ON PNEUMATJC EQUILIBRIUM, 5173 



Hence we obtain an easy method of determining the heights of mountains 

 with tolerable accuracy: for if a bottle of air were closely stopped on the 

 summit of a mountain, and, being brought in this state into the plain below, 

 its mouth were inserted into a vessel of water or of mercury, a certain portion 

 of the liquid would enter the bottle; this being weighed, rf it were found to 

 be one half of the quantity that the whole bottle would contain, it might be 

 concluded that the air on the mountain possessed only half of the natural 

 density, and that its height was 3000 fathoms. It appears also, from this 

 statement, that the height of a column of equal density with any part of the 

 atmosphere, equivalent to the pressure to which that part is subjected, is 

 every where equal to about 28000 feet. 



Many corrections are, however, necessary for ascertaining the heights of 

 mountains with all the precision that the nature of this kind of measure- 

 ment admits; and they involve several determinations, which require a pre- 

 vious knowledge of the eifects of heat, and of the nature of the ascent of 

 vapours, which cannot be examined with propriety at present 



We may easily ascertain, on the same principles, the height to which a 

 balloon will ascend, if we are acquainted with its bulk and with its weight: 

 thus, supposing its weight 500 pounds, and its bulk such as to enable it to raise 

 300 pounds more, its specific gravity must be five eighths as great as that of the 

 air, and it will continue to rise, until it reach the height, at which the air 

 is of the same density: but the logarithm of eight fifths, multiplied by 10000, 

 is 2040; and this is the number of fathoms contained in the height, which 

 will, therefore, be a little more than two miles and a quarter. It may be 

 found, by pursuing the calculation, that at the distance of the earth's semi- 

 diameter, or nearly 4000 miles, above its surface, the air, if it existed, would 

 become sff- rare, that a cubic inch would occupy a space equal to the sphere 

 of Satura's orbit: and on the other hand, if there were a mine about 42 miles 

 deep, the air would become as dense as quicksilver at the bottom of it. 



It appears, therefore, that all bodies existing on or near the earth's surface 

 may be considered as subjected to the pressure of a column of air, 28000 feet 

 high, supposing its density every where equal to that which it possesses at the 



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