VOL. XXXIII.] PHILOSOPHICAL TRANSACTIONS. 87 



the mercury stood at 29.8 1. At the top it fell to 29.45. The height of the 

 hill was 312 feet. 



At the bottom of Halifax hill, commonly called the bank, the mercury was 

 observed to stand at 30.00. At the top, it fell to 29.4]. The height of this 

 hill was found to be 507 feet. 



Mathematicians demonstrate, that the density of the air decreases in a geo- 

 metrical progression, as the elevation increases in an arithmetical one; and con- 

 sequently, that the logarithms of the densities are as the elevations reciprocally. 

 But the weight of the air being as its density, and the height of the mercury 

 in the barometer being always proportional to the air's weight, it follows, that 

 the logarithms of the heights of the mercury are reciprocally as the elevations. 

 Whence, having found by observation, what elevation is required to make the 

 mercury stand at any given height, it will be easy to determine how much is re- 

 quisite to reduce it to any other height proposed. If we make 30 inches the 

 standard height of the mercury, equal to unity, and suppose an elevation of 85 

 feet be required to make it fall -jig- of an inch from that height, as by these ob- 

 servations it is very nearly; then as the logarithm of ---^ is to 85, so is the 



logarithm of -f^ to the number of feet required to make it fall half an inch ; 

 and so of the rest. When the mercury stands above 30 inches, the numbers 

 will be negative, and show the spaces descending; by which method were com- 

 puted the following tables. 



The latter, which contains the differences of the numbers in the former, was 

 of very great use, when in these experiments the mercury stood at any other 

 height in the tube, besides 30 inches, and fell any number of tenths, or parts 

 of a tenth, by adding the numbers answering thereto, or proportionable parts 

 of them, to find the elevation required in the table, to make the mercury fall 

 so much, and thereby readily to compare the heights found by observation with 

 them. And though some small errors, in the observations, make them vary a 

 little from each other, yet in the main they agree as near as possible with the 

 numbers of the table ; as did also several other experiments ; which makes it 

 probable those numbers are not far from the truth. 



That the air is colder, as well as more light and rare, in places that are 

 situated high, than it is in the vallies and low grounds, is generally known; and 

 in order to learn how much it is so, Dr. N. got a friend, who lives higher than 

 himself, to observe the portable barometer and thermometer, at his house, for 

 some days, being placed as near as possible in the same circumstances with his 

 own ; and his baroineter was found to stand at a medium, for 20 days, -^ 



