VIII. QUEST. 15. by R. Tagart, New-York. The difference of latitude of two ports A and B, both north of the equator, is 1800 minutes, the meridional distance of à from B is 652.5, and the meridional distance of B from A is 413 minutes; required the latitudes and difference of longitude of the two ports. IX. QUEST. 16. by W. Thompson, Charleston, S. C. Given r = the radius of a circle described by a horse in turning a machine, and the length of the traces, or the distance of the horse from that end of the beam to which he is yoked; to find x = the length of the same beam, so that the horse may turn the machine with the greatest ease possible. X. QUEST. 17. by G. Baron, New-York. Given r the radius, vthe versed sine, and s — the sine of a circular arc; to discover a more simple theorem than has hitherto been published, for deter mining the tangent of half that arc. XI. PRIZE QUEST. 18. by James Temple, New-York. In lat. 40 deg. 40 min. N. I observed a transit of the star Arcturus, over the castward vertical semicircle, which coincided with the plane of an upright wall. I afterwards observed a transit of the star Antares over the same vertical semi-circle: when I found by my watch, which kept good solar time, that 15 min. 45 sec. had elapsed between these two transits. The right ascension of Arcturus was then 14 h. 6 m. 44 sec. and declination 20 deg. 12 min. 19 sec. N. the right ascension of Antares 16h. 17 m. 26 sec. and declination 25 deg. 59 min. O1 sec. S. Required the azimuth and declination of the wall. ARTICLE VIII. ANSWERS to the Questions proposed in Article VII. I. QUEST. 8. answered by the proposer J. B. Brewer -New-York. BECAUSE 9 sterling sixpences are equal to 15 sixpences, in Pennsylvania currency; we have, 9 : 15, or 3 : 5 :: 8767. 198. sum required. 5 3)4384 15 14617. 11s. 8d. answer. General Rule. Multiply any sum of sterling money by 5; and one third of the product, gives the Pennsylvania currency required. General Rule. Any sum of sterling money increased by of itself, gives the Pennsylvania currency required. II. QUEST. 9. answered by Alexander Walsh, New 15: 9, or 5: 3 :: 436 15 10 sum required. General Rule. Any sum of Pennsylvania currency, increased by of itself, gives double the sterling money required. III. QUEST. 10. answered by Gad Dumbolton, NeivYork. I I Since it is known, that, the reciprocals of numbers are reciprocally, as the numbers themselves; the required shares must be as,,,, and ; or as × 13860, 13860, 13860, X13860, and 13860; where 13860 is the least common multiple of 5, 7, 9, 11 and 12; and therefore 2772, 1980, 1540, 1260, and 1155, are the least integers, which are directly as the shares sought. But 2772+ 1980+ 1540 † 1260 + 1155 =8707; and hence by proportion, N. B. This question is of a similar nature, with quest. 9, in page 96 of the Columbian Accountant. The author, Mr. Shepherd, has answered that question, on erroneous principles. His answers are $ 20.83, $ 16.663, and $ 12.50; the true answers are 2127, 15.95 and 12.762 dolls. This is but a small specimen of what we could give, of the numerary talents of Shepherd. Editors. The same answered, by the proposer, Niel Gray, New York. = A's share; then per q. 7 : 5 : : x: B's, 9: 7 : : 4 x : 1 x D's, and 12 Also per q. ( dol. 27 7200 8707 cts. C's, 11 : 9 :: 7: A's share, B's, 8707 C's, x = 3 53 642 8707 x = 2 89 367 x=265 8707 IV. QUEST. 11. answered by the Rev. Thos. P Irving, Newbern, North Carolina. Put x= then of the number of rails in the fence; per quest. 15x the length of the side, in feet; and 12x = the area of the field in acres, → 12 X 968 5 15x 34848 feet, the length of the side, and 12x=27878.4 acres, the area of the field. The same answered by John Capp, Harrisburg, Penn sylvania. Suppose the tract of land to be inclosed by one an acre, we have 23: 43560 :: 1 rail: 27878-4 the number of rails in the fence, or the number of We think proper, here, to demonstrate the curious proportional theorem, used in this solution, by Mr. Capp. Let 15 feet, the length of a rail, n = 3, f=43560, the square feet in an acre, and x = the number of rails in the fence, or the number of acres in the tract; then is 4ƒ¤ ̧ x×12 12 -n : hence f, or 16n2 Q. E. D. |