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if the data were certain and accurate, the solution might be depended upon, and would supersede all further trouble about the matter. However, in regard that the moon's interapogee angle has never been, nor perhaps ever can be precisely assigned ; and that a very small, even an insensible error therein, produces a very great crror in the sun's distance thence found ; therefore the solution is not at all satisfactory. To Thew that a very small variation in the interapogee angle produces a great difference on the solar force, and still a greater difference in the sun's distance, and that this difference is still the greater the greater that the sun's distance be; I shall subjoin a table, exhibiting the interapogee angles and son's distances corresponding to fixteen different proportions of the moon's gravity to the solar force ; to which I shall add the difference of the limits of the sun's distances, found according to the forementioned method of calculation, and to all shall annex the angles of the fan's horizontal parallax corresponding to the different distances, as follows, viz.
The author of the forementioned essay makes the solar force to the moon's gravity as I to 357-43365, the interapogee angle 363° 4' 7" 30", the sun's distance 495.9315, and the sun's horizontal parallax 6" 54", which fall in between N° 2. and 3. of this table. Now, if a comparison be stated between his numbers, and the respective numbers in N° 2. of the cable, it will be found, that the interapogec angles differ only 5 of 6535238, wbile the solar forces Jiffer 1 of 56289, and the Tun's distances i of 4.05223 ; therefore any error that may bappen in assigning the interapogee angle is here multiplied in the ratio of 56289 to 6535238, or 116 times in the solar force, and in the ratio of 4.05223 to 6535238, or 1612700 times in the sun's distance. Again, if a comparison be stated between the numbers in No 15. and 16. it will be found, that the interapogec angles differ only 1 of 4127532, while the solar forces differ 1 of 35731, and the sun's distances 1. of 28.9885; therefore any crror in the interapogec angle is here multiplied in the ratio of 35731 10 4127532, or 115.8 times in the solar force, and in the ratio of 28.9885 to 4127532, or 142385 times in the sun's distance. Further, any error that may bappen in the interapogee angle in the first comparison is to that which may equally happen in the second as 6535238 to 4127532, and in the solar force as 6535238% 56289 to 4127532, that is ncarly as 24 to 1 ; and in the sun's distance as 1612700X2 to 142285, that is nearly as 28 to 1: wherefore any error in the interapogee angle is 28 times more multiplied in the first comparison than in the fecond; but the sun's distance is greater in the first than in the second; therefore it is a mistake to say, as in preface, p.7. that “ the method proposed would be the “ more accurate the more distant the sun is from the earth.” It is very true, that the limits of the sun's distance found by calculation, according to the method in the essay above hinted, approach nearer to one another when the distance of the sun is greater ; and the dimination of the difference of the limits appears from the table to be (at least) nearly in proportion to the augmented distance, which only makes the method of calculation more exact in greater distances : But though the method of calculation were perfectly exact, that would never render the solution exact, un. Jess the data were also perfectly exact ; and where this is not the case, the solution must be the more erroncous the more the error is propagated, which is where the distance is greater, as is plain from what is above. As all astronomical observations, as well as natural experiments, or mechanical operations, fall short of geometrical accuracy and precision, fo there is no certainty of the interapogee angle being precisely 363° 4' 7" 30"; and therefore there is, a fortiori, no certainty of the sun's distance thence deduced being nearly 495.9315 times the moon's distance, as is given out in the essay. Nay, it would appear, that this determination is at least incumbered with very great doubt; and that any application that can be made of the method itself must be very doubtful; for if the interapogee angle of 363° Aq" 30" be varied only about half a second, and so be stated 36 30 4 q' 59"}, or more exactly 363.66860742207211957329, the sun's distance thence found (retaining the same duplicate periodic ratio, viz. 178.725 to 1,) will be infinite, as in No 1 of the table.' Then with what degree of probability, not to say certainty, can the fun's distance bc thus determined from an angle which is within 31" of the brink of infinite distance! The parallactic angles have greater differences to any two different distances of the fun than the correspondent interapogee angles have ; and therefore, if the parallax can be as precisely ascertained, it will afford a more accurate solution.
