22, REPORT—1905. 
since the scale of magnitude on which our planet is built is immaterial, 
contraction will produce exactly the same effect on shape as augmented 
rotation. I must ask you, then, to believe that the effects of an apparently 
arbitrary increase of rotation may be produced by cooling. 
The figures which I succeeded in drawing, by means of rigorous calcu- 
lation, of the later stages of this course of evolution, are so curious as to 
remind one of some such phenomenon as the protrusion of a filament of 
protoplasm from a mass of living matter, and I suggest that we may see 
in this almost life-like process the counterpart of at least one form of the 
birth of double stars, planets, and satellites. 
As I have already said, Newton determined the first of these figures ; 
Jacobi found the second, and Poincaré indicated the existence of the 
third, in a paper which is universally regarded as one of the masterpieces 
of applied mathematics ; finally I myself succeeded in determining the exact 
form of Poincaré’s figure, and in proving that it is a true stable shape. 
My Cambridge colleague Jeans has also made an interesting sontri- 
bution to the subject by discussing a closely analogous problem, and “he 
has besides attacked the far more difficult case where the rotating fluid is 
a compressible gas. In this case also he finds a family of types, but the 
conception of compressibility introduced a new set of considerations in 
the transitions from species to species. The problem is, however, of such 
difficulty that he had to rest content with results which were rather 
qualitative than strictly quantitative. 
This group of investigations brings before us the process of the birth 
of satellites in a more convincing form than was possible by means of the 
general considerations adduced by Laplace. It cannot be doubted that 
the supposed Laplacian sequence of events possesses a considerable 
element of truth, yet these latter schemes of transformation can be followed 
in closer detail. It seems, then, probable that both processes furnish us 
with crude models of reality, and that in some cases the first and in others 
the second is the better representative. 
The moon’s mass is one-eightieth of that of the earth, whereas the 
mass of Titan, the largest satellite in the solar system, is z;!55 of that of 
Saturn. On the ground of this great difference between the relative mag- 
nitudes of all other satellites and of the moon, it is not unreasonable to 
suppose that the mode of separation of the moon from the earth may also 
have been widely different. The theory of which I shall have next to 
speak claims to trace the gradual departure of the moon from an original 
position not far removed from the present surface of the earth. If this 
view is correct, we may suppose that the detachment of the moon from 
the earth occurred as a single portion of matter, and not asa concentration 
of a Laplacian ring. 
If a planet is covered with oceans of water and air, or if it is form 
of plastic molten rock, tidal oscillations must be generated in its mobile 
parts by the attractions of its satellites and of the sun. Such movements 
must be subject to frictional resistance, and the planet’s rotation will be 
