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

 and, if we put 



a 



the same equations will be thus written, 



P^ {?')/- d<rc-% 



p = p' {I — 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, 



But it is to be observed that, in these expressions, the coeffi- 

 cients y,/', &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 q, or the height z, 

 varies relatively to the density, or to u. 



If we suppose that the height z is not very great, so that 

 the powers of q may be neglected, we shall obtain from the 

 foregoing equations, 



_ / i±f „. 



and hence 



/ ^ ' 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 (p') into its elements. The hygrometer will discover 

 the tension of the vapour at the earth's surface ; and if <^' de- 

 note this tension in inches of mercury, and g' be the density 

 of dry air under the pressure p' and at the temperature t', 

 the following equation is proved in all the late treatises on 

 Natural Philosophy. 



by means of which we obtain 



,3 ^ 



/ ~ /3 L T-T 



