Studies on the Motion of Viscous Flows— II 



horizontal flow is away from the continents, the meeting of the streams near the 

 center of the oceans will produce oceanic ridges there. According to the princi- 

 ple of maximum uniformity, the material in the thin layer of the model will con- 

 stantly move to reduce everywhere its shearing stresses which are constantly 

 imparted to it by the global nonuniformity impressed upon the earth by its rota- 

 tion. It is this constant transfer of locally and globally nonuniform forces by the 

 earth's rotation to the materials of the earth, which is enhanced by the geomet- 

 rical nonuniformities of the figure of the earth and the nonuniformities in the 

 physical constitution of its materials; and the rheological changes in the earth 

 that constantly reduce these nonuniformities in accordance with the principle of 

 maximum uniformity, which cause a constant redistribution of stresses in the 

 earth that culminate in earthquakes. Since this process will continue indefinitely 

 as long as the earth is rotating, nonuniform and nonisotropic stresses will be 

 constantly imparted to its materials and their constant redistribution and con- 

 centration will produce earthquakes more or less indefinitely. A basic struc- 

 tural feature in the earth's crust which actively functions in the reduction and 

 redistribution of shear stress as required by the principle of maximum uni- 

 formity is the geological fault. 



CONCLUDING REMARKS AND DISCUSSION 



The above concepts and considerations draw attention to the fact that the 

 known laws of classical mechanism are dominated by the fundamental aspect of 

 nature designated as force, and that these laws are expressed only in terms of a 

 hierarchy of uniformity which is defined by the equilibrium of forces. This en- 

 ables us to make a sharp distinction between the familiar laws of classical me- 

 chanics which (simply) express a simple relation between all the forces acting 

 on and within a body, and the laws of force which are in principle and essentially 

 independent of them. In other words, we must distinguish between the known 

 laws of mechanics conceived and interpreted as invoking a particular but never- 

 theless general aspect of the principle of maximum uniformity, which is charac- 

 terized by a definite connection between all the forces acting on a body defined 

 as mechanical equilibrium, and the general as well as restricted laws of force 

 which express the connections between particular types of forces and the space - 

 time structure. These considerations, in part, reveal as well as emphasize the 

 facts that: (a) the forces designated by the symbol F in the familiar laws of the 

 classical mechanics of discrete particles dominate these propositions and are 

 therefore, in principle, not defined or determined by them; (b) that this is tanta- 

 mount to and is an aspect of a principle of indeterminacy exercised within the 

 domain of classical mechanics; and (c) that this indeterminacy principle is ex- 

 plicitly revealed on two levels in the case of mechanical systems consisting of a 

 very large number of particles. From these facts, three deductions may be 

 made: the first concerns the fact already noted, that the known laws of mechan- 

 ics do not in principle define and/or determine the forces; second, that even 

 when the forces are prescribed by a force law, the task of computation easily 

 exhausts all available capacities; third, in the case of the three-body problem, 

 where the laws of mechanics are augmented by a law of force, i.e., the universal 

 law of gravitation, the motion and consequent changes in configuration on which 

 changes in the gravitational forces depend cannot, according to Poincare, in 

 principle be determined analytically and precisely by mathematical procedures. 



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