68.431 Fath. (the Distance between the Parallels of the firft and fecond Station) which is equal to an Arch of 1° 11' 57". Therefore the Length of 1 Degr. is 57064 Fath. 3 Feet. Alfo if 57 Fath. (the Difference between 75 and 18) be fubftracted from 78907 Fath. 3 Feet (the Distance between the Parallels of the Places Q and E) the Remainder will be 78. 850 Fath. 3 Feet. (the Distance between the Parallels of the firft and third Station) which agrees to the Arch of 10. 22. 55". Hence Degree is 57.057 Fathoms. Therefore there was taken for 1 degr. 57.060 Fath. an intermediate Number betwixt these two. Thus with great Labour they acquired the Measure of 1 Degr. of the Periphery of the Earth as accurately as poffible. Nevertheless it is to be confeffed, the Difficulty of making Obfervations (especially thofe about the Latitude of the Place) was fo great, that it really baffled the profound Endeavours of the diligent Obfervers. And tho' the Intrument was exquifitly divided, and of 10 Foot Radius, yet they could not avoid an Error of 2 Seconds, which on the Earth make 22 Fathoms; by which the obferved Latitude of each Place might be wrong. Since this Error could not be avoided, it was thought neceffary to measure a greater Space, fo that it might be divided among more Degrees, by which means a leffer Portion of it would fall to any one. This the famous Caffini effeted a few Years ago, at the Command of the moft Chriftian King, as he was marking a Meridian for the Obfervatory at Paris, thro' the South Provinces of France. He then measured with the fame Care all that Space between Paris and the Pyrenean Mountains; to which if the former Distance between Malvofine and Amiens be added, they make 7 Degr. Hence the Measure of the Earth is procured more accurately, and concluded on more fafely, than from the former Obfervations only. And by this Menfuration he found 1 Degr. to make 57. 292 Fath. which by the former was computed to be 57.060 Fath. Monfieur l'Abbé Bignon tells us, that the fame Meridian would have been obferved round the whole World by Monfieur de Chafel (a Person of great Courage and Experience) with the fame Exactness as it was begun; but that the War was at that Time every where' unfortunately kindled, whereby we are deprived of a more accurate Measure. But to proceed. The fame Caffini, by comparing the feveral Degrees in the aforefaid Space, thought himself to have found that there was no certain and determinate Measure to a Degree; but that one furpaffed another continually towards the Equator by almost an 800th Part. So that to a Degree northward from the Obfervatory of Paris there were found 57.055 Degr. and to the next Degree Southward of it 57.126 which is more by 71. See. Hift. Acad. Scien. 1701. But by what we faid above, about the Figure of the Earth, in our Notes upon the third Chapter, it appears there is fome Small Difference between one Degree and another; which can fcarcely be perceived by meer Obfervation. Tho' this Increase is not towards the South, as Caffini thought, but to the North. Nevertheless, because France is almoft an Intermediate between the Pole and the Equator; the Degrees there will be in a Medium betwixt the leaft at the Equator and the greatest at the Pole. According to the aforesaid One Degree of the Circumference of the Earth contains Paris Feet 343752 London 366669 I 103121 25000, 712233 39391077 French Leagues · Rbinland Miles 22671 2023 the three following Methods*. Let PB (Fig. 9.) the Altitude of a Tower or Mountain, be found out by Altimetry; and imagine PS, the furtheft Distance from which it may be feen, to be a right Line, as being fo very fmall a Part of the Earth's Periphery; and the Triangle BPS rectangled. In which having BP and PS given, the Angle PSB may be found; which is equal to the Angle PRS, whofe Measure is the Arch SP (b). Therefore as this Arch is to 1 degr. fo is the Distance PS measured by fome known Measure to the Length of 1 degr. in that Measure. For Example, Let the Altitude BP be 480 Paces or part of a German Mile; and let the Distance of P from S, the Point which terminates the Sight, be 40000 Paces, or 10 German Miles. Then by the