﻿356 Mr. M. Hall on the Determination of 



mercury, are approximately 



t = -66-111, 



Tl =+ 5-037, 



r 2 =- 0-074, 



the temperature being- 18° C. at the surface of the earth*, and 

 — 66° C. at the confines of the atmosphere. 



Now if we put t = </)(p), the mean value of t for a column of 

 air extending from the surface up to a point where the pressure 

 isjt? 1 is 



f 



PQ 



<f>{p)dp 



Po—Pi 



i C p ° 



and therefore t m — — \ <f>(p)dp; and taking p to be 30 inches, 



PoJo 

 t m = -13°C. 



Again, if the mean tension of the vapour be taken as 0*3 inch 

 for the whole atmosphere, m will be 01 ; and the effect of 

 temperature and moisture is to diminish the height of the homo- 

 geneous atmosphere by 0*22 mile. Substituting this corrected 

 value of a in equation (7), we get, finally, 



h=32'l miles. 



With regard to the free surface of the atmosphere, it is not 

 necessary to suppose that the elasticity of the air there is de- 

 stroyed by intense cold; it is sufficient to say that at the surface 

 the elastic force is counterbalanced by the force of gravity. 



We shall now compare this result with that obtained by ob- 

 servations on the twilight arc, which give the depression of the 

 sun below the horizon when the last gleam of daylight disappears. 



But this depression varies with the latitude and with the time 

 of the year, and can never be accurately determined in conse- 

 quence of the dispersion or scattering of the light due to the 

 presence of vapour, or rather of particles of water suspended in 

 the air, during its passage through the lower strata of the atmo- 

 sphere. 



The angle of depression is said to be from 16° to 17° in the 

 tropics, and from 17° to 21° in higher latitudes (Chambers, 

 ' Astronomy ') ; and since the presence of vapour dissolved in 

 the atmosphere will tend to increase the refractive index of the 

 air, and since vapour in the form of particles of water will scatter 



* The mean temperature of the earth's surface is not the mean of the 

 equatorial and polar temperatures. Brewster's formula, t F.=81°"5 cos lat., 

 gives as the mean temperature 64° F., or 18° C. 



