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68.431 Fath. (the Distance be. This the famous Caffini effe. tween the Parallels of the first cted a few Years ago, at the and second Station) which is e. Command of the most Christian qual to an Arch of 1° 11' 57". King, as he was marking a Therefore the Length of 1 Meridian for the Observatory Degr. is 57064 Fath. ' 3. Feet. at Paris, thro' the South Pro

Also if 57 Fath. (the Diffe- vinces of France. He then rence between 75 and 18) be measured with the same Care subftracted from 78907 Fath. 3 all that Space between Paris Feet (the Distance between the and the Pyrenean Mountains ; Parallels of the Places Q and E) to which if the former Distance the Remainder will be 78.850 between Malvoline and Amiens Fath. 3 Feet. (the Distance be- be added, they make 71 Degr. tween the Parallels of the first Hence the Measure of the and third Station) which agrees Earth is procured more accų. to the Arch of 10. 22'. 55", rately, and concluded on more Hence i Degree is 57.057 safely, than from the former Fathoms.

Observations only. And by this Therefore there was taken Mensuration he found 1 Degr. for i degr. 57.060 Fath. an in- to make 57.292 Fath. which by termediate Number betwixt the former was computed to these two.

be 57.060 Fath. Thus with great Labour they Monsieur l'Abbé Bignon tells acquired the Measure of ı Degr. us, that the same Meridian of the Periphery of the Earth would have been observed round as accurately as possible. Ne- the whole World by Minsieur vertheless it is to be confessed, de Chasel (a Person of great the Difficulty of making Obser- Courage and Experience) with vations (especially those about the same Exactness as it was the Latitude of the Place) was begun; but that the War was so great, that it really baffled at that Time every where' unthe profound Endeavours of the fortunately kindled, whereby we diligent Observers. And tho' are deprived of a more accurate the Initrument was exquisitly Measure. . divided, and of 10 Foot Radi- But to proceed. The fame us, yet they could not avoid an Casini, by comparing the seError of 2 Seconds, which on veral Degrees in the aforesaid the Earth make 22 Fathome ; Space, thought himself to have by which the observed Lati- found that there was no 'certude of each Place might be tain and determinate Measure wrong.

to a Degree ; but that one surSince this Error could not passed another continually tobe avoided, it was thought wards the Equator by almost necessary to measure a greater an 8ooth Part. So that to a Space, so that it might be di- Degree northward from the Obvided among more Degrees, servatory of Paris there were by which means à lesser Por- found 57.055 Degr. and to the tion of it would fall to any one. next Degree Southward of it 57.1261, which is more by is not towards the South, as 711. See. Hift. Acad. Scien. Casini thought, but to the 1701.

North. Nevertheless, because But by what we said above, France is almost an Intermediate about the Figure of the Earth, between the Pole and the E. in our Notes upon the third quator; the Degrees there will Chapter, it appears there is some be in a Medium betwixt the small Difference between one least at the Equator and the Degree and another; which can greatest at the Pole. scarcely be perceived by meer According to the aforesaid Observation. Tho' this Increase Dimensions,

One Degree of the Circumference of the Earth contains Paris Feet 343752 French Leagues each 2000 Fath. 28}} London : 366669 English Miles each 5280 Feet 691745 Rhinland 356117 Kbinland Miles each 18000 Feet 1916

The Periphery of the Earth contains Paris Feet - - • • 123750720 French Leagues - -• 103121* London Feet --.- 132000768 English Miles --•• 25000;} Rhinland Feet - - 128202185 Rbinland Miles -.712237

The Diameter of the Earth contains Paris Feet ----- 39391077 French Leagues - - 32824183 London Feet ---- 42017149 English Miles - -.- 7957248 Rhinland Feet --. 40808032 Rbinland Miles - - 2267

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B, French, English | Rbinl. Fren Eng. | Rhin
Feet | Feet | Feet.

Feet Fopy Feet
61115935

95

102 99 11458 12222 11871

191 204 198 3 17188 18333 17806

297
229171 24445 23741

396
28646 305561 29676
34375 36667) 35612

5731 611

594 40104 42778 41547

| 713 | 45834 48889) 47482

791 51563 55000 53418 8591 917 890 | 57292 6111 59353 10 955 1019 989 201145841222231118706 20 19102037 1978 301718761183334 178059 30286530562968 40 12291682444461237411 40381914074 3957 10 2864.60 305557 296764 5047745093 4946 60 1343752 13666691356117! 6015729161115935

Jurin's Appendix.

