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cause the River Elbe rises in the former, and falls into the later. Also from the Danube, the Weser, the Rhine, and the Moselle, we perceive the greater Altitude of those inland Countries, from whence they flow. For this reason, Switzerland and the Country of the Grisons, are accounted the highest Lands in Europe; because the Rhine, the Danube, and the Rhone, derive their source from them, Moreover, the inland Countries are elevated above the maritime Parts, according to the different Declivity and Rapidity of the Rivers.
HERE follow some Problems, by which we may form a Judgment upon the controversial 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 same 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, so that neither of the Angles AFC or A CF may be very acute, but nearly equal. Let the Angles BFC and BCF be observed ; 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) so
(a) By Article 14. of Chap. ii. above,
is FC to BC the Distance of the Top of the . Mountain from C. Then [with a Telescope fixed . to a Quadrant or otherwise] take the Angle BCA, and you will have also the Angle A B C, because the Triangle CAB is rectangular *.
THEREFORE in the Triangle ABC, As the Radius 10000000, is to the Sine of the Angle BCA: so is the Distance BC, to the perpendicular Altitude of the Mountain AB.
FOR Example. Let us suppose that Xenagoras, the Son of Eumelus, used some such Method as this to find the Height of the Mountain Olympus, which he is said to have measured exactly. Wherefore if he found the Angle BFC 84 degr. 18 min. and the Angle B C F 85 degr. 34 min. then was CBF 10 degr. 8 min. And suppose, by measuring, or some 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: so is CF 1200 Feet to BF 6800 Feet, the Distance from the Top. Likewise the Angle BFA being found, by fome Instrument then in Uje to be 53 degr. 30 min. by saying, in the Triangle FAB, As Rad. 100000 to the Sine of the Angle BFA 89500: fo is FB 6800 to A B 6096 Feet, the Altitude of Mount Olympus. But 600 Feet make a Grecian Furlong; therefore dividing 6096 by 600, the Quotient, io Furlongs 96 Feet, is the Height of Mount Olympus in Grecian Measure, as Xenagoras found it. Note, Each of these Furlongs is about so of a German Mile.
ARISTOTLE and several others affirm, that this Mountain, Olympus, is so high, that there is no Rain, nor the least Motion of Air upon the Top of its which he, and the Ancients understood
* By Article 14 of Chap. ii. above.
from their finding the Draughts of Letters made in Ashes, which had been regularly scattered, to remain entire and fresh as they were at first, without being either confused or defaced in many Years; therefore they supposed it to be raised above the second 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 subject to Error because of the small Difference of the Angles (6).
(5) There is a very pleasant expeditious and pleasant, as and expeditious Method of tak- Dr Jurin faith, and with due ing the Height of Mountains by care may be very useful to sethe Barometer, thus: It is to veral purposes; particularly in be observed how many Inches measuring the Height of Islands or Parts of Inches the Quick- above the Sea, by two Obserfilver is depressed at the Top of vers, with well adjusted Baro. the Mountain, we have a mind meters; and at the same Instant to measure, below the Altitude of time, observing the Baroit hath acquired, at the same metrical Heights, by the SeaTime, at the Bottom, or Su fide, and on the highest Part perficies of the Sea; from of the Island. So also it may whence the true Height of the serve to give an Estimate of the Mountain is found by an elta- Height of a Fountain, or Riblished Proportion. This Pro- ver, that we would have conportion may be known by the veyed to some Miles Distance. Table we have added below to But in all those Experiments, it Chap. xix. Prop. 7. Also, by is necessary that the Barometer this Table, the Height of the (as I said) should be well adQuicksilver at the Surface of the jufted, and (if two Observers) Sea may be found, by observing that the Observations should be it's Height at any Place, whose made at the same time, to preAltitude above the Sea is known. vent errors that may arise from But this is to be observed, that errors in the Barometer, or the Altitudes found this way from the Alteration of the will be more accurate, the near. Weight of the Atmosphere; er the Height of the Quicksil- which sometimes changes in ver is to 28 French Inches or the very time of Observation, 10 29;} English.
if we are not speedy therein, Jurin's Appendix. For the Discovery of a MounThis ways of taking the tain's, or any other, Height, Dr Height of Mountains, is very Halley (from Barometrical
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, suppose F to be a Tower 300 Foot high, and from it's Top, or some 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.
The perspicuous Altitude of a Mountain being given, to
find what Distance we are from it ; by a Quadrant [Theodolite) or any other Surveying Instrument, for taking Heights or Angles.
LET the Height of the Mountain A B be known beforehand, by the Observations of others, to be io Grecian Furlongs g6 Feet, or 6096 Feet. And let the Place of Observation be at F; (Fig. 13.) the Distance FA is supposed to be required. Let the Angle BFA by a Quadrant or [Theodolite] be found 63 degr. 30 min. Then in the rightangled Triangle B AF, 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: so is AB 6096 to AF 3040 Feet, or 5 Furlongs
Observations on Snowdon-Hill) with excellent Instruments at concludes, that the Quicksilver divers Altitudes in St Paul's descends a Tenth of an Inch, Dome, and when the Barometer every 30 Yards of Ascent. And was at a different Height, he Dr Derham (by good Observa- found, at near 90 Feet, the tions on the Monument in Lon- Quicksilver funk is, and at don) reckons 82 Feet for every somewhat less than double, and tenth of an Inch. Vid. Lowe treble that Height, to and ', thorp's Abridg. Vol. 2. p. 13, according to Dr Halley's Table, &c. But by very nice Obfer- ibid. p. 16, and Mr Cassini's _ vations he afterwards made referred to in this Note (6.)
40 Feet, the Distance required between the Place of Observation and the Mountain.
THERE are some Instruments by which you may perform this, without making use of the Canon of Sines, &c. as is apparent from their Defcription, but the Result is this way less accurate, for Want of Exactness in the Lines of Proportion, .
Note. In both these Problems we have taken the Distance FA for a right Line, because of the small Difference between it and a Curve ; but shall consider it as Part of the Periphery of the Earth in the following Methods.
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 Inand of Teneriff, one of the Canaries, commonly called the Pike of Teneriff. Let AFC. (Fig. 14.) whose Center is Ř, 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 RF.) Mariners affirm, that they first discover the Top of this Mountain when they are 4 Degr. of the Meridian distant 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, supposing their Relation to be true, and the first visual Ray BF to come in a direct Line from the Top B, let us endeavour to find out the Alti