D. Kirkwood on certain Harmonies of the Solar System. 13 
The radii of gyration of the primitive rings, together with 
their differences, are as follows:— 
1) == 25°20061 | d;,, = 1751756 log = 1-2434736 
f.., = T8305 1d... == Satis log = 0-7194821 
$5; <2 P4419) d,.y = “1°h08ss log = 0°1954906 
M4) == 0°87270\d,,, = 0°469350 log = 16714991 
. 5) == 0°40335|d,,, = 0°140455 log == 1:1475076 
1») == 0°26289|d,,, = 0042026 log = 26235161 
Tq) == 0°22086|d,,, =< 0°012575 log = 2:0995246 
Ts) == 0°20828/d,,, = 0:003763 log = 35755331 
oy a= 020451) d,,, = 0°001126 log = 3:0515416 
19) == 0°20338 | d,,,,= 0°0003369 log = 45275501 
Cc. &e. &e. &e. &e. 
Toe) == 0:20299\d,,, = 0:0000000 log =— @ 
Remarks. 
must have been included between the present limits of Mercury’s 
orbit. The union of the two rings and the formation of a single 
planet may thus have resulted from the eccentricity of the prim- 
itive annuli. Bie 
2. The sum of the infinite series 
d,,jk 1751756 K 3°34189 
diy day +45) + ke, = 7-5 = —seaarap = 2499762; 
and 25:20061—24-99762 = 0:20299 = the distance from the sun’s 
cury been diminished, during the immensity of past time, from 
the same cause? Or may this slight and only exception to the 
strict accuracy of the law be referable to zones or groups of 
asteroids in the vicinity of Mercury’s orbit, the existence of 
which has been indicated by the researches of Leverrier?™ 
4 Runkle’s Math. Monthly, vol. ii, p. 240. 
