206 LECTURE XXII. 



on a graduated scale, the degree in which the large ball is made to prepon - 

 derate in the receiver of the air pump, by the rarefaction of the air, less- 1 

 ening the buoyant power which helps to support its weight. (Plate XIX. 

 Fig. 252.) 



From this combination of weight and elasticity in the atmosphere, it fol- 

 lows, that its upper parts must be much more rare than those which are 

 nearer to the earth, since the density is everywhere proportional to the 

 whole of the superincumbent weight. The weight of a column of air one 

 foot in height is one twenty eight thousandth of the whole pressure ; conse- 

 quently that pressure is increased one twenty eight thousandth by the addi- 

 tion of the weight of one foot, and the next foot will be denser in the same 

 proportion, since the density is always proportionate to the pressure ; the 

 pressure thus increased will therefore still be equal to twenty eight thousand 

 times the weight of the next foot. The same reasoning may be continued 

 without limit, and it may be shown, that while we suppose the height to 

 vary by any uniform steps, as by distances of a foot or a mile, the pressures 

 and densities will increase in continual proportion ; thus, at the height of 

 about 3000 fathoms, the density will be about half as great as at the earth's 

 surface ; at the height of 6000, one fourth ; at 9000, one eighth as great. 

 Hence it is inferred that the height in fathoms may be readily found from 

 the logarithm of the number expressing the density of the air ; for the 

 logarithm of the number 2, multiplied by 10,000, is 3010, the logarithm of 

 4, 6020, and that of 8, 9031 ; the corresponding logarithms always in- 

 creasing in continual proportion, when the numbers are taken larger and 

 larger by equal steps. (Plate XIX. Fig. 253.) 



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, if 

 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 ap- 

 pears 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 28,000 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 

 previous knowledge of the effects 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 10,000, is 2040 ; and this is the number of fathoms contained 



