1876.] o2J [Trowbridge. 



on the same surface, li" the hight of a column of mercury on the unit of 



surface on a planet, at the temperature tg above 32° ; then the mass of the 



first column will be 47rh'D' very nearly since h' is about 30 inches, and the 



weight will also be 4rrh'D', and this will be equal to Pq the pressure on 



the unit of surface on the earth. Hence 



Po = 4;rh'D' (12). 



The mass of the second column will be 



4;:h"D' 

 4,rh"D" = — - (13); 



1 + /'to 



4;rh"gD' 

 and the weight will be -_ , which is equal to the pressure P on the 



unit of surface. Hence 



4-h"gD' 

 P = — - (14). 



l + /'to 

 So long as the temperature is constant the density is proportional to the 



PAn 



pressure ; or P,, : P : : Ao • ~p — 5 ^^^ under different circumstances of 

 temperature the density is inversely as the volume for the same mass, so 

 that for the temperature to above 32°, the density just found will become 



Pa 



n _L -jt" \-p ' ^^^ tliis must represent the actual density A at the surface of 

 (,i -f- Xioji^o 



the planet. Hence 



_ Ao _P _ 4;,h"gD' Ao _ Aogh^^ 



^ - (1 + /to)- Po - 4;rh'D'(l+A/to)' (1+^to) ~ h'(l+/'toJ (l+/to) 



(15). 



3. Let m be the mass of any one of the planets, that of the Earth being 



1, A the mass of the Earth's atmosphere, and KAm that of the planet's, then 



A = 4;Th'D' (16) ; 



4-h"D'r2 



and KAm — (17) ; 



l+/'to 



and hence 



KAm 4-h"D' 



—^ = KAg = 4,TKgh'D' = ^ ^ ..^^ , or 



h" = Kh'g (1 + /'to) (18). ' 



This value in (15) gives 



_A. _ gg^ = I (19). 



Ao 1 + /to Po (1 + /to) 



Equation (10) is independent of the extent of surface on which the at- 

 mosphere presses, since it gives onlj^ the law of the variation of density of 

 the atmosphere in ascending through it. R is therefore a linear measure, 

 and on the Earth it has been found from observations to be 26,126.5 Eng- 

 lish feet, or 4.948 English miles. To compare this with a similar quantity 

 for any one of the planets, we must make r = 1 in Eq. (9), and we shall 

 make 



4rrR„-^^ ^'*^^' 4-TgR' = -^- (~1)' 



