\%0 LUNAR ATMOSPHERE. 



may suppose the attractive force uniform. The height of 

 the centre of gravity is determined by dividing the fluent of 

 a;3/i- by the mass, or by 1 — y; but, since — cy zzyx, 



xyx ~ — cxj>, X being zz c (H.L. — ), or, according to a 



mode of expression lately employed by one of your corre- 



1 ~ 



Spondents, cm{- 1), when m is infinite ; hence — ctj^ 



^ccm{j — y""""'^)? of which the fluent is e ■+ c c m 



I i—i 1— i 



'^ — 1 I y '") n e — cxy — cy "^, or e — c x i/ 



m 



—^cy'j which must vanish when y=l and .rzzO; conse- 

 quently e =: c, and the height of the centre of gravity is 



c — ^-^; and when y — O, this height is equal to that of 



i—y 



the column c, which for the Earth's atmosphere is 5'28 miles, 

 and for the moon's as much greater as the force is smaller, 

 that is, 27*75 miles. The centre of gravity being therefore 

 elevated 514 feet, or ^Jy- of its lieight, in a century, the 

 mean density of the column must also be reduced about 

 «j»-^ ; but since a certain part of this elevation depends on 

 the supposed acceleration of the more distant portions, which 

 would produce no sensible effect in the neighbourhood of 

 the moon, we cannot estimate the mean rarefaction of the 

 part remaining more nearly in its original situation, at more 

 than about -j-J-^ ; and this will be reduced to about one fourth 

 for the mean of the whole atmosphere, surrounding the moon 

 on all sides : so that we may take t i'Tro for the mean rare- 

 faction of such a lunar atmosphere in the course of the first 

 century. 

 Sensible ef- So small a rarefaction as this would certainly not be di- 



fects. rectly observable at the distance of the Earth. Supposing 



that the atmosphere would be visible until its density became 

 equal to a given quantity, the point, at which this density 

 would be found, would be depressed only about 18 miles, if 

 the whole density of the atmosphere were reduced to one 

 half, and by a diminution of -j-^^'o^, only -^Vu of 27-75 miles, 

 or about 120 feet. Tiie effect of an atmosphere would how- 

 ever 



