Chase] 412 [Oct. 



lo'-j. Probabiliti/ of Anticipated Results. 



It is not likely that any one Avould ever think of attribuling the angles 

 of crystals to accident, although it would not be so unreasonable to do so 

 as it would be to account for much closer harmonies in that way. The 

 laws of cr3'^stallizalion are obscure and almost Avholly unknown, and yet 

 we are not slow in believing that there are such laws, in spite of the 

 irregularities which were pointed out in Note 233. The laws of elasticity, 

 which lead to nodal action, are as well understood as any of the funda- 

 mental truths of physical science, yet there are many who fail to recognize 

 them, and who seem to think that no explanation -is needed of the har- 

 monics which thrust themselves upon us on every hand. I am not aware 

 that any attempt has ever been made, bj' any one who believes in the pos- 

 sibility that connected harmonies may be merely accidental, to confirm his 

 belief by framing a series of such harmonies. In ordinary investigations, 

 the discovery of a single fact, through anticipations which are grounded 

 upon theoretical assumptions, is hailed as a wonderful scientific achieve- 

 ment. In the study of rhythmic elasticity such successful anticipations 

 may be endlessly multiplied before their importance becomes generally 

 understood. And yet each one of those verified anticipations lends a con- 

 firmation to the photodynamic hypothesis which is little, if any, short of 

 absolute certainty, and which f.mnnt l.c inr'.i^nr.d liv nnv onlin.irv test of 

 mathematical probability. 



254. A Photoclyiiandc " Piobhui of Three Bodies." 



We have now gathered, by strictly Baconian methods, all the facts 

 which are needed for framing and solving the following problem : To 

 find simple stellar, planetary and satellite relations of mass, position and 

 iBthereal density, that will satisfy tendencies to the formation of three pri- 

 mary harmonic nodes, in an elastic medium which propagates undulations 

 with the velocity of light. 



1. Nodal tendencies presuppose some deviations from absohite homo- 

 geneity, which lead to differences of direction and vclocitj' in the subsid- 

 ing particles, thus giving rise to oscillations which continually incline to 

 take some form of synchronism. As long as there is any liberty of motion 

 among the particles, those which are at the boundary line, betAveen the 

 constraining inertia of central stellar nucleation and ajtherealimpulse, will 

 oscillate with the greatest rapidity, tending to assume paths which will 

 alternately receive and exhaust the projectile energies of the a^thereal 

 medium. Those energies cannot be completely exhausted until enough 

 time has elapsed to communicate the velocity, of light (i\), to an a;thercal 

 particle which is at rest at the beginning of the oscillation. The central 

 inertia makes the oscillations circular, changing free elliptic revolution 

 into constrained axial rotation, each oscillation of half-rotation occupying 

 a time {t) which gives gt = v^; (jt^ = modulus of light = M; M-^ r:' = 