According to the method in the essay, if as the interapogee angle, c= a circle or four right angles, g to i as the moon's geocentric gravity to the solar force affeAing it, p to 1 in the duplicate ratio of the earth's periodic time round the sun to the moon's periodic time round the earth, d= the difference between g and 28, then shall sa
-30-a c'=g, 8–3xc" =-5-5=a, and 38+4ptèxit 38+4p-4xd=the sun's distance very nearly. Thus, by one calculation, without finding limits, the sun's distance may be found from the fame data that by the method of finding limits requires two calculations. But if the limits should be required, they are, 38+4px}-V38+4p-dXd=the one limit, and 38+ 4tdX1/38+41Xd=the other. Calculations to find a, when c is one of the data, will be much facilitated, by putting for c any cube number, as 1, 8, 37, 6c. and a will then be found an angle in such parts as c is put, which may be easily reduced to any other parts, as degrees, minutes, wc. I am, &c.
lators ; and yet, it may be presumed, , Mr URBAN,
Aug. 1768. he will not froin thence conclude, that I AM one of those who are highly plea- what goes before, or what follows, is
sed with the present collation of the not genuine : if therefore the omillion, Hebrew MSS, in order to procure a more proves nothing in the one cale, why perfect copy of the Hebrew Bible (345.]: ihould it have weight in the other ? as the mistakes of transcribers, in many The strongelt objection against the, instances, are evident, I heartily wish text in question, is, that. Bethshemesh Dr Keonicott success in restoring them. was but an inconsiderable town, beng. There are, however, a few things in neither mentioned in the catalogue of which I differ from him, and which I beg cities, joihua xv. 20. &c. nor enumeraleave to point out.
ted among the cilies that had kings at On 1 Sam. vi. 19. (312.] the Doctor the time when there was one and thirty observes, " That W98 [men] is expreff kings in Canaan; and yet one of those ed twice, once after the number 70. royal cities, Ai, is said to have but and again after the number 50,000; and 12,000 inhabitinis in it, men and wothat the leffer number is put before the men; it is bighly improbable therefore, grealer; though both these are contrary thut as ai the Daughter was among the to the usual mode of expresion in Amiar nien of Beththemelli, that there could be cases." —Here I must diffent from him, 50,cco dien llaughtered : 10 that number, Gen. v. and xi. the larger number is al. is probably wrong, and we must let it ways preceded by the smaller, and the right if we can. word D'JW. (years) is constantly re- The Doctor thinks that 50,000 must peated after the same manner. "' Seth be an interpolation; and to prove it p:o. lived five years and a hundred years, and duces two MSS that have not this num. begat Enoh ; and Seth lived after he ber. But two MSS against the avino. begat Enos, reven years and eigit hun- rity of two hundred does not appear 10, dred years, and begat sons and daugh. me to have much weigl.i: iet us ibereters.”. More instances might be produ. fore endeavour to clear us the dificulty ced, but these are sufficient.
more consistently with the majority of But what the Doctor lays most stress MSS. upon, is, “ that the two numbers are The Hebrews anciently exprefled their not connected by the conjunction » [and], sacred numbers by numeral letters; but which is absolutely necessary, in order to thele numeral letters were noi, 23 the make, of the two, one juni-totul: and Doctor fufpoles, the same with those therefore, as they stand thus oddiy de- made use of by the modern Jews fince tached, they afford a well-grounded pre- the finals have been invented. It is this fumption, that the one or the other is that probably has milled the Doctor, not genuine.” But this conjunction, as The following table will thew the anthe Doctor knows, is omitted in several cient manner of notation, and perhaps other places, and supplied by our trani- remove the whole ditřiculty.
