Chase.] 4.0Z [June 17, 



If we make the greatest possible allowance for uncertainties of data, the 

 relations of inter-planetary and inter-stellar distances to the three import- 

 ant masses, which are shown by the present note and the three foregoing 

 notes, are close enough to be very curious, even if we could think them 

 merely accidental. Inasmuch as they have been discovered by a simple 

 consideration of the consequences which ought to follow, through the 

 known laws of elasticity, from the interruption of luminous vibrations 

 and the formation of nodes by cosmical inertia, they are more than curious, 

 for they are indicative of the unity of energy which has long been thought 

 to control all i^hysical manifestations. 



50. Harmonic 3Iasses. 



Twice modulus is the radius of rectilinear oscillation, which would be 



synchronous with orbital oscillation about a major axis equivalent to that 



of the homogeneous sethereal atmosphere. The dei^endence of modulus 



upon solar mass and radius makes it probable that there may be a harmonic 



dependence, of a like character, among the principal planetary masses. 



We find, indeed, that the four extra-asteroidal planets have harmonic 



masses, inasmuch as they may all closely be represented by the formula 



Sun 3 X Modulus 

 pT -— , = ~ , in which n is integral, so that the second member 



of the equation gives four terms of a harmonic progression. 



Computed Values. Authority. 



1047.88 = Sun -^ Jupiter. Bessel. 



3501.6 = Sun -~ Saturn. 

 22600. = Sun -^ Uranus. Newcomb. 

 19380. = Sun ^ Neptune. 

 That these approximations are not accidental, may be shown hj com- 

 paring the probable with the actual deviations from exact accordance. 

 Probable. Actual. P -=- A. 



The deviations are so far within the limits of probable errors of mass 

 that the accordance may, perhaps, be exact. But absolute exactness, in 

 the satisfaction of any mechanical tendencies is not to be expected. There 

 are so many and so various modifying influences, in all cases, that any 

 result which is in complete accordance with theory should be regarded as 

 more suspicious than one which suggests slight perturbations from some 

 unknown cause. 



51. Subordinate Masses. 



If "the exception proves the rule," we may find that the perturbations, 

 which were spoken of in the foregoing note, may introduce apparent ex- 

 ceptions, in subordinate masses, which are really confirmatory of the har- 



