8 Experimental Philosophy. [Lecture 7. 



the earth : at two leagues high, it must be four 

 times thinner and less dense, and at three leagues 

 eight times thinner and lighter, and so on. In- 

 stead of Dutch leagues, suppose we took a Ger- 

 man league of seven miles, and that it was four 

 times less dense at the height of the first German 

 league, then it would decrease in the same pro- 

 portion, and be four times less dense than the 

 first at the second league, that is, sixteen times; 

 and four times less dense than the second at the 

 ,third league, that is, sixty-four times ; and four 

 times less dense than the third at the fourth 

 league, that is, two hundred and fifty-six times 

 less dense than at the surface. In short, what- 

 ever decrease it received in the first step, it will 

 continue to have the same proportion in the 

 second, third, and so on, and this, as was ob- 

 served, is called geometrical progression. 



Upon the same principle it was attempted to 

 calculate the height of the atmosphere. By carry- 

 ing a barometer to the top of a high mountain, 

 the density of the air at two or three different 

 stations was easily ascertained. But, alas ! so 

 feeble are human efforts in endeavouring to com- 

 prehend and measure the works of the Creator, 

 that this theory was soon demolished. It was 

 found that the barometrical observations by no 

 means corresponded with the density which, by 

 other experiments, the air ought to have had ; 

 and it was therefore suspected that the upper 

 parts of the atmosphere were not subject to the 