Let us now try some of the larger Bio of oilver. In the table above, the letble numbers according to this table. ter p expresses 1oo, or icoo, or 100po,
In 1 Chron, xxii. 14. Darid is said or 100000. A hundred thousand tiients to have prepared for the house of the of gold is five hundred millions of our LORD a hundred thousand talents of money: This fun exceeds belief. Ten gold, and a thousand thousand talents thousand talents of gold is fifty millions VOL. XXX.
of our money: This also seems too much. words at length where the tumbers are A thousand talents of gold is five mil. doubtsul, but I would restore the numeral lions of our money. This is moderate letters. enough ; and by proportionably reducing Thus as pn is put for 500, or soco, the filver, the whole will amount to a- or 50000, 'or 500000, restore the dutie. bout ten millions of our money; a sum ral ietters, and print i Sam. vi. 19. after adequate to the undertaking.
this manner : So in . 3. David is g faid three thousand talents of gold, and les •
48.4.Dy2 77 783 ven thousand talents of fiver. In the above table the numeral letter w stands “ And he smote among the men of for 300, or 3000, ar 30c0o, or 300000; Beth Memesh, because they looked into and the letters wn for 700, or 7000, the ark of the LORD ; even be smote or 70000, or 700000; but these three among the people, five hundred and le. Jait sums are too much to come out of venty men." A terrible Naughter in that the privy purse of the greatest monarch little towo. - I am, &c. R. YATE. jo the world, therefore the first must be right ; which added together, amount to
Blindness cured by the gall of a barbel. about two millions of our money. A A Journeyman - watchmaker, named present worthy of King David !
Cenfier, having heard that the gali In 2 Chron. xvij. ore million and one of a barbel was the remedy which To. hundred and fixty thousand mighty men bias employed to cure his father's blinde of valı ur are suid constantly to have nels, resolved to try its effe& on the wiwaited upon King Jebolhaphat in Jeru- dow Germain, his inother-in-law, whose falem. This appears incredible ; but eyes had for six months been affiliated fet down the several numerals that make with ulcers, and covered with a film, un the mighty number, ?, 7, nnp. which rendered her totally blind. CenW717, and in their lowell value, sier having obtained the gall of that til, kuev will be 3000, and 2800, and 2000. squeezed the liquor out of it into a phial, and 2cco, and 18co, in all 11600. A and in the evening he rubbed it with very fufficient garrison for Jerusalem. the end of a feather into his mother's
lo 2 Sum, viii. 4. it is said David took eyes. It gave her great pain for about feven hundred horsemen; and in 1 Chron. half an hour, which abated by degrees, xvii. 4. these horsemen are said to be and her eyes watered very much. Next leven thousand. These different num. morning the could not open them, the hers were expressed by the same nume- water, as it were, glued her eyes up : ral letters wn, and the context proves he bathed them with pure water, and the greater to be right ; for the horse- the began to see with that eye wbich had mnen must be more than the chariots, received the most liquor. He used the and there were a thousand chariots taken. gall again in the evening; the infam. So it is said Kings iv. 26. that Solomon mation dispersed, the white of her eyes had forty thousand tails for chariot. became red, their colour returned by dehorses; and yet in z Chron. ix. 25. these grees, and her light became strong. He stalls are faid to be but four thuurand. repeated it a third time, with all the de. Look into the table for the numeral lec. fired fuccess. In short, the recovered per luv which 4000o is exprefed, and you her light without any other remedy. will find the same letter n stands for The widow Germain is in her fifty-third 4000: lo that here was no difference in year. She had been pronounced blind the original, till in after times the num. by the surgeons of the Høiel Dieu ; and hers were written out in words at lengili, her blindyess and cure have been attested and then a small dot or struke mistaken by order of the Lieutenant-General of caused the error.
