A19 
412 {July 19, 
Ohase.] 
2 
radial terminus to a centre of*explosive oscillation), at 4 and 3 (=dis- 
tance to a centre of linear oscillation), at } (distance to linear centre 
of gravity), and at 4 and % (distance to a centre of reverse or direct ex- 
plosive oscillation). The various possible combinations of these numbers 
favor phyllotactic and other systematic arrangements to such a degree, 
that the very wealth of planetary illustration becomes burdensome and 
perplexing, and the attempt to trace the development of our cosmical 
system to simple laws seems almost hopeless. 
If the primitive disturbance is accompanied (as it must almost neces- 
sarily be), by rotation, the ratio 1 : 9 assumes special importance, inas- 
much as it represents the proportionate distance of the centre of rotation 
from the rotating centre of explosive oscillation. Assuming 7—Sun’s 
radius, as our fundamental unit, we are at present unable to determine 
whether there is any permanent limit at 9r, that point being within the 
sphere of solar atmospheric retardation ; but I have shown in my com~- 
munication of March 1, 1872, that there are important divisions, 
Near 97, the inner limit of the planetary system.............+++++- @ 
Near 97, the dividing mean between the intra- and the extra-aster- 
oidal planets..... PI WOE UE UOTE a ahs 
Near 9*7, the outer planetary limit...............- See ue es was r 
The other ratios are exemplified by the positions of 
Haburm and INSptine, £23......5. 06.0... Py woe aee spy ae 0 
[Db nadib epee AN nds PIeONG | ees areas ere ee riroe a bu eeu gin Ua eee 
MAUURM AOC WiaMUSi 2a a. ee ee ys eine ies ante Fle Nines es 
Uranus and Neptune, from Saturn, 4:9......... see v ene e eet eeeeee H 
Uranus and Jupiter, trom Neptune,4 59 ..40....05 ca. te oe 0 
grupiter and Satming 5390 wo Oe es ae, See apes as ee 
Ido not find so much evidence of the marked cosmical influence of 
centres of linear oscillation, as I do of centres of direct and explosive 
; : : une 4p 4p : 
oscillation. The positions rm and 9X g? we both within the sphere of 
: 4p 
retardation ; but at 92> 5 ==367, we are near the centre of explosive oscil- 
lation between Mercury and the Sun, and also near the limit of the Sun’s 
possible atmosphere,* which is probably not less than 35.597 (according 
to Spérer’s estimate of the time of solar rotation), and not greater than 
37.227 (according to Hornstein’s estimate of the 264 day magnetic cycle). x 
et 
Near 9° 5 ==B247, we find ili glatiet Mars. 0.2... .0..5.eese sevens A 
: ’ 
se ON ay ne . ; i A . 
9*x 9 29167, isa centre of explosive oscillation between Uranus 
gnd Saturn Mae ene cast Peal ere bse Ie 
* The limit of equal equatorial centrifugal and centripetal force. 
