method, if any miflake fhould have been made in the obfervations, it will be divided into fo many parts, according to the number of years, that it will be infenfible for the space of one year. To this method alfo Mr. Kennedy objects, and calls it likewife unaftronomical; pretending to have discovered the exact length of a tropical year, by the affumption of arbitrary numbers; which, though not directly deduced from actual obfervation, yet ferve to calculate the revolutions, eclipfes, &c. of the fun and moon with greater exactness than can be done by any numbers, taken from tables of equation, founded on obfervation. In proof of this, he hath given us a multiplicity of calculations, tending to fhew a greater conformity, or nearer coincidence, between his numbers and the feveral obfervations of aftronomers, than there is between the numbers extracted from the best aftronomical tables and the fame obfervations. He appeals alfo to future obfervations for the like confirmation; and challenges the aftronomers to calculate from any number of years back, down to any future tranfit or eclipfe; fully confident that his numbers will be found to come nearer the truth of the obfervation than theirs. This method of decifion, it must be owned, is very fair; and, if purfued, will in time put it out of all doubt, how far Mr. Kennedy is, or is not, mistaken. For our own part, however, we should not be furprized to find our Author, in this, frequently right, even admitting him to be in general wrong; for, notwithitanding his numbers may be called merely arbitrary, the lengths both of his tropical ́year and felar day appear to be mean proportionals of different numbers deduced from the o fervations of afronomers. At the fame time, it may not be amifs to animadvert on the circumftances that might induce our Author to purfue this mode of investigation. In forming a fyftem of chronology fo extenfive as to refer back to the commencement of time, it was very natural to inquire whether any regularity of æra could be founded on aftronomical principles; thefe, when once eflablifhed, being more fatisfactory, and lefs liable to controverfy, than any others. The exact quantity, however, of a folar tropical year, as well as a folar day, appearing indeterminate by the obfervations of modern aftronomers, it feems as if Mr. Kennedy would have been totally at a ftand had not the lucky thought fuggefted itfelf, that both years and days muft be equal, notwithstanding their inequality by oblervation. The expedient of taking the mean of feveral different obfervations, however unexceptionable to practical aftronomers, appeared to him very bungling and unaftronomical; and the phyfical reafons, given for the irregulari Ff4 ties ties of the planetary motions, however convincing to the phyfiologifts, feemed as unphilofophical and inconclufive. The unlucky expreffions which have dropt from Sir Ifaac Newton and others, refpecting the irregularity of the planetary motions*, the wafte of matter in the fun, and its occafional fupply from the comets, have been a ftumbling block in the way even of many a promifing Newtonian; we need not wonder, therefore, that our chronological theologue fhould, from fo extravagant a theory, deduce nothing in favour of practical obfervation; especially as the only method of fecuring obfervers from falling into any material error was itfelf fufficient to make him conclude the obfervation falfe and unaftronomical. How Mr. Kennedy could get over the known and obvious effect of planetary attraction, we cannot conceive; or indeed, how he could lay down any kind of aftronomical principles in which the planets Mercury, Venus, Jupiter, and Saturn had no manner of influence or concern. But this we must say in his favour, that fome of the principal errors, we conceive he hath fallen into, have been in fome measure owing to the ignorance of geometricians in philofophical matters, and their inaccurate and unguarded modes of expreffion, even in their mathematical reasonings. Our learned Author doth not appear to fet up for a geometrician or a practical astronomer; fince he hath very implicitly quoted the definitions of the one, and borrowed the obfervations of the other. It would be unjuft, therefore, in them to cenfure him for the mistakes they have led him into on the contrary, they would do well to reconcile their own incon fiftencies, and take care to exprefs themselves with more precifion for the future. Mr. Kennedy hath given a fufficient proof of the neceffity of this, in the beginning of his fecond Differtation, where he quotes