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caufe the River Elbe rifes in the former, and falls into the later. Alfo from the Danube, the Wefer, the Rhine, and the Mofelle, we perceive the greater Altitude of thofe inland Countries, from whence they flow. For this reafon, Switzerland and the Country of the Grifons, are accounted the highest Lands in Europe; because the Rhine, the Danube, and the Rhone, derive their fource from them, Moreover, the inland Countries are elevated above the maritime Parts, according to the different Declivity and Rapidity of the Rivers.

HERE follow fome Problems, by which we may form a Judgment upon the controverfial Writings handed down to us, about the different Altitudes of Mountains.

PROPOSITION II.

To take the Height of a Mountain by Altimetry.

THIS is performed the fame Way as we take the Height of a Tower, provided the very Top of the Mountain be perceptible by any Mark.

LET AB (Fig. 12.) be the Altitude of a Mountain, A the Foot of it, B the Mark seen at the Top. Take the Line FC at a convenient Distance, fo that neither of the Angles AFC or ACF may be very acute, but nearly equal. Let the Angles BFC and BCF be obferved; and the Sum of their Degrees being taken from 180 the Remainder will give the Angle CBF (a). Then let C F the Distance of the two Stations be accurately measured; which done, say, as the Sine of the Angle FBC, to the Sine of the Angle CFB: (or of FCB: if you would find FB) fo

(a) By Article 14. of Chap. ii. above.

is

is FC to BC the Distance of the Top of the Mountain from C. Then [with a Telescope fixed to a Quadrant or otherwife] take the Angle BCA, will have alfo the Angle ABC, because the Triangle CAB is rectangular *.

and you

THEREFORE in the Triangle ABC, As the Radius 10000000, is to the Sine of the Angle BCA fo is the Distance BC, to the perpendicular Altitude of the Mountain AB.

FOR Example. Let us fuppofe that Xenagoras, the Son of Eumelus, used fome fuch Method as this to find the Height of the Mountain Olympus, which he is faid to have measured exactly. Wherefore if he found the Angle BFC 84 degr. 18 min. and the Angle BCF 85 degr. 34 min. then was CBF 10 degr. 8 min. And fuppofe, by measuring, or fome other Method, he found FC 1200 Grecian Feet, or 2 Furlongs. Therefore as the Sine of the Angle CBF 10 degr. 8 min. 17594 is to the Sine of the Angle BCF 85 degr. 34 min. 99701: fo is CF 1200 Feet to BF 6800 Feet, the Distance from the Top. Likewise the Angle BFA being found, by fome Inftrument then in Ufe to be 53 degr. 30 min. by faying, in the Triangle FAB, As Rad. 100000 to the Sine of the Angle BFA 89500: fo is FB 6800 to AB 6096 Feet, the Altitude of Mount Olympus. But 600 Feet make a Grecian Furlong; therefore dividing 6096 by 600, the Quotient, 10 Furlongs 96 Feet, is the Height of Mount Olympus in Grecian Measure, as Xenagoras found it. Note, Each of thefe Furlongs is about % of a German Mile.

ARISTOTLE and feveral others affirm, that this Mountain, Olympus, is fo high, that there is no Rain, nor the leaft Motion of Air upon the Top of it; which he, and the Ancients understood

By Article 14 of Chap. ii. above.

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from their finding the Draughts of Letters made in Afhes, which had been regularly scattered, to remain entire and fresh as they were at first, without being either confufed or defaced in many Years; therefore they fuppofed it to be raised above the fecond Region of the Air.

THERE is also another Method of taking the Altitude of Mountains, by two Stations in the fame Plane, with the perpendicular Height of the Mountain; but this is fubject to Error because of the fmall Difference of the Angles (b).

(5) There is a very pleafant and expeditious Method of taking the Height of Mountains by the Barometer, thus: It is to be observed how many Inches or Parts of Inches the Quickfilver is depreffed at the Top of the Mountain, we have a mind to measure, below the Altitude it hath acquired, at the fame Time, at the Bottom, or Superficies of the Sea; from whence the true Height of the Mountain is found by an eftablifhed Proportion. This Proportion may be known by the Table we have added below to Chap. xix. Prop. 7. Alfo, by this Table, the Height of the Quickfilver at the Surface of the Sea may be found, by obferving it's Height at any Place, whofe Altitude above the Sea is known. But this is to be observed, that the Altitudes found this way will be more accurate, the nearer the Height of the Quickfilver is to 28 French Inches or to 291 English.

