cause the River Elbe rises in the former, and fall into the later. Also from the Danube, the Weset the Rhine, and the Moselle, we perceive the greate Altitude of those inland Countries, from whenc they flow. For this reason, Switzerland and th Country of the Grisons, are accounted the highei Lands in Europe; because the Rhine, the Danubt and the Rhone, derive their source from them Moreover, the inland Countries are elevated abov the maritime Parts, according to the different De clivity and Rapidity of the Rivers. HERE follow some Problems, by which w may form a Judgment upon the controversial Wri tings handed down to us, about the different Alti tudes of Mountains. P ROPOS ItlON II. 2o take the Height of a Mountain by Mtimetry, THIS is performed the fame Way as w take the Height of a Tower, provided the ver Top of the Mountain be perceptible by an; Mark. LET AB (Fig. 12.) be the Altitude of: Mountain, A the Foot of it, B the Mark seen a the Top. Take the Line F C at a convenien Distance, so that neither of the Angles A F C o A C F may be very acute, but nearly equal. Le the Angles B F C and B C F be observed j anc the Sum of their Degrees being taken from i8c the Remainder will give the Angle CBF (a) Then let C F the Distance of the two Stations bi accurately measured v which done, fay, as the Sin of the Angle F B C, to the Sine of the Angli CFB: (orofFCB: if you would find FB) fe {ti) B-j Article ix. of Chap. ii. above. . .. I 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 B C A, and you will have also the Angle ABC, because the Triangle CAB is rectangular *. T H E R E F O R E 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 die 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 CF 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 BF6800 Feet, the Distance from the Top. Likewise the Angle BFA being sound, by some Instrument then in Use to be 63 degr, 30 min. by saying, in the Triangle FAB, As Rad. 100000 to the Sine of the Angle BFA 89500: so 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 these Furlongs is about 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 it; which he, and the Ancients understood * By Article 14 of Cbap. it. above. from from their finding the Draughts of Letters mat in Aslies, which had been regularly scattered, remain entire and fresh as they were at first, wit out being either confused or defaced in mar Years•, therefore they supposed it to be raised bove the second Region of the Air. THERE is also another Method of takii the Altitude of Mountains, by two Stations in t] fame Plane, with the perpendicular Height the Mountain •, but this is subject to Error becau of the small Difference of the Angles (b), ALS (£) There is a very pleasant 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 Quicksilver is depressed at the Top of the Mountain, we have a mind to measure, below the Altitude it hath acquired, at the same Time, at the Bottom, or Superficies of the Sea; from whence the true Height of the Mountain is found by an established Proportion. This Proportion may be known by the Table we have added below to Chap. xix. Prop. 7. Also, by this Table, the Height of the Quicksilver at the Surface of the Sea may be found, by observing it's Height at any Place, whose Altitude above the Sea is known. But this is to be observed, that the Altitudes found this w«y will be more accurate, the nearer the Height of the Quicksilver is to 28 French Inches or to 29 I f Englijb. juriris Appendix. This way""' of taking the Height of Mountains, is very expeditious and pleasant, Dr Jurin faith, and with d care may be very useful to veral purposes; particularly measuring the Height of Iflar, above the Sea, by two Obs< vers, with well adjusted Bar meters; and at the fame Insta of time, observing the Bai metrical Heights, by the S( side, and on the highest P of the Island. So also it m serve to give an Estimate of t Height of a Fountain, or h ver, that we would have cc veyed to some Miles Distant But in all those Experiments, is necessary that the Baromet (as I said) should be well a justed, and (if two Observe that the Observations should made at the same time, to pi vent errors that may arise fro errors in the Barometer, from the Alteration of t Weight of the Atmofpher which sometimes changes the very time of Obfervatk if we are not speedy therein. For the Discovery of a Mot, tain's, or any other, Height, 1 Hallty (from Barometrii Obseri 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 jtfelf; 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 ifhe Height of the Tower is to be added: P A. PROPOSITION III. 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 10 Grecian Furlongs 96 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 A F, where three Things are given, it will be as the Radius 100000 is to the Tangent of the Angle ABF 26 degr. 2,0 mm. 49858: so is AB 6096 to AF 3040 Feet, or 5 Furlongs Observations on Srtozodtn-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 Derbam (by good Obferva- found, at near 90 Feet, the tions on the Monument in Lon- Quicksilver sunk n,, and at don) reckons 8 z Feet for every somewhat less than double, and tenth of an Inch. Vid. Low- treble that Height, ,\ and ,4, tborfs Abriig. Vol. 2. p. 13, according to Dr Hallefs Table, {Sfc But by very nice Obser- ibid. p. 16, and Mr Cajstni's Tritfons he afterwards made referred to in this Note (6.) 40 Feet 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 os Sines, &c. as is apparent from their Description, 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. 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 os the Mountain. L E T 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.) whose 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 distant from it (and they need not be at a loss for finding the Distance from any Mountain in Degrees when they are sailing under the same Meridian it is in). Therefore, supposing their Relation to be true, and the first visual Ray B F to come in a direct Line from the Top B, let us endeavour to find out the Alti 2 tude |