DIASTROPHISM AND THE FORMATIVE PROCESSES 479 



of iron. In the lo-mile body this higher density is put at 7, which is thought to 

 be as dense as any such natural aggregate, inevitably more or less mixed and 

 porous, would be likely to be. 



Column / gives the maximum acceleration of gravity at the surface of 

 the given body, stated in percentages of the acceleration of gravity at the 

 surface of the earth. Column g gives, in miles per second, the parabolic veloc- 

 ity ( = velocity required to give to a projected body a parabolic path = velocity 

 capable of carrying a body to infinity = velocity acquired in a free fall from 

 infinity = "velocity from infinity")- In discussions of the limitations of atmos- 

 pheres, this "velocity from infinity" has very commonly been used erroneously 

 as "the critical velocity of escape," but by referring to column i it will be seen 

 that a molecule shot away from these bodies may reach the limit of the body's 

 control very much short of an infinite distance. If one wishes to show that 

 the molecules must escape, and desires to make his statement conservative by 

 leaving a good "margin of safety" to cover defects in data and otherwise, 

 the parabolic velocity is a very suitable criterion to use. If, on the other hand, 

 one wishes to show that molecules will be retained, and desires, as before, to 

 leave a margin of safety for retention somewhat above that, the figures in 

 column // form convenient criteria. Strictly speaking, these represent the 

 velocity required to give a particle a circular orbit at the surface of the body, 

 and this velocity forms a dividing line between the ordinary collisional atmos- 

 phere and the orbital ultra-atmosphere. The latter forms the transition stage 

 through which molecules may escape from control with the least velocity. 

 The velocity in a circular orbit has a fixed ratio to the parabolic velocity for 

 the same point, viz., i:]/'2. The figures for the parabolic velocity and for the 

 velocity of circular orbit or "velocity of retention" each becomes lower as 

 the points of reckoning rise above the surface. The minimum velocities 

 required for escape lie between the velocity for circular orbit and the velocity 

 of fall from the limit of the sphere of control and are dependent on the mode 

 of escape. 



Column i gives the diameters of the spheres of control of the several 

 bodies in competition with the sun at the earth's distance. It is important to 

 note the qualifying clause, for spheres of control vary with the distance from 

 the controlling body. The actual spheres of control of Venus and Mars are 

 given in parenthesis. For the present discussion spheres of control at the 

 distance of the earth are most serviceable. In the case of the moon, the 

 figure in parenthesis represents the moon's sphere of control as against the 

 earth, within whose sphere of control it revolves. 



It is worthy of note that the spheres of control at the lower end of the 

 series, notwithstanding their diminution, still have notable dimensions. These 

 spheres of control give concrete pictures of the areas over which the several 

 bodies exercise collecting as well as holding power, while the figures in columns 

 g and h give data for realizing, in terms of velocity, how limited is the power 

 of this influence in the smaUer masses. 