Jurin's Appendix. This way of taking the Height of Mountains, is very

ALSO

expeditious and pleafant, as Dr Jurin faith, and with due care may be very useful to several purposes; particularly in measuring the Height of Iflands above the Sea, by two Obfervers, with well adjusted Barometers; and at the fame Inftant of time, obferving the Barometrical Heights, by the Seafide, and on the highest Part of the Island. So alfo it may ferve to give an Estimate of the Height of a Fountain, or River, that we would have conveyed to fome Miles Distance. But in all thofe Experiments, it is neceffary that the Barometer (as I faid) should be well adjufted, and (if two Observers) that the Obfervations should be made at the fame time, to prevent errors that may arife from errors in the Barometer, or from the Alteration of the Weight of the Atmosphere; which fometimes changes in the very time of Observation, if we are not speedy therein.

For the Discovery of a Mountain's, or any other, Height, Dr Halley (from Barometrical

Obferva

ALSO having the Height of a Tower given, and it's Distance from the Mountain, we may more accurately find the Height of the Mountain itself; thus, fuppofe F to be a Tower 300 Foot high, and from it's Top, or fome convenient Place, let BFP be observed to be 83 degr. 30 min. then will BP be found to be 5796 Feet, to which the Height of the Tower is to be added: PA.

PROPOSITION III.

The perfpicuous Altitude of a Mountain being given, to find what Distance we are from it; by a Quadrant [Theodolite] or any other Surveying Inftrument, for taking Heights or Angles.

LET the Height of the Mountain AB be known beforehand, by the Obfervations of others, to be 10 Grecian Furlongs 96 Feet, or 6096 Feet. And let the Place of Obfervation be at F; (Fig. 13.) the Distance FA is fuppofed to be required. Let the Angle BFA by a Quadrant or [Theodolite] be found 63 degr. 30 min. Then in the rightangled Triangle BAF, where three Things are given, it will be as the Radius 100000 is to the Tangent of the Angle ABF 26 degr. 30 min. 49858: fo is AB 6096 to AF 3040 Feet, or 5 Furlongs

Obfervations on Snowden-Hill) with excellent Inftruments at concludes, that the Quickfilver defcends a Tenth of an Inch, every 30 Yards of Afcent. And Dr Derham (by good Obfervations on the Monument in London) reckons 82 Feet for every tenth of an Inch. Vid. Lowthorp's Abridg. Vol. 2. p. 13,

. But by very nice Obfervations he afterwards made

divers Altitudes in St Paul's
Dome, and when the Barometer
was at a different Height, he
found, at near 90 Feet, the
Quick filver funk, and at
fomewhat lefs than double, and
treble that Height, and,
according to Dr Halley's Table,
ibid. p. 16, and Mr Caffini's
referred to in this Note (b.)
40 Feet

40 Feet, the Distance required between the Place of Obfervation and the Mountain.

THERE are fome Inftruments by which you may perform this, without making ufe of the Canon of Sines, &c. as is apparent from their Defcription, but the Refult is this way lefs accurate, for Want of Exactnefs in the Lines of Proportion.

Note. In both thefe Problems we have taken the Distance FA for a right Line, because of the fmall Difference between it and a Curve; but shall confider it as Part of the Periphery of the Earth in the following Methods.

PROPOSITION IV.

Having the Distance between a Mountain and the Place where it's Top may be first seen, given: to find Geographically the Height of the Mountain.

LET us take, for Example, the prodigious high Mountain in the Island of Teneriff, one of the Canaries, commonly called the Pike of Teneriff. Let AFC. (Fig. 14.) whofe Center is R, be the Periphery of the Earth, or the Meridian of the Mountain, and let AB be the Mountain itself. Draw from B the right Line BF a Tangent to the Periphery, and F will be the first or last Point from which the Top of the Mountain can be seen, (Then Draw R F.) Mariners affirm, that they first discover the Top of this Mountain when they are 4 Degr. of the Meridian diftant from it (and they need not be at a loss for finding the Distance from any Mountain in Degrees when they are failing under the fame Meridian it is in). Therefore, fuppofing their Relation to be true, and the first vifual Ray BF to come in a direct Line from the Top B, let us endeavour to find out the Alti

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