the Angle PBG being given, the Side B G is found to be 34018 Perches (which Snellius makes only 33930, for he abated 88 Perches on Account of the Stations where the Elevation of the Pole was obferved). But the Arch BG, as was faid before, is 71 min. therefore as 71 is to 1 degr. or 60 min. fo is 33930 (or 34018) to 28473 Perches; or the round Number 28500 for 1 degr. equal to 19 Dutch Miles. Or by spherical Trigonometry; having A B, A P, and the Angle ABP given, find the Arch BP 1 degr. 14 min. which equals 34710 Perches; therefore 1 degr. will be 28300 Perches, or 18 Miles. The Reason why this Account differs from that of Snellius is; 1. He did not observe the Elevation of the Pole from the very Tops of the Towers B and P themselves, from whence the Angle GBP was taken, but from fome Eminence or rifing Ground a little remote from them: yet without Doubt the Altitudes of the Pole were the fame on the Tops of the Towers. 2. Another Reason is, he took BG, BP, PG for right Lines, which are indeed circular; tho', in fo fmall an Arch, the Difference is of little or no Moment. Therefore, granting Snellius's Measure of a Degree to be 28500 Perches, equal to 18 Miles, (and mine 28300 making 18) the Perimeter of the Earth will be, according to Snellius, 10.260.000 Perches, or 123.120.000 Feet, that is 6.840 Holland Miles (a). (a) The Measure of the Earth which Snellius with great Industry discovered, hath been defervedly embraced by the Learned; as being much more accurate than any of the former. Nevertheless, in a Matter of fuch Moment, and which is involved with fo many Dif The ficulties, the curious have not thought it fafe to confide in any one, tho' the moft skillful, Mathematician; which we see confirmed by Caffini the Son of the famous Aftronomer of that Name. For he having calculated the Numbers arifing from Snellius's Obfervation, af The fifth, but firft Terrestrial, Method. HOW to perform the Work without Celestial Obfervations, or a Meridian Line, is explained in the figned a much greater Measure they propofed to find the Di to the Earth than Snellius; and alfo discovered fome Errors in his Calculation, which fpoiled the whole Procefs of his Work. See Hift. Acad. Scien. 1702. Add to this, that the Latitude and Angle of Pofition of Places can now be taken more accurately by Telescopes, which are begun, fome Years ago, to be fitted to Aftronomical and Surveying Inftruments, inftead of bare little Pins, which Snellius ufed. Tho' feveral others had fet about this Work; yet fome French Mathematicians, Fellows of the Royal Academy of Sciences, did moft fuccefsfully perform it: whofe Menfuration far exceeds all others, both in the Number and Accuracy of their Obfervations, and also in the Furniture of most exquifite Infruments. Wherefore we efteem it well worth the while, to give the whole Method of Operation in fhort. The Points in the Figure which are marked with Roman Letters, fhew the Places chofen for Obfervation; whofe Bearing, or Situation, in respect of the Royal Obfervatory at Paris, is feen in a Geographical Map. (See Fig. 8) By the fame Method of Menfuration which Snellius used, tance between the Parallels of the Places N and E, or the Line Na in Fathoms; so that this Distance being known, and the Latitude of each Place N and E, or the Difference of Latitude; that is an Arch of the Meridian intercepted between the two Parallels, being found, it will appear how ma ny Fathoms make any determined Arch of a great Circle of the Earth, fuch as the Meridian is: from whence it will be eafily found how many Fathoms equal a Degree, or the whole Periphery of the Earth. Afterwards it was thought fit to measure the Line N B, the Distance between the Parallels of the Places N and Q; fo that the Latitude at Q being alio obferved, there might be had an Arch of the Meridian equal to the whole Distance Ba. For by this Means, they could more accurately determine the Measure of the Earth's Periphery, when