Problem Cap. 2. fay, As PS 40000 Paces is to 480: fo is the Radius 10000000 to 11904, the Trangent of the Angle BSP, or SRP, or of the Arch SP, which is 41. min. And as 41 min. is to 60: fo is 40000 Paces to 59000; that is, about 15 Miles for 1 Degree. OR the Semidiameter PR may be found without the Table of Sines, thus; As BP is to PS: fo is PS to PR: Or as 480 is to 40000: fo is 40000 to 3333333 Paces, for the Semidiameter PR (c). The fixth, but fecond Terrestrial, Method without knowing the Distances. THE fame Semidiameter P R (Fig. 9.) may be thus found. Suppose P B to be a high Mountain, & *The three following Terreftrial Methods, are more to be admired for their Theory, than for any Truth in their Practice. For tho' they be all Geometrically true; yet Refraction and want of Accuracy, in taking the Height and Horizontal Diftances of Mountains, hinder the Exactness which is required in a Matter of fuch Nicety. (b) Euclid. Lib. 6. Prop. 8. (c) Euclid. Coroll. to Prop. 8. Lib. 6. or or a Tower. If a Tower, it's Altitude may be found by a Plumb-line to be, fuppofe, 100 Paces: If a Mountain, the Height PB may be known by Altimetry to be, fuppofe, 480 Paces. Then with a Quadrant at the Top B, find the Angle at the furtheft Point of Sight PBS 88 degr. 37 min. wherefore BRS will be 1 degr. 23 min. Let the Sine of 88 degr. 37 min. be taken from the Canon of Sines, and fubftracted from the Radius 100000000, and then fay; As the Remainder is to the Sine of 88 degr. 37 min: fo is BP 100 Paces to the Semidiameter SR in Paces (d). The feventh, but third Terrestrial, Method. THIS Method (Fig. 9.) feems to be more accurate and fitter for Practice, where two Mountains or Eminences are used, whofe Distance (without their Altitudes) is found by Longimetry. For Example, Let BP be a Mountain, Tower, or Caftle; and let ST be another, whofe Distance, fuppofe, 5 German Miles. First, by a Quadrant (or otherwise) find the Angle BTR 89 degr. 45 min. and on the other Mountain the Angle TBR 89 degr. 55 min. which will make the Angle PRS to be 20 min. because the three Angles T, B, and R, are equal to two right Angles, or 180 degr. Then fay as 20 min.: 60 min. :: 5 miles to 15 Miles for 1 Degree (e). THESE are the chief Methods of meafuring the Earth; for by knowing the Measure of 1 degr. the whole Perimeter, Diameter, Superficies, and Solidity, may be found. BUT the Perimeter of the Earth, according to Snellius, is 6840 Dutch Miles, or 10260000 Rhinland Perches, or 123120000 Feet. Therefore the (d) See Prop. 14. of Chap. z. above. 2 (e) Ibid. Semidi Semidiameter of the Earth is, by the Prob. of Chap. 2. found to be 1088 Miles, or 1633190 Perches, or 19598300 Feet; and the Superficies 18811353 fquare Dutch Miles*. AND the Solidity of the whole is 40956831512 Cubic Miles. BUT because accounting by German Miles is more common, 15 of which make a Degree, these may be used on this Condition, that 15 of fuch Miles may equal 19 Holland Miles, or that one Mile may contain 1900 Rhinland Perches, or 22800 Rbinland Feet. OF fuch Miles the Circumference of the Earth is 5400, the Semidiameter 860, the Superficies 9278181 fquare Miles, and the Solidity 265693384 cubic Miles. YET the Italian Miles are moft commodious, 60 of which make a Degr. and a Mile a Minute. Tho' thefe Italian Miles are to be computed fuch as each of them may contain 475 Rhinland Per@hes. The Circuit of the Earth in this Measure is 21600 Miles, and it's Semidiameter 3440. THESE Things being explained, let us next confider why the abovementioned Measures of feveral Authors differ; and what is wanting in each. IN the first Method, thefe Things are dubious, 1. The Elevation of the Pole might, perhaps, have been taken wrong. 2. It may be doubted whether the Places obferved were in the fame Meridian or no. 3. Their Distance is not particularly known; nor the Meafure which the Arabians then ufed, So that in this Menfuration thefe Things are required. 1. The Length of their Mile (accounted *According to our Norwood, and the Famous Caffini, the Measures are thus; the Diameter 7,967,7 English Miles; the Surface, 199,444,201 Miles; and the folid Content, 264,856,000,000 Miles. |