Police. She sees Itronger and clearer now To these instances, many inore might than before the accident. The gall of be added, and there is rea!on to believe the barbel has since been on the eyes of that the Bible numbers were thus expref a dog and a oat: they appeared immeed by letters, long before the Rabinical diately to feel acute pain, and their eyes finals, or perhaps the square Hebrew was were infiamed for three days ; but after, invented. Were I therefore to print a wards returned to their natural Nate. Hje brey Bible, I would not sci down the Bibliotheque des Sciences,
$1$ PROCEEDINGS in the Sefion of ParLIAMENT 1766-9, continued. [181.) TO the account of the proceedings on sustain their credit with their mothers
the bill for restraining the assembly country. As the nature of the petition of New York, in which the colonies seem ers commerce, when free from the late to have been treated with no little se• restraints, ought to be understood, they verity, we shall bere add a circumstance beg leave to observe, that their produce which happened little earlier in the then feut to our own and the foreign seflion. On the 16th of February, illands, was chiefly bartered for lugar, the Lord Clare (from the cominisioners rum, melasses, cotton, and indigo ; that of trade and plantations) acquainted the the sugar, cotton, and indigo, served as house, that his Majesty had commanded remittance to G. Britain, while the ruin them to inform the house, that they had and melasses constituted essential branchies received, inclosed in a letter from Sir of their commerce, and enabled them to Henry Moore, Bt, (Governor of New barter with our own colonies for fish and York), a petition of the merchants in rice, and by that means to pursue a vathe city of New York, addressed to the luable trade with Spain, Portugal, and house of Commons, which the Governor Italy, where they chiefly obtained mosays he transmitted to the commislioners ney, or bills of exchange, in return; and of trade and plantations, at the request likewise qualified them for adventures to of a committee of merchants of New Africa, where they bad the advantage of York. This petition, which certainly putting off great quantities of Britilli deserved a particular attention, from manufactures, and of receiving in exthat regard to the trade and prosperity of change, gold, ivory, and flaves; which this kingdom and our plantations, which last being disposed of in the West-India ought always to actuate every branch of iliands, commanded money or bills. Rum the legislature, would not certainly have was indispensable in their Indian trade, been treated with so little regard as and, with Brilish marufactures, procured it was, had it not been for the isl tem. furs and skins, which both served for per of the majority of the members then considerable returns to G. Britain, and present,
increased its revenue. The trade to the This petition being brought up, and bay of Honduras was also of great imread, set forth, That the commerce of portance, it being managed with small the North-American colonies is so sea cargoes of provisions, rum, and British verely clogged and restricted by the sta- manufactures, which, wbile they were at tutes of the 4th and 6th of his present liberty to send foreign logwood to the Majesty, [xxvii. 13. xxix. 401.],' as to different ports in Europe, furnilhed them afford a melancholy presage of its de- with another valuable branch of remicstruction ; the fatal effects of which, tance. From this view it is evident, though tirst felt there, must be finally that sugar, sum, melasles, and logwood, transferred to G. Britain, and center with cotton and indigo, are the effenwith ber merchants and manufacturers ; tials of their return-cargoes, and the that an evil so extensive, could not fail chief sources from which, in a course of of alarining the petitioners, whose fitua. trade, they have maintained their credit tion exposes them to the first impression with G. Britain. That considering the of this calamity; whence they think it prodigious confi.mption of the produce of their duty to implore the house to resume ihe West Indies in G. Britain, Ireland, the consideration of the plantation-trade, and the colonies on the continent of An for effectual redress. It is the fingular merica, the rapid increase of those culus disadvantage of the Northern British co. nies, the vast accellion of subjects by the Jonies, that, while they stand in need of late conquests, the utter incapacity of valt quantities of the manufactures of G. our own inands to supply fo great a de. Britain, the country produces very little mand, will, the petitioners prelume, he that affords a direct remittance thither out of all question; on the other hand, in payment, and therefore from necellity the lumber produced from claring this they have been driven to seek a market is mense territory, and the prosilions exfor their produce, and, by a course of tracted from a fertile fuil, muut raise a tratfick, to acquire either money, or such supply for exportation much greater than merchandise as would answer the purpose a!i cur idlands can confuine : it lee:139 of a semittance, and enable them to therefore conistent with bond policy,