Chase.] d44 [ Jan. 1, 



GRAVITATING WAVES. 



By Pliny Earle Chase, 



Professor of Physics in Haverpord College 



{Bead before the American PhilosopMcal Society, January 1st, 1875.) 



In my various discussions of luminous and gravitating liarmonies, I 

 have shown many slight discrepancies, between theoretical and observed 

 results, which are of the same order of magnitude as planetary orbital 

 eccentricities. Although it would be unreasonable to look for any speedy 

 and complete solution of those discrepancies, I think it right to try such 

 questionings of nature, as seem likely to lead to a fuller understanding 

 of the common laws of molar and molecular force. 



The hypotheses of Newton and Le Sage seem necessarily to involve a 

 repellent action of the gethereal waves between two bodies or particles, 

 as well as a centripetal appulsion by the exterior waves. If the ratio of 

 these activities is discoverable, it seems reasonable to look for it in the 

 relative positions and motions of the three controlling bodies in the prin- 

 cipal subdivisions of our system, — Sun, Earth, and Jupiter. 



In the sim]5lest form of gravitating or other central revolution, the 

 tangential ' ' lines of force ' ' are continually deflected, by radial centripetal 

 waves, so as to form a system of semi-circular undulations. The velocity 

 of circular orbital motion communicated by any central force being repre- 

 sented by radius, (or twice the virtual centripetal appulsion), the length 

 of the aggregating radial wave : the length of the deflected semi-circular 

 wave : : 1 : -. But the length of the wave of dissociation * : the length 

 of the limiting wave of aggregation : : 3 : -^. Combining these propor- 

 tions, we find that the length of the dissociating or repelling wave : the 

 length of the primitive wave : : 2 : tt^ or : : .0645 : 1. If the repulsion 

 of the surfaces of two bodies from their common centre of gravity is 



2 

 —^ of the appulsion towards the centre of gravity, the distance of 



the common centre of gi'avity from, the principal centre of mass 

 =: (l +^) 7- = 1.0645?-. 



The mean distance of Jupiter from Sun being 1117.87 r, the mass of 

 (Sun ^- Jupiter) should be, to accord with this hypothesis, 1117.87 

 -- 1.0645 = 1050.14. 



I have already shown that the limit of dissociating velocity («o) for 

 Jupiter and Earth, corresponds to the limit of planetary velocity for Sun, 

 thus indicating an equality of radial and tangential action, such as we might 

 reasonably have anticipated. If we adopt Cornu's determination of the 



* Proc. Am. Assoc, Hartford Meeting, 1874 ; Am. Jour. Sci., " Velocity of Primitive Un- 

 dulation," Nov. 1874. 