feveral paffages from Keil and Fergufon, in which both affirm, that the earth turns round its axis in twenty-four hours, and yet both allow that the fixed ftars appear to go round the earth in twenty-three hours, fiftyfix minutes, and four feconds. Now Mr. Ferguson, as well as every other aftronomer, knows that an abfolute turn of the Of this kind is the paffage quoted, page 195. in Mr. Kennedy's work. "Dum cometæ moventur in orbibus valdé excentricis undeque et quoquoverfum in omnes cœli partes, utique nullo modo fieri potuit ut coco fato tribuendum fit, quod planetæ in crbibus concentricis motu confimili ferantur eodem omnes; exceptis nimirum irregularitatibus quibuf dam, vix notatu dignis, quo ex mutuis planetarum et cometarum in fe invicem actionibus oriri potuerint; quæque verifimile eft fore ut longuinquitate temporis majores uique evadant, donec hæc nature compages manum emendatricem fit defideratura." earth L earth on its axis is a fidereal, and not a folar day; fo that the earth exceeds a revolution in twenty-four hours. Not but that Mr. Kennedy might have very well understood these expreffions in the meaning they were certainly intended to convey: for, though Keil in his XVIII. Lecture fays, the earth has a vertiginous motion round her axis in twenty-four hours; and Ferguson in his XLVII. Section fays the fame; yet the former in his XXV. Lecture, and the latter in his CCXXI. Section, exprefsly make the diftinction above mentioned between the fidereal and folar day. So that what had been faid before fhould have been understood as a general expreffion in whole numbers, which is allowable, or at least commonly practifed, in giving the firft general idea of the objects of any treatife, and fhould not have been quoted by our Author as a flat contradiction. Again, Mr. Kennedy appears to have entirely misunderstood and mifapplied a scheme, taken from Ferguson's Aftronomy, to explain the caufe and quantity of the difference between the fidereal and folar day; that difference not being produced in the manner he hath illuftrated; which is by fuppofing it a mere equatorial scheme, as if the orbit of the earth's annual motion lay in the plane of the equator. But whether this error should be imputed moft to misapprehenfion in our Author, or to the want of perfpicuity in Mr. Ferguson's scheme, we shall not take upon us to fay. Certain it is, that aftronomers have fallen into the inaccuracy of expreffion above cenfured, in their illuftrations of this very phænomenon: for they fay, "because the earth goes round the fun in the fame direction as it turns round its axis, namely, from west to eaft, and thefe motions are within the sphere of the ftars, in comparison of which the earth's annual orbit is only a dimenfionless point; let the folar days in a year be what they will, the number of fidereal days will be one more. For the effect of one turn of the earth on its axis, with respect to day and night, is loft by the earth's motion round the fun; juft as it would be to a traveller, in going quite round the earth from eaft to weft, following the apparent diurnal motion of the fun: for let him take what time he would to go round the earth, he would reckon one day lefs at his return than the people would do who remained all the while at the place from which he fet out." Now can any thing be more natural than for a Reader, who perhaps never formed a geometrical idea of the fituation and revolution of the planets, to conclude from this paffage that the earth actually revolved round the fun in the plane of the equator; or that the lofs of a folar day in its annual revolu lution lution was directly owing to the revolution of the earth on its axis in the very plane of its orbit: in which cafe, the difference between the fidereal and folar days would appear to be exactly one day, and all thefe days perfely equal and commenfurate to each other! And, in fact, thus Mr. Kennedy feems to have understood this matter; for, in his illuftration of Fergufon's fcheme, he fuppofes his traveller to go round the globe full eatt on the equator; whereas he should have fuppofed him to proceed in the oblique direction of the ecliptic. The aftronomers will doubtless excufe themfelves by faying, they have elsewhere exprefsly declared, that if the earth proceeded equally round the fun in the plane of the equator, the folar days would be all equal and commenfurate to the fidereal. But what is this but a fair confeffion, that they are guilty of these inconfiftencies and obfcurities, which Mr. Kennedy charges on them? For they will not furely maintain