they had found it the fame by two Operations. These Lines they measured by a continued Series of Triangles drawn from the Line AB; for it being directly plane and ftraight, they had the Advantage of measuring it with Iron Rods as accurately as could £ 2 be, be, and found it to be 5663 Fathoms. The Latitudes of the Places were taken by an Instrument, whofe Radius was 10 Paris Feet; and the Angles of each Triangle by a Quadrant of a Circle whofe Semidiameter was 3 Feet; both which Inftruments were accurately divided by Diagonal Lines. In the first Triangle ABC. There are known by Obfervation The SCAB 54° 04' 35'. ABC 95. 06. 55. Ang. ACB 30. 48. 30. Found by Fath. Fe. AB-5663. 00. measuring Hence by Calculation is found the In the eighth Triangle HGI. HGI 31. 50. 3o. HG 12523. 00. In the ninth Triangle HIK HIK 49. 20. 30. HKI 53. 06. 40. Fath. Fe. HI 9570.00. Hence IK 11683. 00. In the tenth Triangle IK L. LIK 58. 31. 30. Fath Fath. Fe. IK 11683. 00. Hence KL 11188. oz. And IL 11186. 04. In the eleventh Triangle KLM. LKM 28. 52. 30. KML 63. 31. 00. Fath. Fe. KL 11188. 02. Hence LM 6036. oz. If the Sum of the three Angles ILK, KLM, MLN. be taken from 360 Degrees, there will remain the Angle ILN 119 degr. 32 min. 40 fec. In the 12th Triangle LMN. LM 6036. oz. In the 13th Triangle ILN. LN 10691. 00. forefaid Lines might be verified, and fo be a Foundation to them in their proceeding to the Point Q Here are found three Parts of the Space intercepted between the two Places E and N, viz. EG, GI, IN, not exactly in the Meridian Line it felf Na; but fo as the Meridional Distances may be found by the following Operations. Alfo after they had found the Length of GI and IN by another Series of Triangles, as they had done before in the Line GE, they proposed to measure a new ftraight Line RS (and found it to be 3902 Fath.) by which the Measures of the a **E 3 found the Lines IG 17564 Hence were SML 6037. IN 18907.. GE 31895. O. pounded, fhewing the Distance Hence Ge, or a 31894. 0. between QB and as, Parallels of Latitude of the Places Qand E. For this being found, and an Arch of the Meridian intercepted between the fame Parallels being known, they had in Effect obtained their Defire, viz. the Measure agreeing to a known Part of the Periphery of the Earth. Let therefore 6N'ya, 10, γ. Gebe Parts of the Meridian Circle, paffing thro' the Places N, I, G; alfo B, I, G, and a E Parallels of Latitude paffing perpendicularly thro' thofe Meridians in the Places QIGE. દ Then in the Triangle QBN rightangled at B, the Inclina tion of the Line QN to the Meridian Line Nẞ is obferved, viz. The Angle QNB 180. 55'. Fath. Fe. And the Line NQ is 11161.4. Hence NB 10559. 3. In the Triangle Ny Irectangled at y NI 20. 9' 10. Fath. Fe. IN 18907. 0. Hence Ny 18893. 3. In the TriangleGI8, rect angled at 0, GI 1. 9. o. Fath. Fe. IG 17564. o. Hence 10, or y 17560. 3. 2 Hence the Distance between the Parallels of the Places N and E, viz. the Sum of the three Lines, Ny, yd, d. γ is 68348 Fathoms; to which if the Line NB be added, it will make up the Distance between the Parallels of the PlacesQ and E 78907 Fath. 3 Feet. Then it remained to obferve the Difference of Latitude of the Places E, N, and Q; or the Arches of the Meridian intercepted between their Parallets. To which end there were taken three Stations, a little distance from the Places themselves; for the fake of better Obfervation. The firft Station was distant from the Place E 18 Fathoms Southward; the fecond from the Place N 65 Fathoms Northward; the third from the Place 75 Fathoms Eaftward. The Arch of the Meridian intercepted between the first and fecond Station was found to be 10. 11. 57′′. 'between the fecond and third was 122. 35: But if 83 Fath. (the Sum of 18 and 65, by which the firft and fecond Station were further than the Plače N and E) be added to 68.348 (that is to the Line Na the Distance between the Parallels of the two Places N and E) the Sum will be |