the Surface-Temperature of the Planets. j 75 



Now it' 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 atmosphere 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 divided by 3*5, giving 

 2*7 times as much air for the Earth per unit of surface. The 

 difference between 2*7 and 4't> thus found may perhaps be 

 attributed to the loss of air Mars has since suffered on the 

 supposition 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 bv the ratio of gravity at the surfaces of the 

 two. that is by 38/100. 



For the density being proportional to its own increase, if 

 I) denote, the density at any point, we have 



dJ)=-J)r/cLc, 



where <j denotes the force of gravity at the surface of the 

 Earth and x is reckoned from that surface outward into 

 space, whence \ 



D = Ae~2< 



A being the density at the surface of the planet. 

 For Mars we have correspondingly 



I) 1 = A l e-^'\ 



For the whole mass of air over a space dy dz we have, for 

 the Earth, 





A x=ao A 



Similarly for Mars it is 



A. 



and as the whole mass of the Earth's atmosphere over any 

 space dydz = <i'6 that of Mars at a similar point and ^ = '38^^ 

 we have 



1 -38 



whence, as A = 30 inches of barometric pressure, A 1 = 2\> 

 inches. 



Boiling-point on Mars. — Owing to the less amount of 

 the Martian air and the smaller gravity at the surface of the 

 planet, the boiling-point of water is greatly reduced, being 

 probably in the neighbourhood of one hundred and eleven 



