||g LUNAR ATMOSPHERE. 



Inquiry into the air, with a density always proportional to the pressure., 

 *vl^ TT^^^*' t The inquiry involves a great variety of considerations, and 

 traction upon it would be extremely difficult to make an exact calculation 

 theatmosphere of ^H the particulars connected with it; but it may be shown 

 of the moon. ^ , • • , , t ,• . ■ ,, 



from some general prmciples, that the dimmution would 



have become perceptible to a spectator situated on the Earthy 



in the course of a few centuries. 

 Equilibrium of If a be the distance of the moon from the earth, and x 

 SDhere"'^^'""' t^^ distance of any other point in the line joining them, the 



Sphere. 



force of gravitation will be as — r — „r. 1 ^ , ; and the 



° X* 70 [a — x) * 



centrifugal force, arising from the revolution round the com- 

 mon centre of gravity, to be added for the terrestrial atmo- 

 sphere, and to be subtracted for the lunar, being equal to the 

 force of gravitation at the distance of the centres, the joint 

 force f acting on the particles of the atmosphere will be as 



a:* ~~ 70 [a—xY "'' 70 a'^' ^" x^ '~ 70 {a~xy ~~ a^ ^^' 

 spectively: or, since/must be equal to unity at the Earth's 

 surface, wheri x is equal to the Earth's semidiameter b, 



f— — near the Earth, without sensible errour, and 



x* 



b^ h^ b'^ 

 f — —-— ■—' — , „ -i for the lunar atmosphere. Then 



'^ x^ 70 (a — x)^ «^ ^ 



the density being y, which may also be called unity at the 

 Earth's surface, we have — cy znj'y x, and it is obvious that 

 c must express the height of a column of air of uniforni 

 density capable of producing the pressure by its weight, in 

 order that — cj may be initially equal to x. Hence we 



haveH.L. — = — .//i^; but/i--i^f ~~ -£- «. 

 y c •'•^ ' -^ V.r^ 70 {a—x^ 



^Y therefore H.L.-i±ACd- A ^1 ^\ d 



aV 1/ c\ x 70 [a— x) a^ J 



being, without sensible errour, 1 -\ . Now b is 3958, and 



c 5.28 miles, and at the moon's surface x is about 606, and 



0, — X Tj b; whence H . L. — zz 685.G9. Again, wheny va- 



nishesj 



