LUNAR ATMOSPHERE. J J^ 



nishes, and the deftisity is least, — r: ^A , and 



x'^ 70 [a — x)2 a^ 



X is nearly .825 a, whence H . L. — r: 724.3 1 ; and this den- 



1/ 

 sity is to the density at the moon's surface as 1 to the num- 

 ber of which the hyperbolic logarithm is 38.6'2, and the 

 common logarithm 16.773: and supposing the density to 

 be increased in any given ratio, the proportion will remain 

 the same, the number c still indicating the lieight of a co- 

 lumn equal ia density to the atmosphere, thus condensed, 

 at the Earth's surface. 



Now the expansion of the lunar atmosphere, supposing it General law of 

 to be equal in density to that of the Earth, and to extend to "^^''°"" 

 the point where the force y vanishes, which is the most fa- 

 vourable condition for its permanence, may be determined 

 from this general principle; that the motion of the centre of 

 gravity of any system of bodies, some of which are urged 

 by a greater force in one direction than in another, must be 

 the same as if the difference of the forces acted on the 

 whole system, collected into the centre of gravity. Thus, 

 if the pressure of the highly rarified air, at the termination 

 of the supposed lunar atmosphere, which would have kept 

 it in equilibrium, be removed, the elasticity of the column 

 pressing on the moon will be by so much greater than its 

 gravitation ; and the centre of gravit)' of the column will be 

 repelled, with a velocity as much smaller than that of a 

 body falling at the Earth's surface, as the pressure removed 

 is smaller than the weight of the column : but this ratio is 

 compounded of that of the densities at the opposite ends of 

 the column, and that of the force of gravitation, or rather 

 the force f, near the moon's surface, to its force at the sur- 

 face of the Earth, since the mass required to produce the 

 given density, by its pressure, is as much greater, as the gra- 

 vitation is smaller; and if we diminish in this proportion the 

 space which a falling body would describe in a century, we 

 shall have 514 feet, for the elevation of the centre of gravity 

 of a column of the lunar atmosphere in that time. 



But in order to estimate the effect of such a change, we Centre of gra- 

 must calculate the actual height of the centre of gravity of ^^'^^^f^^j^^'"' 

 a given column of an elastic fluid : and for this purpose we 



may 



