94 Lrftucnce of Gravity on Mooris Surface. 



Case \sL Let the atmosphere (Kg. 1) be so closely at- 

 tached to the surface, that its depth is very small compared 

 with tlie radius of tlie planet. Let A B C 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 a" b". By this latter 

 supposition the same amount of atmospherical particles will 

 be included in tlie solid, represented sectionally by A a" b" b, 

 as was formerly included in A a' b' b. But the solid A a" 

 b" b is to the solid A a' b' B nearly as A a" is to A a', that 

 is the amount of atmospherical jwticles included in a given 

 space varies (cceteris paribus) inversely Avith the depth of the 

 atmosphere. But the length of th§ pencil of light exposed 

 to the action of the atmosphere varies nearly in proportion 

 to the square root of the depth of the atmos])]iere, 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 a a" b" b very nearly 

 as (a a')^: (a a"/ or as the cube of the depth of the atmos- 

 pliere, but the lengtli 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 woidd not ( coiteris parilms) 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 Avould encounter more particles in 

 the atmosi)here of tlie 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 



