Chase.] ^40 [April 21, 



163. Ilarmonic Categories. 



The simple tliscoveiy of so many harmonies, in all departments of 

 physical sfeience, would be interesting, even if it were accidental or wholly 

 empirical. The fact that the discovery has sprung from systematic in- 

 vestigations, under the guidance of well-known laws, adds much to its 

 importance. The following results seem to be especially important, and 

 somewhat typical. 



1. The equality of gt, in the solar oscillations of half-rotation, to the 

 ■Mlodty of light. Notes 17, 162, etc. 



2. Tlie relations of mass and vis vim which satisfy cosmical tendencies 

 to nodality, subsidence, oscillation and orbital revolution. Notes 5, 23, 

 79, 91, 156, 158-61. 



3. The far-reaching evidence of elastic influence which establishes 

 measurable progressive relations between the solar system and the fixed 

 stars. Notes 46. 111-5, 130-2, 155. 



4. The simplicity of the relations between elastic and cosmical vis viva, 

 which furnish data for approximate estimates of Sun's mass and distance 

 by means of barometric fluctuations. Notes 104-5. 



5. The relations of magnetic and cosmical vis viva, together with the 

 evidence which they furnish of the dependence of solar and lunar mag- 

 netic disturbances upon thermal and tidal influences. Notes 2, 116-22, 

 125-6. 



6. The curiously symmetric harmony in Mars and its satellite-system. 

 Note 28. 



7. The varied harmonies of spectral lines, together with the relations of 

 planetary positions to luminous nodes. Notes 36-45, 109, 141-2, 144-53, 

 157. 



8. The confirmations of predictions which were founded upon evidences 

 of the influence of harmonic laws. Notes 33, 133, etc. 



9. The interchangeable convertibility of physical units. Notes 90, 96. 



10. Atomic phyllotaxy. Notes 135-9, 143. Although Gerber's divisors 

 were found empirically, they represent natural elementary groups. His 

 utter want of suspicion that they had any physical meaning makes them 

 much more important than they would have been if his investigations had 

 been biased by a preconceived hypothesis. The kinetic theory of gases 

 necessitates harmonic action, and the tendency to division in extreme and 

 mean ratio leads to one of the most simple kinds of harmony. There is 

 no necessary inconsistency between the doctrine of atomic phyllotaxy and 

 Prout's hypothesis. 



164. Mercury's Virtual Area. 



The fundamental ratio of successive virtual areas, }, represents the ratio 

 of the locus of linear centre of gravity of a simple pendulum to the locus 

 of its centre of oscillation, as well as the exponential ratio of nucleation to 

 limitation in an elastic medium. The intermediate step between the har- 

 monic areas for Mars and Venus, Note 159, may, perhaps, be distributed, 



