266 PHILOSOPHICAL TRANSACTIONS. [aNNO 1728, 



asserts, that the highest mountain cannot be above 15 stadia, or 9375 Roman 

 feet high. But Plutarch fixes tlie perpendicular height of the highest moun- 

 tains, as also the greatest depth of the sea, only to 10 stadia, or 6230 Roman 

 feet. 



It will appear, by the sequel of this paper, that the height of mountains, as 

 determined by these early writers, does not so very much deviate from truth 

 as one would be apt to suspect from the infant state of arts and sciences in 

 those times. Particularly the 1 5 stadia of Cleomedes, which make out 9375 

 Roman, or 10,214 Paris feet, will be found by the following observations to 

 come very near the height of the mountains of Switzerland, which, though 

 the highest of Europe, do not rise above 10,000 Paris feet above the level of 

 the sea ; and it may seem surprising that subsequent writers, even such as were 

 otherwise deeply skilled in mathematical learning, have run them up to an 

 extravagant, and altogether unnatural height. 



At first, it is not improbable, they went only upon bare conjectures. But 

 afterwards, when geometry came to be more and more improved, quadrants, 

 semicircles, and other geometrical instruments were brought into use, by means 

 of which, and by a trigonometrical calculation, the heights of places could be 

 determined in a more satisfactory manner. And yet, however true the prin- 

 ciples be, on which this method is founded, however nice the instruments, and 

 however curious the observer, the method itself must be owned, and has been 

 found by undoubted experiments, to fall far short of that accuracy which it 

 seems to promise ; and the more considerable the heights are, the more uncer- 

 tain it will be. For in the first place, as the state of the air is very different 

 in different seasons and different weather, its refraction also becomes thereby 

 greatly altered, which occasions the tops of mountains to appear higher at some 

 times than they do at others, and at all times higher than they actually are. 

 But besides, there is another inconveniency, which whoever is acquainted with 

 the true state of mountainous countries, must needs be sensible of, and that 

 is the extreme difficulty of meeting, at the bottom of high mountains, with 

 plains large enough for a proper horizontal stand, or basis, to such a triangle, 

 as an accurate and knowing observer would think satisfactory to determine a 

 considerable height, making even proper allowances for the air's refraction. 



Among the many improvements in natural philosophy, which are owing to 

 the Torricellian tube, one of the most considerable inventions of the last cen- 

 tury, it has been thereby enriched with a new method of measuring the re- 

 spective heights of places, and their elevation above the level of the sea; a 

 method which, though it must be owned that it has not as yet, and per- 

 haps, considering the inconstancy of the air, hardly ever will be brought to an 



