONNIER.

This, like the preceding memoir, points out the errors in the tables: and it alfo relates to the difference observable in the right afcenfion and declination of the different ftars in the Pleiades in 1748, 1755, and 1785: hence the refults of this observation are fubfervient (which is a circumftance that the academician has not mentioned) to the determination of the obliquity of the ecliptic and of the preceffion of the equinoxes. Occultations of certain Stars of the Pleiades by the Moon, on April 11, and December 13, 1785. By M. MESSIER.

The occultations on the 11th of April not being announced in the ephemerides, were in part paft, before M. MESSIER applied himself to his telescope. He has given the true times of the immerfions of feven of the ftars.