Chase.] t)i\J [Nov. 4, 



4. The relations of ms viva between the chief centres of density and of 

 nebulosity, Earth and Jupiter (3j. 



5. The relations between mean tendencies to belt-rupture and to secular 

 stability, between the chief centres of nebulosity and of planetary inertia, 

 Jupiter and Saturn, in the chief belt of planetary aggregation (7). 



6. The tendency of incipient subsidence towards the chief centre of 

 nucleation, and of incipient rupture from the chief centre of density, 

 Venus, Sun and Earth (5). 



7. The tendency of incipient subsidence at the chief centre of density, 

 together with mean tendencies of subsidence at the chief centre of planet- 

 ary inertia, Earth, Saturn and Mars (9). 



8. The combination of incipient tendencies of subsidence at the chief 

 centre of density and at the inner margin of the outer planetary belt, with 

 mean rupturing tendencies at the outer margin of the outer belt (11). 



9. The combination of incipient tendencies of rupture at the chief centre 

 of dcn.sity, with mean rupturing tendencies at the chief centre of 

 nebulosity and mean subsidence at the inner margin of the outer belt (13). 



Mercury, with its greM orbital eccentricity, the asteroids, comets and 

 meteors, doubtless serve to complete the exact adjustment which the sta- 

 bility of the system requires. 



157. Relations of Fraunhofer Lines to Density and Vis Viva. 



Astronomers do not waste their time in inquiring whether planetary 

 motions are in accordance with the laws of gravitation, neither need 

 physicists ask whether cyclical undulations are harmonic. Knowing that 

 they must be so, the wiser way is to question nature in order to find what 

 the harmonies are. The simplest harmonies are those which are based 

 on multiples of 2 or 3. If we take X = 392.78 as a unit, we find the fol- 

 lowing approximation of wave-lengths, as measured by Gibbs, to harmonic 

 values : 



Harmonic. Observed. 



11 =r 687.37 B 686.71 



f ;. == 654.63 C 656.21 



j;. =589.17 Di 589.51 



1^ =523.71 E 536.87 



a;, =490.97 F '486.07 



A/ 3; = 392.78 H., 393.30 



The probable error, in each instance, is one-fourth of the harmonic di- 

 visor, in accordance with Schuster's proposed test. The greatest discrep- 

 ancy, F, is only \ of the probable error, or only ^ as great as we might 

 look for without invalidating the evidence of harmonic influence. Such 

 accordance is surely satisfactory enough to encourage further examination. 



If we take I = 2? /"- ^s a unit, so as to provide for the requirements of 

 centripetal, linear and conical oscillation, (2 X 3x4; see Notes 5, 23, 

 156), we find the following approximations : — 



