Chase.] -^^0 r April 21, 



luminifcrous aether, as it is to suppose a luminiferous aether. 5. All nebular, 

 aethereal, and other unverifiable hypotheses are useful only so far as they 

 serve to coordinate categories of phenomena which occur as they Avould if 

 the hypotheses were true. 6. I showed, long ago, that no merely physical 

 theory or hypothesis has ever been framed which would explain the instan- 

 taneous transmission of velocity, and that such transmission, if it exists 

 and is not physical, must be regarded as spiritual. 



198. Varying Oravitating Velocities. 



The foregoing objections may be further obviated by a consideration of 

 the fact that gravitating velocities begin with mere tendencies to motion, 

 and that some time must elapse before the velocity becomes appreciable. 

 The difficulty which Faraday found, in reconciling the conservation of en- 

 ergy and the correlations of force with gravitating tendencies which vary 

 inversely as the square of the distance, is a mathematical difficulty which 

 is equally involved in heat, light, electricity and all other manifestations 

 of radiant energy. The element of constancy may be found in a uniform 

 eleriaentary velocity, as in the general expression for stellar gravitating 



acceleration, «7^ = t- in which g^ is the acceleration of a particle at the 



distance n, vk, is the velocity of light, and t^ is the time of a single oscil- 

 lation or half-rotation if the star were uniformly expanded until it had a 

 radius equal to n. 



199. Commensurdbility and Incommemur ability. 



In his original paper {Math. Monthly, i, 245), Chauncey Wright said : 

 *' But if now we seek a uniform and symmetrical distribution as well as a 

 thorough one, the interval between the successive points must be constant, 

 and if the circumference is to be indelinitely subdivided, this interval is, of 

 course, incommensurate." Such indefinite subdivision can hardly be 

 looked for in any of the ordinarj' concrete phjsical phenomena, hence we 

 find that the chemical and other approximations which Ave have examined 

 are better represented by exact phyllotactic ratios than by the surd distrib- 

 utive tendencies. Still it seems likely that the want of precise commensur- 

 ability, which is found in Clarke's table, may arise from a residual tendency 

 to indefinite subdivision, and for this reason we may find that no increased 

 accuracy in the determination of atomic weights will lead to the establish- 

 ment of any series of divisors which are absolutely exact. I can think of 

 no case in which the incommensurability of the surd divisors seems likely 

 to be more completely represented than in the Amperian currents (Note 

 194). 



200. "Celestial Che?nistry." 



Dr. T. Sterry Hunt iP)-oc. Camb. Phil. Soc, reprinted in Am. Jour. Sci., 

 Feb. 1882), recites "certain views enunciated almost simultaneously 

 by the late Sir Benjamin Brodie, of Oxford, and" himself, in the line of 



