1832.] 237 rr>K 



■■ [Chase. 



Photodynamic Notes, V. By Pliny Earle Chase, LL.D. 



{Read before tlie American Philosophical Society, April 31st, 1882.) 



158. Synchronovs Areas. 



Kepler's second law is grounded upon principles which must modify 

 rotation and subsidence, so as to introduce harmonic tendencies among the 

 synchronous areas which are described by different bodies, under the con- 

 trolling activity of a common centre, as well as in the virtual areas whicli 

 represent the reaction of the subordinate masses upon the centre of gravity 

 of the system. In orbits of small eccentricity, the instantaneous area of 

 a particle is nearly proportional to the square root of its mean radius 

 vector. If we take r = (i)' = .125, as a harmonic divisor, the first of 

 these tendencies is shown by the principal planets, as may be seen in the 

 following table : 



Harmonic Areas. Synchronous Are.as. Difference. 



5 ^ .625 Mercury .6223 4- .0028 



"^ ^ -875 Venus, .8505 + .0245 



8^ 1-000 Earth, 1.0000 .0000 



10 r 1.250 Mars, 1.2344 +.0156 



18 r 2.250 Jupiter, 2.2810 —.0310 



25^' 3.125 Saturn, 3.0885 ,+ .0365 



35 r 4.375 Uranus, 4.3799 — .0049 



44 r 5.500 Neptune, 5.4803 +.0197 



All the differences are within the limits of probable error, .03125 except 

 Saturn's. Jupiter's area is nearly f of Saturn's, and the combined masses 

 of these two planets is so great as partially to override the simple tendencies 

 of subsidence towards the chief centres of condensation and nucleation 

 Earth and Sun. 



The synchronous areas of Mercury and Mars, the outliers of the dense 

 belt, are nearly in the ratio 1:2; Venus and Earth, 7:8; Uranus and 

 Neptune, 4 : 5. The difference is less than ,l of the probable error in the 

 first of these comparisons ; less than i of the probable error in the second ; 

 less than ^^g of the probable error in the third ; the "probable error," in 

 each case, being i of the common divisor, or the deviation which would 

 be admissible without weakening the evidence of harmonic tendency in a 

 cera causa. 



159. Virtual Areas. 



The virtual areas of synchronous reaction, or the instantaneous areas 

 which a particle, at Sun's mean distance, would describe about the principal 

 planets if it were not restrained by stronger influences, vary as Vmr. Vis 

 viva may be represented by orbital areas, as well as by distances of pro- 

 jection against uniform resistance, therefore we may add a third law to 



