39G Astronomical and Nauticul Collections. 



every impartial mathematician, to an Gibers, a Bessel, or a 

 Brinkley, whether or no the convergence of the series is not 

 sufficiently exemplified, to prove its utility for any computations 

 of this kind that may be required. And even if four subdivi- 

 sions had been employed, or twice four, instead of two, the 

 labour of computation would still have been trifling, in compa- 

 rison with the complicated expedients that are required in other 

 methods. 



iv. The Variation of the Temperature of the Atmosphere 

 deduced from the mean Refraction. 



The best proof that the formula, published in the Nautical 

 Almanac, is not deserving of the reproach of being merely em- 

 pirical, will be found in the facility that it affords of deducing 

 the actual density of the air, at a given height, from the table of 

 astronomical refractions. For, by comparing the original series 



p ~ V — -I- ( _3_ ~ s- ] — + ( 2 — + _^ — ) — + . . ., 

 s \ mp J 2s' \mp mp^ J 6s' 



with the expression in the Nautical Almanac, p = r !!. + (2.47 



s 



+ .5 u' ) 1^ + 3600 V — + . . .,yie obtain ^ = 2.97, 

 S" s^ 2 mp 



J-^ + ^, = 3600 1', JL := 2484 ", - 1.2855, and 

 bmp bmp^ mp s 



^ rr 537.6 _ ; and from these values we may immediately de- 

 duce the diminution of the temperature in ascending, and the 

 rate at which that diminution varies at different heights, without 

 any hypothesis whatever respecting the constitution of the 

 atmosphere. 



The number of feet, in which the temperature is depressed a 



degree of Fahrenheit, being called/, we have for the va- 



494/ 



riation of density in a foot dependent on this cause ; but the 



variation of the pressure y for a foot is A ?/ = ^' 



20 900 000 



; and this, if the temperature were uniform, would be the 



27300 



