Mechanism and Functions in Celestial Mechanics. 307 



Having the higher rate of increase of power over the 

 Moon, the Earth's influence is the chief variable. The 

 Sun's power forms a relatively even and less variable 

 background upon which the Earth compels the Moon to 

 revolve in epicycles of greater or smaller radius, as tem- 

 porary influences or hypothetical conditions may require, 

 unti]., at a certain determinate orbital distance a differen- 

 tial adjustment is attained and stability is established. 

 In a geometrical diagram, the relation of the centripetal 

 and centrifugal forces may be shown by two gently curved 

 lines. At the point marking the Moon's present distance 

 from the Earth, the two lines would intersect, on account 

 of the different rates of variation of the forces they repre- 

 sent, and this point would mark the place of the differen- 

 tial balance of forces and the distance of the determinate 

 orbit of stability from the Earth. Nearer to the Earth, 

 and also farther away, the lines would gradually diverge 

 and would indicate conditions of instability, with the 

 centrifugal forces slightly the stronger in orbits nearer 

 to the Earth, and the centripetal forces slightly the 

 stronger in orbits farther out. 



Tliis, as I see it, is the mechanism of determinate 

 stability. Whether this principle is true or not depends 

 mainly, in the first instance, upon what it explains or 

 seems to explain — how many important things, how 

 wide a range of phenomena — and later, upon what 

 results are attained by mathematical treatment. Being- 

 unable to offer mathematical proofs, my method has been 

 to proceed by assumption. Taking the principle of deter- 

 minate stability as here set out to be true, I proceeded to 

 explore the fertile fields of astronomy, more particularly 

 that of the Planetary system. It is a well established 

 principle in modern science that a hypothesis which 

 explains things in a reasonable and plausible way is 

 worthy of at least temporary consideration, and that one 

 which explains not only the things which it was intended 

 to explain, but also many other things which were not 

 contemplated at the time it was formed, carries with it 

 a strong presumption that it is true or comes sufficiently 

 near to the truth to warrant further study and investiga- 

 tion. For first proofs, which, it seems to me, ought to 

 be regarded as justifying further research, I can only 

 call attention to the many remarkable correspondences 

 of phenomena with expectation based on this hypothesis, 

 and to the beauty, harmony, and wide unity of the pheno- 



