273 LECTURE xxir, 



specific gravity of the air, even if the exhaustion is only partial, provided 

 that we know the pvoportion of the air left in the vessel to that which it 

 originally contained. The pressure derived from the weight of the air is also 

 the cause of the ascent of hydrogen gas, or of another portion of air which 

 is rarefied by heat, and carries with it the smoke of afire; and the effect is 

 made more conspicuous, when either the hydrogen gas, or the heated 

 air, is confined in a balloon. The diminution of the apparent weight of a 

 body, by means of the pressure of the surrounding air, is also shown by the 

 destruction of the equilibrium between two bodies of different densities, upon 

 their removal from the open air into the vacuum of an air pump. For this 

 purpose, a light hollow bulb of glass may be exactly counterpoised in the air 

 by a much smaller weight of brass, with an index, which shows, on a graduated 

 scale, the degree in which the large ball is made to preponderate in the re- 

 ceiver of the air pump, by the rarefaction of the air, lessening the buoyant 

 power which helps to support its weight. (Plate XIX. Fig. 252.) 



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

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

 nearer to the earth, since the density is every where 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; consequently 

 that pressure is increased one twenty eight thousandth by the addition 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 in- 

 creased 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 10000, 

 is 3010, the logarithm of 4, 6030, and that of 8, 9031; the logarithms of 

 numbers always increasing in continual proportion, when the numbers are 

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



