666 PEOCEEDINGS OF THE AMERICAN ACADEMY. 



polar caps. These would combine to give it an albedo of .13. This, 

 however, is illuminated by so much of the light as penetrates the 

 atmosphere only, about three quarters of the whole. Whence the ap- 

 parent albedo of the surface must be about .10. As the total albedo 

 of the planet is .27, the remaining .17 is the albedo of its air. 



Taking the density of the air as proportionate to its brilliancy, which 

 would seem to be something like the fact, since the denser the air the 

 more dust it would buoy up, we have for the Martian air a density 

 about two ninths our own over each square unit of surface. 



Now, if the original mass of air on each planet was as its own mass, 

 we should have for the ratio between the Earth and Mars, 9.3 of atmos- 

 phere on the former to 1 on the latter. This being distributed as their 

 surfaces, which are in the proportion of 7919^ to 4220^, must be di- 

 vided by 3.5, giving 2.7 times as much air for the earth per unit of 

 surface. The difference between 2.7 and 4.5 found above may perhaps 

 be attributed to the loss of air Mars has since suffered on the supposi- 

 tion of proportionate masses to start with. 



Air Density at Surface of Mars. 



To get the relative density of the air at the surfaces of the two 

 planets these amounts must be divided by the ratio of gravity at the 

 surfaces of the two, that is, by .38. 



For the density being proportional to its own increase, if D denote 

 the density at any point, we have 



dD = — Dgdx, 



where g denotes the force of gravity at the surface of the earth, and 

 X is reckoned from that surface outward into space, whence 



D = Ae-<", 



A being the density at the surface of the planet. 

 For Mars we have correspondingly 



For the whole mass of air over a space dydz we have, for the Earth, 



X' 



A A 



iJ 9 



