1881,} • ^^* [Chase. 



33. Infra- Mercurial Photodynamic Nodes. 



In my original anticipation* of harmonic nodes between Mercury and 

 the Sun, I looked for possible unknown planets, planetoid groups, or other 

 seats "of solar and planetary perturbation." The announcement f to the 

 Royal Society, seven wrecks afterward, of a sun-spot period which was 

 synchronous with the revolution of the first infra-Mercurial node, furnished 

 conclusive evidence of the predicted perturbations ; the observation of sup- 

 posed planetoid bodies, by Watson and Swift, rendered it probable that 

 some of the perturbation is due to actual planetoid influences ; the discus- 

 sions of planetoid sun-spots, by Kirkwood, Mouchez, Gaillot, and Von 

 Oppolzer, indicated four additional periods % in close accordance with four 

 other harmonic nodes ; a sixth node (.139) marks the locus (.140) of orbital 

 time, which is a mean proportion between Earth's day and year ; the six 

 inner nodes have important photodynamic relations which merit special 

 consideration. 



The vis viva, and consequently the modulus of the velocity of any re- 

 volving particle, varies inversely as the radius vector. Hence, the photo- 

 dynamic modulus of aggregating velocity (M^) : modulus of reacting mass 

 (M ) : : radius of reacting mass (r^) : radius of aggregating velocity (^x)- 

 Thequotientof modulus by the radius of rotation is equivalent to (- v)^, (/ be- 

 ing the quotient of V gr by the velocity of rotation. The controlling bodies 

 of the system are Sun and Jupiter, and if we take Jupiter's mass as the re- 

 volving unit of mass, Sun, the reacting mass, will be represented by 

 1047.879. If n designates the quotient of Earth's semi-axis major by Sun's 



(31558149 \2 

 J ; M^ = C^ X 1047.879)2. lfn = 

 497.827 X 3 ^ 7*2/ '^ 



214.5, M^ = (688.873)2; ^ ^ 688.873 ^ tt =^ 219.28 : r^ =^ M^ -^'^k = 



22.84 ; the time of revolution at Sun's surface (i;,,) = 31558149 sec. -^ 214.5- 



= 10045.5 sec; the time of solar half- rotation, or the time in which gravi- 



/gt\ 

 tating reaction i o" / ^g^'iist photodynamic action equals the velocity of 



light, {t^) = "H-^o = 12.747 days; r^ is the locus which I have designated 

 as Helios,§ or the distance at which a planet would revolve in t^. This 

 gives, for the fundamental radius of my harmonic forecasts. 3.5134 X Earth's 

 semi-axis major, which exceeds Jupiter's mean locus of subsidence col- 

 lision (§ of 5.2028) by less than 1.3 per cent. The closeness of the in- 

 dependent verifications, by various observers, is shown in the following 

 table : 



* Proc. Am. Phil. Soc, xili, 238 ; New York Tribune, May 2, 1873. 



■j-Proc. Am. Phil. Soc, xlii, 470. 



t lb. xviii, 35, 209. 



J Proc. Am. Phil. Soc, xviii, 35. 



