1 ^9, 



Chase.] ±0 - [March 21, 



exceeding one per cent., but this merely shows that the successive lines, 

 are arranged nearly at such intervals as may be used in harmony. Table 

 IV. shows more satisfactory agreements between remoter notes, in 

 Table II. 



IV. Accordant Intervals in Light and Sound. 



BG -=- FG = CE and 2 Semitones. 



£ = Minor Sixth.* 



f — Major Third. 



| = Sixth, f 

 J/ = Minor Tone. 

 CA h- CE = Fourth. 



| = Major Tone. 



Ponton's explanation of such harmonies as these, "that the ratios are 

 those of the respective amounts of vis inertke possessed by the vibrating 

 atoms which originate the lines, "J seems quite satisfactory; but I can 

 hardly agree with him in believing that " their arithmetical coincidence 

 with certain musical intervals is merely accidental, and such as might be 

 expected, according to the law of probabilities, when so large a number 

 of lines are concerned." His conclusion, however, was based upon 

 observations of the more minute lines, to which I have already referred, 

 as less satisfactory. I know of no law of probability which would ex- 

 plain such close approximations as are shown in Tables II., III. and IV., 

 without supposing some kind of harmonica! dependence upon one funda- 

 mental vibration. 



The existence of analogous harmonies in atomicities, chemical compo- 

 sition, phyllotaxis, and planetary relations, suggests the hypothesis that 

 the vis inertke itself may be determined by harmonic vibrations. The 

 two forces which are commonly exclusively considered in explaining 

 orbital revolution, are centripetal gravitation, and tangential inertia. 

 There must, also, be a force of centrifugal emanation which enables the 

 Sun to radiate his continual supply of light and heat, and I believe that 

 a proper application of mathematical analysis in the investigation of such 

 a force, would open a wide field for interesting and valuable research. 



If the ultimate particles of bodies are mathematical points, the poten- 

 tial energies of cosmical globes are proportional to the products of their 

 masses by their radii. The density of particles in elastic fluids varying 

 as the squares of the times of molecular diffusion, let us suppose that 

 the time of diffusion is determined by the ratio of orbital time, to time 

 of fall to an attracting centre (y 32). Then, if I represent the length of 

 elastic undulation, we may have some reason to look for the following 

 proportionality : 



mr oc j oc vd oc vf- oc 32 v. 



* Or, Fourth and Minor Third. t Or, Fourth and Major Third. 



$ Loc. cit. p. 100. 



