272 Mr. D. Vaughan on the Stability of Satellites in small Orbits, 
effecting a simultaneous dilapidation of the entire planetary 
structure. 
I have regarded it as important to trace the precise manner in 
which these sublime catastrophes must take place; not so much 
on account of their connexion with the existence of planetary 
rings, as for the light which they throw on the nature of 
temporary stars. In an article published in the Supplemental 
Number of the Philosophical Magazine for December 1858, I 
maintained that these singular displays of stellar brilliancy were 
great meteoric displays in the atmospheres, or rather the dormant 
photospheres, of dark central bodies of space, as they were tra- 
versed by the wrecks of dilapidated worlds. The same theory 
has been set forth in my paper presented to the British Associa- 
tion in 1857; and I have endeavoured in other publications to 
support it with satisfactory proof. But the most conclusive evi- 
dence on which it depends, is to be derived from the instanta- 
neous manner in which the attendant of a dark central body 
must undergo a total dismemberment, as it explains the sudden 
manner in which these celestial curiosities are ushered into exist- 
ence with all the splendour of distant suns. Humboldt, in the 
third volume of his ‘Cosmos,’ calls special attention to the fact 
of the extreme brilliancy of the temporary stars in their incipient 
stages, regarding it as a remarkable peculiarity, and one well 
deserving of consideration. 
Without adducing any further evidence on this subject, I shall 
now proceed to trace the condition which matter must assume in 
the region where such disturbing forces render it imcapable of 
forming a single mass, held together by the power of gravity. 
On the dismemberment of a satellite on this dangerous ground, 
the resulting host of fragments would scatter into numberless 
orbits; and the wide range over which they must extend may 
be estimated from the greatest and least size of the elliptical 
paths which their velocities and positions should assign to them. 
For these, however, we can only give at present approximate 
values, taking no cognizance of the mutual disturbances of the 
fragmentary host. And in this case the matter from the most 
distant part of the satellite would describe an ellipse, the dia- 
meter of which is equal to 
23 (a + A) 
2u°—(v+A)* 
The fragments from the nearest point of the dismembering mass 
would describe an elliptical orbit the diameter of which is 
2a°(u—A) | 
22° —(e2—A)§ 
