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6?431 Fatb. (the Distance be- This the famous Cafsinieffe
tvveen 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 i° 11' 57". King, as he was marking a
Therefore the Length of 1 Meridian for the Observatory
Degr. is 57064 Tatb. 3 Feet, at Paris, thro' the South Pro
Also if 57 Fatb. (the Diffe- vinces of France. He then
rence between 75 and 18) be measured with the same Care
substracted from 78907 Fatb. 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 Malvostne and Amiens
Fatb. 3 Feet, (the Distance be- be added, they make 73 Degr.
tween the Parallels of the first Hence the Measure of the
and third Station) which agrees Earth is procured moreaccu
to the Arch of i°. 22'. 55". rately, and concluded on more
Hence 1 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 1 degr. 57.060 Fatb. an in- to make 57. 29zFath. which by
termediate Number betwixt the former was computed to
these two. be 57.060 Fath.
Thus with great Labour they Monsieur 1'Abbe Bignon tells
acquired the Measure of 1 Degr. us, that the fame Meridian
of the Periphery of the Earth would have been observed round
as accurately as possible. Ne- the whole World by Monsieur
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 un
the profound Endeavours of the fortunately kindled, whereby we
diligent Observers. And tho' are deprived of a more accurate
the Instrument was exquisitly Measure.
divided, and ofio Foot Radi- But to proceed. The fame
us, yet they could not avoid an Casjini, by comparing the se
Error of .2 Seconds, which on vefal Degrees in the aforesaid
the Earth make. 22 Fathoms; Space, thought himself to fiave
by which the observed Lati- found that there was no cer
tude of each Place might be tain and determinate Measure
wrong. to a Degree} but that one sur
Since this Error could not passed another continually tobe avoided, it was thought wards the Equator by almost necessary to measure a greater an 8oo'h 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 a lesser Por- found 57 055 Degr. and to the tion of it would fall to any one. next Degree Southward of 'E + it it 57.I which is more by 71 -j. See. Hist. Ac ad. Scien. 1701.
But by what we said above, about the Figure of the Earth, Jn our Notes upon the third Chapter, it appears there is some small Difference between one Degree and another; which can scarcely be perceived by meer Observation. Tho' this Increase
is not towards the South, as Cajstni thought, but to the North. Nevertheless, because France is almost an Intermediate between the Pole and the Equator; the Degrees there will be in a Medium betwixt the least at the Equator and the greatest at the Pole.
According to the aforesaid Dimensions,
One Degree of the Circumference of the Earth contains Paris Feet 343752 French Leagues each 2000 Fath. 28s H London 366669 Englijh Miles each 5280 Feet 69, Rbinland 356117 Rbin land'Miles each 18000 Feet 19s f so'o"
The Periphery of the Earth contains Paris Feet » - - - 123750720 French Leagues-- - 10312^
London Feet 132000768 Englijh Miles - - - - 25000^
Rbinland Feet -- 128202185 Rhinland Miles 7122^
'she Diameter of the Earth contains
Paris Feet 39391077 French Leagues - - 3282^^
London Feet 42017149 Ettglijb Miles 7957?i£!
Rbinland Feet --- 40808032 Rbinland Miles - - 2267xf§§i
the three following Methods *. Let P B (Fig. 9.) the Altitude of a Tower or Mountain, be found out by Ætimetry j and imagine P S, 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 B P S rectangled. In which having B P and P S given, the Angle P S B may be found; which is equal to the Angle P R S, whose Measure is the Arch S P (b). Therefore as this Arch is to 1 degr. so is the Distance PS measured by some known Measure to the Length of 1 degr. in that Measure. For Example, Let the Altitude B P 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 1 o German Miles. Then by the Problem Cap. 2. fay, As PS 40000 Paces is to 480: so is the Radius 10000000 to 11904, the Trangent of the Angle BS P, or S R P, or of the Arch S P, which is 41. mm. And as 41 ntin. is to 60: so is 40000 Paces to 59000; that is, about 15 Miles for 1 Degree.
O R the Semidiameter P R may be found without the Table of Sines, thus •, As B P is to P S: so is P S to P R: Or as 480 is to 40000: so is 40000 to 3333333 Paces, for the Semidiameter PR (<:).
The sixth, hut second 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 Ter- Height and Horizontal Di
restrial Methods, are more to be stances ofMountains, 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- (b) Euclid. Lib. 6. Prop. 8.
trically true; yet Refraction and (<■) Euclid. Ctroll. 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, rob Paces: If a Mountain, the Height P B may be knowri 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. 37 min. wherefore B R S will be 1 degr. 23 min. Let the Sine of 8 8 degr. 37 min. be taken from the Canon of Sines, and substracted from the Radius 100000000, and then fay •, As the Remainder is to the Sine of
88 degr. 37 min: so is B P 100 Paces to the Semidiameter S R in Paces (d).
He 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 S T be another, whose Distance, suppose, 5 German Miles. First, by a Quadrant (or otherwise) find the Angle BTR 89 degr. 45 min. and on the other Mountain the Angle T B R
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 measuring the Earth; for by knowing the Measure of 1 degr. the whole Perimeter, Diameter, Superficies, and Solidity, may be found.
B U T the Perimeter of the Earth, according t6 Snellius, is 6840 Dutch Miles, or 10260000 Rhin~ land Perches, or 123120000 Feet. Therefore the
Semidiameter of the Earth is, by the Prob. of Chap. 2. found to be 108 8i Miles, or 1633190 Perches, or 19598300 Feet; and the Superficies 18811353s square Dutch Miles *.
A N D 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 Rhinland Perches, or 22800 Rbinland Feet.
OF such 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 Meridian or no. 3. Their Distance is not particularly known; nor the Measure which the Arabians then used. So that in this Mensuration these Things are required. " 1. The Length of their Mile (accounted
mAecordMtg to our AfcraW, 'the Surface, T99.444.201 *ffd 'the Famous Caffini, the Miles; and the solid Content, Measures are thus; the Diame- 264,856,000,000 Miles, ter 7.967,7 Englijb Miles;