509 668/

692

76

815

the three following Methods *. Let PB (Fig. 9.) the Altitude of a Tower or Mountain, be found out by Altimetry; and imagine PS, the furthest Distance from which it may be seen, to be a right Line, as being so very small a Part of the Earth's Periphery; and the Triangle BPS rectangled. In which having B P and PS given, the Angle PSB may be found; which is equal to the Angle PRS, whose Measure is the Arch SP (b). Therefore as this Arch is to i degr. fo is the Distance PS measured by some known Measure to the Length of i degr. in that Measure. For Example, Let the Altitude BP be 480 Paces or s 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. say, As PS 40000 Paces is to 480: so 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: so 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 B P is to PS: so is P S to PR: Or as 480 is to 40000 : so is 40000 to 3333333 Paces, for the Semidiameter PR (C). The Sixth, but Second Terrestrial, Method without

knowing the Distances. THE fame Semidiameter PR (Fig. 9.) may be thus found. Suppose P B to be a high Mountain,

* The three following Ter. Height and Horizontal Direftrial Methods, are more to be ftances of Mountains, hinder the admired for their Theory, than Exactness which is required in for any Truth in their Practice. a Matter of such Nicety. For tho? they be all Geome (6) Euclid. Lib. 6. Prop. 8. trically true ; yet Refraction and (c) Euclid. Coroll. to Prop. want of Accuracy, in taking the 8. Lib. 6. .

or

or a Tower. If a Tower, it's Altitude may be found by a Plumb-line to be, suppose, 100 Pa. ces: Ifa Mountain, the Height PB may be known by Altimetry to be, suppose, 480 Paces. Then with a Quadrant at the Top. B, find the Angle at the furthest Point of Sight PBS 88 degr. 34 min. wherefore BRS will be i 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 B P 100 Paces to the Semidiameter SR in Paces (d). .

The seventh, but third Terrestrial, Method.

THIS Method (Fig. 9.) seems to be more accurate and fitter for Practice, where two Mountains or Eminences are used, whose Distance (without their Altitudes) is found by Longimetry. For Example, Let BP be a Mountain, Tower, or Castle; and let ST be another, whose Distance, fuppose, 5 German Miles. First, by à Quadrant (or otherwise) find the Angle BTR 89 degr. 45 min, and on the other Mountain the Angle T BR 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 i Degree (e).

THESE are the chief Methods of measuring the Earth ; for by knowing the Measure of i 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 Rhin land Perches, or 123120000 Feet. Therefore the

(d) See Prop. 14. of Chap. 2. above.

(e) Ibid. .., 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$ square 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 such Miles may equal 19 Holland Miles, or that one Mile may contain 1900 Rbinland Perches, or 22800 Rhinland Feet.“

OF fuch Miles the Circumference of the Earth is 5400, the Semidiameter 860, the Superficies 9278181 square Miles, and the Solidity 265693384 cubic Miles.'

YET the Italian Miles are most commodious, 60 of which make a Degr. and a Mile a Minute. Tho' these Italian Miles are to be computed such as each of them may contain 475 Rbinland Perahes. The Circuit of the Earth in this Measure is 21600 Miles, and it's Semidiameter 3440.;

THESE Things being explained, let us next consider why the abovementioned Measures of several Authors differ; and what is wanting in each. . .

IN the first Method, these Things are dubious. 1. The Elevation of the Pole might, perhaps, have been taken wrong. 2. It may be doubted whether the Places observed were in the fame Mac ridian or no. 3. Their Distance is not particularly known; nor the Measure which the Arabians then used, So that in this Menfiration these Things are required.'* 1. The Length of their Mile (ac

i. :.. . . counted According to our Norwood," the Surface, 199,444,201 and the Famous Caflini, 'the Miles; and the solid Content, · Measures are thus ; the Diame- 264,856,000,000 Miles. ier 7,967,7 Englile Miles ;

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