218 t. c. chamberlin the greater earth 



The Eoche Limit 



Diagram III is intended to visualize certain dynamic distinctions much 

 nearer the earth-body. The outer line, E. L., represents the Eoche limit 

 of the earth. This is the limit within which the differential attraction 

 of the earth would disrupt a satellite approaching it on an inrunning 

 spiral, under certain specified conditions. This important dynamic fea- 

 ture was disclosed by the mathematical researches of Eduard Eoche, of 

 Montpelier, France, more than a half century ago ; but it has not received 

 all the recognition it merits. It interposes a bar to certain cosmological 

 evolutions which, in neglect of it, have been rather freely postulated and 

 widely aecejDted. The specific conditions on which Eoche based his com- 

 putations were rather artificial. The planet and satellite were both as- 

 sumed to be homogeneous and incompressible and of the same density, 

 while cohesion was neglected. Under these assumptions the limit of dis- 

 ruption was placed at 2.44 times the radius of the planet. When properly 

 modified, the dynamics involved are applicable to a wide range of actual 

 instances. The Eoche limit on the diagram is placed at 11,000 miles 

 from the earth's center, following Sir George Darwin. This recognizes 

 a certain measure of concentration of matter toward the center of the 

 earth, but no allowance is made for the elastic factor that is inevitably 

 present because of compression and internal heat. Most compressed hot 

 bodies would obviously tend to explode if their gravity was neutralized 

 in any large measure by the attraction of another body. This expansive 

 factor would probably much more than offset cohesion. If the moon were 

 to approach the earth on an inrunning spiral, I think it would be frag- 

 mented by expansion and explosive action much before it reached the 

 assigned Eoche limit. The rings of Saturn are possibly made up of the 

 dissevered and scattered residue of one or more satellites drawn within 

 the Eoche limit by the growth of Saturn in an early stage of their for- 

 mation. 



Tidal Zones 



Inside the Eoche limit is another dynamic boundary of some signifi- 

 cance. It defines areas within which the tidal reactions of the earth and 

 moon have contrasted effects on the orbit of the moon. Outside the line 

 T. Z. the tidal reaction between the earth and the moon has the effect of 

 driving the moon into a constantly enlarging orbit ; on the inside it would 

 draw the moon toward the earth. This critical distinction was recognized 

 by Kelvin and Darwin, and the dividing line has been recomputed by 

 Moulton and Lunn independently. Eoundly, for the present rate of rota- 



