ADDRESS. 15 
law concerning the distances at which the several planets move about the 
sun. It is true that the planet Neptune, discovered subsequently, was 
found to be considerably out of the place which would be assigned to it 
by Bode’s law, yet his formula embraces so large a number of cases with 
accuracy that we are compelled to believe that it arises in some manner 
from the primitive conditions of the planetary system. 
The explanation of the causes which have led to this simple law as to 
the planetary distances presents an interesting problem, and, although it 
is still unsolved, we may obtain some insight into its meaning by con- 
sidering what I have called a working model of ideal simplicity. 
Imagine then a sun round which there moves in a circle a single 
large planet. I will call this planet Jove, because it may be taken as 
a representative of our largest planet, Jupiter. Suppose next that a 
meteoric stone or small planet is projected in any perfectly arbitrary 
manner in the same plane in which Jove is moving ; then we ask how 
this third body will move. The conditions imposed may seem simple, 
yet the problem has so far overtaxed the powers of the mathematician 
that nothing approaching a general answer to our question has yet been 
given. We know, however, that under the combined attractions of the 
sun and Jove the meteoric stone will in general describe an orbit of 
extraordinary complexity, at one time moving slowly at a great distance 
from both the sun and Jove, at other times rushing close past one or 
other of them. As it grazes past Jove or the sun it may often but just 
escape a catastrophe, but a time will come at length when it runs its 
chances too fine and comes into actual collision. The individual career 
of the stone is then ended by absorption, and of course by far the greater 
chance is that it will find its Nirvana by absorption in the sun. 
Next let us suppose that instead of one wandering meteoric stone or 
minor planet there are hundreds of them, moving initially in all con- 
ceivable directions. Since they are all supposed to be very small, their 
mutual attractions will be insignificant, and they will each move almost 
as though they were influenced only by the sun and Jove. Most of these 
stones will be absorbed by the sun, and the minority will collide with Jove. 
When we inquire how long the career of a stone may be, we find 
that it depends on the direction and speed with which it is started, and 
that by proper udjustment the delay of the final catastrophe may be made 
as long as we please. Thus by making the delay indefinitely long we 
reach the conception of a meteoric stone which moves so as never to come 
into collision with either body. 
There are, therefore, certain perpetual orbits in which a meteoric 
stone or minor planet may move for ever without collision. But when 
such an immortal career has been discovered for our minor planet, it still 
remains to discover whether the slightest possible departure from the 
prescribed orbit will become greater and greater and ultimately lead to a 
collision with the sun or Jove, or whether the body will travel so as to 
cross and recross the exact perpetual orbit, always remaining close to it. 
