Mr. Ivory on the Theory of the Astronomical Refractions. 387 



L = 



P' 



/(1+/30 



1+ f • 

 Now the small additional factor in the value of — -tt- is not 



taken into account in the measurement of heights by the ba- 

 rometer, no distinction being usually made between dry air 

 and moist air. In order to form some estimate of its effect, 

 we may instance the mean atmosphere of our climate, the 

 temperature of which is 50° Fahrenheit; the greatest possible 

 tension of vapour in such an atmosphere is '36 of an inch of 

 mercury ; at a medium, if we make <^' = '18, and p' = 30 

 inches, we shall have, 



.3 4>' _ 1 



~ 8 ' jo' ~ 44'4'* 



It thus appears that in our climate, when the mean portion 



of aqueous vapour is mixed with the air, the value of — ~- 



is less than it would be if the air were perfectly dry by its 



- — th part, a quantity too minute to be perceptible in most 



experiments. A small part only of the refractions depend 

 upon f, about a twelfth part of the whole at the horizon ; so 

 that, neglecting the minute variations which f undergoes 

 by the gi'eater or less portions of aqueous vapour mixed 

 with the air, the effect of which on the refractions is insen- 

 sible, we may assume that it has the same value in all at- 

 mospheres. The same thing applies with greater force to 

 the other coefficients y',y", &c., which having themselves 

 hardly any influence on the refractions, their minute changes 

 in dijEFerent atmospheres may be wholly disregarded. 



If we substitute for (p') its equivalent p' ( 1 — — . — 7 jin the 



foregoing value of cr, we shall obtain the following equation, 

 which is sufficient for the problem of the refractions in an at- 

 mosphere of moist air: 



1 y r ^ (l.c-^Uc, „, 



3 <^' 'J'X''~'J' c--du "•^* 



dd.c-^R^ 



. - ^ , ^ ----- , du"" 



''"8'7 



- &c.| (10.) 



In which expression the coefficients j/^y, &c., may be consi- 

 dered the same in all atmospheres, the quantity u varying 

 from zero at the earth's surface to be infinitely great at the 

 top of the atmosphere. 



2C2 



