Chase.] O Jo j^jan. if 



The greatest deviation is § of one per cent. The two mean asteroidal ac- 

 cordances are nearly as exact as those in Note 371. All of the direct and re- 

 ciprocal influences are in the asteroidal belt. The direct influence at secu- 

 lar aphelion (4.341) points to a "viscous" rupturing influence of the 

 Jupiter-Saturnian belt (.4 of 10.855 =: 4.342). The exact agreement of the 

 general means is very satisfactory. 



374. Centripetal Influence of Rotary Vis Viva. 



Some of my critics have supposed that it would be possible to find har- 

 monic accordances with series which were taken at random, or with no 

 known kinetic basis, but none of them have offered any such accordances 

 to confirm their supposition. I have never published any harmonies which 

 were not the natural outgrowth of well-known elastic laws, and the abun- 

 dant confirmation which I have found for my anticipations is beyond all 

 cavil or gainsaying. In Note 370 I gave evidences of the centrifugal influ- 

 ence of rotary vis viva, w^hich may be compared with the following evi- 

 dences of mean centripetal influence. 



375. Lines of Force and of Motion. 

 Taylor [op. cit. p. 28), very properly calls attention to the fact that "no 

 atom can perform an oscillation or a revolution, or follow any other path 

 than a straight line, excepting under the coercion of other atoms attracting 

 and repelling. The first law of motion is that of perfect continuity both in 

 amount and in direction. A shuttlecock rebounding in the empty air w^ould 

 not be more conspicuously a dynamic solecism and impossibility than the 

 kinematists 'vibratory particle.' " His doctrine {lb. p. 9), that elasticity is 

 "a fact of nature, a property of matter, w^hich can neither be interpreted 

 by any form of motion, nor resolved into any mechanical concept," is in 

 precise accordance with the due regard to "lines of force" which guided 

 Boscovich and Faraday, and which has been very helpful in my own re- 

 searches. My first paper on barometric estimates of solar mass and distance 

 {Pi'oc. Amer. Phil. Soc, ix, 283-8) was attacked by kinematists, because it 

 violated some of their preconceived notions respecting the composition and 

 resolution of forces. It did not receive much favor, until the productive- 

 ness of the harmonic methods showed that the composition and resolution 

 of motions, in elastic media, may often enable us to dispense with intricate 

 integrations, which it would be difficult, if not impossible to solve, and that 

 it is always safer to be guided by the facts of nature, than by any precon- 

 ceived theoretical interpretation of those facts. 



