MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 199 



it would therefore be superfluous to attempt, by the consideration of particular ex- 

 periments, any further elucidation of a theory which is, in a manner, identical with 

 observation, as far as our knowledge extends. 



Atmosphere of air mixed with aqueous vapour. 



Continuing to represent the pressure and temperature at the earth's surface by jo' 

 and r*, and the like quantities at the height a by /? and r, the symbols (f'), (f) may 

 be used to denote the respective densities in the case of air mixed with aqueous 

 vapour. When the pressure and density vary, all the gases, and mixtures of gases 

 and vapours, are found to follow the same laws of dilatation and compression : and 

 hence the same equations that express the equilibrium of an atmosphere of dry air, 

 will hold equally in one of moist air. In the present case these equations will there- 

 fore be, • 



(-^y 





and if we put 



c = 



1+^ 



1+^ 

 a 





1+/3t'-^ y, (^') 



the same equations will be thus written, 



p-=.p^ {\ — q) c"". 



The three quantities <r, q, u are severally equal to zero at the surface of the earth : so 

 that, by the same procedure as before, we shall obtain these formulas, 



f =/»-(/-/) I' +&C. 



But it is to be observed that, in these expressions, the coefficients /',/', &c., are not 

 exactly the same as in an atmosphere of dry air: for the quantities mentioned, 

 although they have determinate values in the same quiescent atmosphere, depend 

 upon the manner in which the temperature y, or the height s, varies relatively to the 

 density, or to u. 



If we suppose that the height % is not very great, so that the powers of q may be 



* This equation is equivalent to the one in p. 18 of M. Biot's dissertation, on which that author lays so 

 much stress. 



