MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 197 



Outlines, states that the decrease of heat is nearly uniform for the greatest heights 

 we can reach ; and that it may be taken on an average as equal to 1° of Fahrenheit's 

 thermometer for 270 feet, or 45 fathoms, of perpendicular ascent. The same rate has 

 the authority of Professor Leslie, to whom Meteorology is so much indebted. If 



we make ^ = 45 fathoms, t' ^ r ■=■ 1°, (3 = ^, we shall obtain 



l±/_ JL-r; /--l 



which are the numbers assumed in the paper of 1823. 



According to Dr. Dalton, another eminent philosopher who has studied meteoro- 

 logy very successfully, and made many experiments with great care, the average 

 ascent for depressing Fahrenheit's thermometer 1° is 300 feet, or 50 fathoms : this 

 gives 



f - 905 - ^ ^• 



Ramond, in his Treatise on the Barometrical Formula, has recorded the heights for 



depressing the centigrade thermometer 1°, in 42 different experiments. Setting aside 



four of this great number on account of their excessive irregularity, he states the 



mean of the remaining 38 at 164™*7. A good average maybe expected from so many 



experiments, made by observers of the greatest eminence, in different quarters of the 



world, in every variety of height and temperature. Now 4347*8 fathoms = 7951"; 



3 

 |3 = ^^ ; 2 = 1647 ; consequently 



800 



1 +/ 800 X 164-7 



= 5-5 



/ — 7951 X 3 



It would be a great omission in this research to leave out the celebrated ascent of 

 Gay Lussac in a balloon. Acccording to Laplace, the whole height ascended, or %, 

 is 6980*", the depression of the thermometer, or r' — r, being 40°'25 centigrade : hence 



!_+/ _ 800 6980_ _ 



/ — 7951 X 3 '^ 40-25 — ^ »• 



It is to be observed that, although experience and theory both concur in proving that 

 z and r^ ^ r increase together in the same proportion to considerable elevations in 

 the atmosphere, yet, at very great elevations, there is no doubt that % increases in a 

 greater ratio than '^ — r-. so that when very great heights are used for computing 



—f^i the resulting value will be greater than the true quantity. What is said ac- 

 counts sufficiently for the excess of r. deduced from Gay Lussac's ascent, above 



the other values found from moderate elevations. Without further research we may 

 adopt the following determinations as near approximations derived from a multitude 

 of experiments, 



l+/_5.5./-_l. 



