200 MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



neglected, we shall obtain from the foregoing equations, 



y 1 +/ 



and hence 



/ - /3 • p' 't'-t' 



In order to ascertain how far this value is different from the like value in the case of 

 dry air, we must resolve the complex density {^') into its elements. The hygrometer 

 will discover the tension of the vapour at the earth's surface ; and if <p' denote this 

 tension in inches of mercury, and f' be the density of dry air under the pressure j»' and 

 at the temperature </, the following equation is proved in all the late treatises on 

 Natural Philosophy, 



(.')=/.0-l-J)= 



by means of which we obtain 



p' 



L = 



p'{l +/3t')- 



Now the small additional factor in the value of —^ is not taken into account in the 



measurement of heights by the barometer, 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 60° Fahrhenheit ; 

 the greatest possible tension of vapour in such an atmosphere is "36 of an inch of 

 mercury ; at a medium, if we make (p' = "18, and p' = 30 inches, we shall have, 



8 p' "" 444 



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 TTith part, a quantity too minute to be perceptible in most experiments. 



A small part only of the refractions depend upon/, about a twelfth part of the whole 

 at the horizon ; so that, neglecting the minute variations which f undergoes by the 

 greater or less portions of aqueous vapour mixed with the air, the effect of which on 

 the refractions is insensible, we may assume that it has the same value in all atmo- 

 spheres. The same thing applies with greater force to the other coefficients /',/", &c., 

 which having themselves hardly any influence on the refractions, their minute changes 

 in different atmospheres may be wholly disregarded. 



If we substitute for (§') its equivalent ^' ( 1 — -I* • -^^ ) in the foregoing value of <r. 



