94. Influence of Gravity on Moon's Surface. 
Case 1st. Let the atmosphere (Fig. 1) be so closely at- 
tached to the surface, that its depth is very small compared 
with the radius of the planet. Let a Bc be part of a great 
circle section of the planet, let a’ B’ be the boundary of the 
atmosphere, and by an alteration of circumstances suppose 
this atmosphere afterwards extended to 4” B”. By this latter 
supposition the same amount of atmospherical particles will 
be included in the solid, represented sectionally by a a” B” B, 
as was formerly included in a 4’ B’B. But the solid a a” 
B” Bis to the solid A A’ B’ B nearly as A A” is to A A’, that 
is the amount of atmospherical particles included in a given 
space varies (ceteris paribus ) inversely with the depth of the 
atmosphere. But the length of the pencil of light exposed 
to the action of the atmosphere varies nearly in proportion 
to the square root of the depth of the atmosphere, therefore 
the closer the atmosphere lies upon the surface, the greater 
will be the mass of particles which the pencil has to encounter. 
Case 2nd. Suppose (Fig. 2nd) that the depth of the at- 
mosphere is very great in comparison with the radius of the 
planet. Here the solid a a’ B’ B is to 4 A” B” B very nearly 
as (A A’)?: (A A”)? or as the cube of the depth of the atmos- 
phere, but the length of a pencil of light passing near the 
planet immersed in the atmosphere will vary directly with 
the depth of atmosphere, hence in this case also, the deeper 
the atmosphere the fewer particles will the pencil encounter. 
These are the two extreme cases, and perhaps this demon- 
stration is accurate enough to entitle us to conclude that 
when a given mass of atmosphere is closely attached to a 
planet, a pencil of light passing close to the surface will en- 
_ counter a greater mass of particles, and probably deviate 
more from its direct course, or in some other manner indicate 
the existence of an atmosphere than when the same mass of 
atmosphere is more loosely attached. If, therefore, each 
square inch of the moon’s surface were charged with the 
same mass of atmosphere as the same extent of the earth’s, 
it would not (ceteris paribus ) cause a star to deviate so much 
as the terrestrial atmosphere. It might also be shown (Fig. 
3rd) that were the atmosphere in precisely the same state for 
both planets, the pencil would encounter more particles in 
the atmosphere of the larger body being immersed in it to a 
greater length. And, finally, if the amount of atmosphere 
be proportional to the mass of the planet, we cannot look for 
the same mass of atmosphere on each square inch of the 
moon’s surface as on the same extent as our earth’s. - These 
