Mr. J. Ivory on the Constitution of the Atmosphere. 85 



by expanding the exponentials, 



- _ d = -, X Jl + -^ . -^ + - . ^ + &c. }. 



Now I is about five miles ; and the greatest height hitherto 

 ascended in the atmosphere is only 4 1- miles; therefore, for 

 all accessible heights, we may suppose that the series in the 

 last expression coincides with its first term : thus we have 



_L - fi = -^- 



Let T denote the difference of the temperatures at the height x 

 and the surface of the earth in degrees of the centigrade ther- 

 mometer; then, allowing 90 fathoms of ascent for eveiy de- 

 gree, we get X ■= r X 90 : consequently, 

 1 . ISO 



and 



= 25(1-.). 



This is the Professor's formula, which after all appears to 

 be no more than a deduction from the usual barometrical 

 theory, combined with the hypothesis of an equable decrease 

 of heat in proportion to the altitude. It is not so much a 

 physical discovery as it is an algebraic transformation of the 

 expressions of the pressure and temperature that prevail in the 

 atmosphere. In whatever form we obtain the quantities men- 

 tioned, the formula is still readily deduced as a corollary. 

 Thus, if we use the expressions of the pressure and tem- 

 perature mentioned a little above, we have 



1_«T = (1 - w)-*; 



where a stands for ^§y, or the dilatation for one degree of 

 the centigrade thermometer. Now, rejecting the square and 

 higher powers of w, we get 



6 2 



uT ■= — : 

 4 

 and by exterminating to, 



r = 26-7(4- -fl); 



and this formula will probably be found more exact in prac- 

 tice than the other. 



Among the inferences drawn by Mr. Leslie from his for- 

 mula, there is one it will l)e proper to mention here. He 



makes 



