208 MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



10. The equation (C.) supposes that the atmosphere consists entirely of dry air: 

 we have next to consider what modification must be made when it contains a portion 

 of aqueous vapour. 



In the first place, when //' and r', the pressure and temperature at the surface of the 

 earth, are given, as they are in the mean atmosphere which produces the refractions, 

 the quantity a, or the refractive power of the air, is not liable to be altered by any 

 possible mixture of aqueous vapour. For if an addition of vapour to dry air diminish 

 the refractive power by making the density less, the greater action of the vapour upon 

 light is found almost exactly to compensate the defect. Laplace first made this ob- 

 servation ; which has been confirmed by MM. Biot and Arago, who have established 

 by experiments, that the refractive power of air, whether dry or mixed with vapour, 

 is the same, when the pressure and temperature are the same. It thus appears that, 

 as far as the quantity a, or the refractive power of the air at the earth's surface, is 

 concerned, the astronomical refractions are independent on the hygrometric condi- 

 tion of the atmosphere. 



But a mixture of vapour may produce changes in the expression of the refraction, 

 by altering the coefficients or the integrals. Now, if we attend to the formulas that 

 have been found for an atmosphere of moist air, and in the equation (10.) make the 

 same substitution as in the case of dry air, viz. 



we shall obtain 



0- s 



— = V + a a;. 



p' L(l +/3t') ^' 



\ 8 y / 





a{p') _ »___ \ 8 pf J 



p' " i L(l + ^t' 



= X: 



and further, it will appear that the same relation subsists between x and u in the at- 

 mosphere of moist air as between the quantities represented by the same letters in 

 the atmosphere of dry air. The same procedure will therefore lead, in both cases, to 

 the same integrals extending between the same limits. The only difference lies in the 

 values of X and i, which in the case of moist air acquire, as a multiplier or divisor, 



the small factor ( 1 g- • — ^j depending on the tension of the vapour at the earth's 



surface. If the hygrometer afforded an easy practical method of ascertaining the 

 tension of the vapour, the minute variations of the refractions, arising from moisture 

 in the atmosphere, might be corrected by the method usually employed for compen- 



