earth's sphere of gravitative control 215 



its being ever since. The sphere of control of the earth-nucleus was a 

 vital factor in the collection of the planetesimals to which the earth's 

 main growth is assigned under the planetesimal hypothesis. A related 

 process is the assigned means by which the essential constitution and 

 measurable uniformity of the earth's atmosphere has been maintained. 

 The latter most easily and concretely illustrates the indispensable impor- 

 tance of the earth's sphere of control in its vital career. According to 

 the kinetic theory of gases, the molecules of the earth's atmosphere are 

 liable to acquire very high velocities by reason of successions of collisions 

 and rebounds whose effects happen to be cumulative. It follows that cer- 

 tain molecules are- escaping from the control of the earth at more or less 

 frequent intervals, as also from all other bodies that have effective atmos- 

 pheres. The critical velocity of escape and the frequency of escape are 

 determined, not by the attraction of the earth regarded as a body isolated 

 in space, but by the relative values of its attraction and that of its chief 

 competitor, the sun. In neglect of this, it has been common practice to 

 take the parabolic velocity of the earth — that is, the velocity that would 

 carry a molecule to infinity— as "the critical velocity of escape." This 

 prevalent error and others related to it have greatly retarded the general 

 acceptance of the important doctrine of Stoney, that the atmospheres of 

 planets are controlled by the gravities of the planets. It is obvious, how- 

 ever, on the inspection of the diagram, that it is only necessary that a 

 molecule should acquire velocity enough to carry it beyond the limit of 

 the earth's sphere of control, into the sphere of control of the sun, to 

 insure its loss to the earth's atmosphere. It is obvious from a mere in- 

 spection of the case, in the light of the kinetic theory of gases, that the 

 earth must be throwing molecules into the sphere of control of the sun 

 all the time, and the sun must be reciprocating in due measure. The 

 interchange naturally tends toward an equilibrium. Whichever ultra- 

 atmosphere becomes the richer, for any reason, throws the more molecules 

 into the one which is the poorer until the two reach a stage of equivalent 

 richness. In this automatic way the control of the atmosphere is assured 

 and the conditions essential to terrestrial life are perpetuated.^ 



Diagram II illustrates the sphere of control of the earth on a larger 

 scale, with the sphere of "equal" gravity added. The smaller radius of 

 the earth's sphere of control is about 1,000,000 kilometers (620,000 

 miles) and its greater radius about 1,500,000 kilometers (930,000 miles). 

 The latter lies in the line joining the sun and earth. The counterglow 

 (Gegenschein) lies just outside it, opposite the sun, according to the 

 theory of Moulton. The limit of "equal" gravity between the earth and 



'The origin of the earth, 1016, pp. 25-27. 



