1875.] U-i< [Chase. 



Jupiter and Saturn also diifer by 180°. These accordances seem to point 

 to a primitive nebular arrangement of alternating nucleal points, as 

 represented in the accompanying figure. 

 W 224 h 168 Q 105 2i ITo (^ ^^ ^^ compare the rotation-radii 



I 1 1 1 1 for Neptune's mean aphelion and 



Uranus, we find the ratio of -velocity from infinite fall to orbital 

 velocity ; the mean radius gives us the ratio 7:5; Uranus : Saturn : : 5 

 : 3 ; Jupiter : Saturn : : radius of spherical gyration : radius of homo- 

 geneous mass; the difference between Uranus and Jupiter : Jupiter : : 

 Uranus : Saturn, The four exterior planetary orbits therefore furnish 

 the folio vying harmonic series : yj |> | ; f, f? fj f ] h h f* 



Having shown that the limit of equality, from or towards which the 

 rotating and orbital velocities of a solar equatorial particle both tend, is, 

 like the ratio of the electric units, a quantity of the same order of mag- 

 nitude as the velocity of light, let us start from that velocity, and see 

 how nearly our results agree with those already given. 



Let the velocity and time of describing radius at Sun's equator be 

 represented by 



■a^, i ,, in solar rotation ; 



V r) t^ in equatorial revolution ; 



i-'i P^ 

 t)y ty by the velocity of light ; 



V . = the velocity of light ; 



Then t^ oc r' ; v^ = gt = oc 



' a ' 



J_ 



tp CC r2 ; «^ = gt^ = ^ OC /,, 



t OC ?•; « = gt^ — — , constant 

 Taking Sun's radius as the unit of length, and a second as the unit of 



214.86 385.2584X86400 ^ ^^^ 



time, V = ^9^-^ = .4316 r per s ; t = i" = 1595 s.;v = 



^ ' A • 2- (214.86) - 1-' 



r — .000627r: »„ = w^ _^ ^ — .000000911?-; time of rotation = 



T'593" ^ C- p I 



2-r -T- v^ = 25.409 days. The rotation-radii of the several planets, 



/ound by dividing the square roots of their orbital times by the square 

 Jtoot of the time of solar rotation, are as follows : 



Neptune 48.6693 Mars 5.1997 



Uranus 34.7531 Earth 3.7915 



Saturn 20.5777 Venus 2.9738 



Jupiter 13.0581 Mercury 1.8607 



These values, being given in solar radii, should be multipled by eight 

 A. p. S. — VOL. XIV. 4c 