the propriety of faying, that a body, moving in the plane of the eclip ic, and revolving round its axis in that of the equator, proceeds and revolves in the fame direction. A feaman might as well maintain the propriety of faying, two fhips fteer the fame course, when there is two or three points of the compafs difference. Hence, though it fhould be found true, even to a geometrical demonstration, that, while the ecliptic preferves an obliquity to the equator, the fidercal days must be as incommenfurate to the folar, as the fide of a fquare to its diagonal; yet we think the aftronomers may thank themfelves for many of the blunders Mr. Kennedy has fallen into, refpccting this fcience, as well as for the trouble he may give them to refute him. This, however, may not be a great deal, as any one may very fafely undertake to demonftrate, both by theory and obfervation, that folar days are not equal; and that, on the fuppofition of the earth's revolutions on its axis being perfectly equable (which is admitted on both fides) the face of four minutes affumed by Mr. Kennedy as the complement or exact difference between the fidereal and folar day, however convenient it may prove to the purpose of his calculations, is arbitrary and unaftronomical. With refpect to the length and equality of the tropical year, the arguments that might be brought from theory and obfervation, are alfo equally cogent to prove Mr. Kennedy abfolutely miftaken. The precife length of the folar tropical year he affirms to be 365 days, 5 hours, and 49 minutes, to a mathematical exaétnefs; having never varied the fma left part of time fince the creation. This exact measure he deduces, by dividing the time elapfed between the firft autumnal equinox, as gathered from the Pentateuch, and the fun's entrance in the fame equinoctial point, as obferved by the late Dr. Bradley at Greenwich, wich, by the number of years from the creation to the time of Dr. Bradley's obfervations. Now, fuppofing Mr. Kennedy not to be mistaken in the number of his divifor, what hath he done in this particular, but followed the example of the aftronomers, who determine the length of the year, as before obferved, by dividing the time clapfed between two equinoxes obferved at many years diftance from each other, by the number of those years? It is true, he takes a greater number of years, and therefore may be fuppofed to come nearer the truth; but the uncertainty of ancient hiftory, as well as of ancient obfervation, is fo great, that a confiderable latitude was thereby afforded him to affume fuch a number of years as would beft concur with aftronomical obfervation: fo that whatever ufe may be made of his calculations in chronology, no inference can be drawn from them to prove aftronomically, that the tropical year and folar day are always equal to themfelves, or that the fidereal and folar day are commenfurate to each other. We do not deny, though we think it doubtful, that a period can be ascertained, in which the different revolutions of the earth may be completed exactly at the fame inftant. Mr. Kennedy, indeed, pretends to have difcovered it; and this, he says, is 1440 years exactly; a day, though not an aliquot part of a year, being the aliquot of 1440 years, and all the mutiples of that number; but difcoveries founded on the mere coincidence of numbers, however near they may approach to the truth, or however ferviceable they may prove to the Chronologist, are not fufficient to afcertain aftronomical principles. We are furprized however, to find Mr. Kennedy fo difpleased with approximation, which, he fays, always involves a mixture of error; when his own methods of deducing his whole numbers is fo near a kin to it. We would afk him, what he calls the method exemplified in Fage 165 of his work, for finding out the 45 minutes above the measure of the mean Julian year? If this be not approximation, it is fomething liable to much greater exceptions; being an abitrary method of deducing mean integers, and applying them to quantities, without knowing whether thefe quantities are integral and applicable, or not. Procruftes like, however, Mr. Kennedy, finding one meafure too fhort for his purpose, lengthens it; and if another be too long, he fhortens it to his ftandard. But our Author hath not only thus determined the exact time of a folar tropical year and of a folar day, but also of a mean lunation, which, he fays, is 29 d. 12 h. 44 m. 1" 45"", and this he affirms to be true, even to mathematical precision; having never been more or lefs fince the creation. Thefe num bers, |