VOL. LXVII.J I'HILOSOPHICA'L TRANSACTIONS. 213 



gravity on the particles of the air at different distances from the earth's centre, 

 which should doubtless enter into the account, and which would occasion the 

 density of the atmosphere to decrease in a ratio something greater than the 

 present theory admits of. In a height of 4 English miles Dr. Horsley finds 

 (Phil. Trans., vol. 64) that the diminution of density or volume from the acce- 

 lerative force of gravity would be only tHtb- P^i"*^ of the whole, or about 48 feet; 

 and I may add to this, that this effect will be in the duplicate ratio of the heights, 

 so that at one mile high it becomes only 3 feet. A like effect takes place also 

 below the surface of the earth, as in measure of the depths of mines, &c. with 

 this difference, that here it is but half the quantity in the former instance; 

 gravity within the earth being simply as the distance from the centre; they are 

 both of them however circumstances that deserve no attention in practice. 



Sir G. S. has drawn up in a commodious form, the necessary tables and pre- 

 cepts for calculating any accessible heights or depths from barometrical observa- 

 tions, without which he thought the preceding memoir would be incomplete. 

 He has avoided the method of logarithms, proposed by Dr. Halley, and adopted 

 by Mr. De Luc, both because such tables are not in the hands of every body, 

 and because he had perceived that many persons of a philosophical turn, though 

 skilled only in common arithmetic, have been frightened by the very name: a 

 method less popular, however elegant, he thouglit would have been less generally 

 useful. To these tables is subjoined a list of several altitudes, as determined by 

 the barometer: this served to show the use he had made of the instrument, and 

 at the same time exhibits the level of a great number of places in France, Savoy, 

 and Italy. But first he premises the following short principles as the grounds 

 of the computation. 



1st. The difference of elevation of two places may be determined by the 

 weight of the vertical column of the atmosphere intercepted between them. 2d. 

 If then the weight of the whole atmosphere at each place can be ascertained, 

 the weight of this column, viz. their difference, will be known. 3d. But the 

 height of the quicksilver in the barometer expresses the total weight of the 

 atmosphere in the place of observation ; the difference therefore of the height 

 of the barometer, observed in two places at the same time, will express the 

 difference of elevation of the two places. 4th. But further, the weight of this 

 column of the atmosphere is liable to some variations, being diminished by heat, 

 augmented by cold; and again, a similar alteration takes place in the column of 

 quicksilver, which is the measure of this weight. 5th. If then the degree of 

 these variations can be determined, and the temperature of the air and quick- 

 silver at the tine of observation be known, the weight of this column of air, 

 or the difference of elevation of the two places, will be concluded as certainly as 



