232 RESULTS OF RECENT RESEARCHES ON THE 
unseen tides in every part of the heavens. In a fluid universe tides necessarily result 
from gravitation, and are as universal as this great law of nature. In my later researches 
I have therefore been much concerned to show from the discussion of reliable observations 
that gravitation is really universal* and consequently that the tides we have assumed 
actually exist in the bodies of the stars. It is thus made certain that the foundation upon 
which our cosmogonie speculation rests is as enduring as the Newtonian theory itself. 
We now come to the second part of the problem: By what process did the stars 
separate ? In college lectures I had heard the annular theory of Laplace expounded for 
the solar system, and yet I failed to see how this theory could account for the separation 
of equal or comparable masses, such as we observe among the stars. Realizing that 
the double stars are in fact made up of two bodies of comparable mass, I reached the 
conclusion while still at the Missouri University that there must exist some process by 
which a nebula divides into equal or comparable parts, in a manner analogous to that 
of fission among the protozoa. About November, 1889, very soon after I entered upon 
my studies at the University of Berlin, I found that Darwin had recently published an 
important mathematical paper on the figures of equilibrium of rotating masses of fluid, 
and had referred therein to the profound work of Poincaré. published about a year 
before. When I beheld the figures of equilibrium which these mathematicians had com- 
puted, I recognized at once the cosmical process I had already assumed to exist; it 
was indeed a great satisfaction to see a demonstration that under gravitational contrac- 
tion homogeneous incompressible fluid masses may divide into equal or comparable 
parts. The next question was: Are there nebulee of this form in the actual universe? 
In searching over the paper of Sir John Herschel in the Philosophical Transactions 
for 1833, I found some drawings of double nebule almost exactly like the figures 
mathematically determined by Darwin and Poincaré. It was no longer possible to doubt 
that the real process of double-star genesis had been discovered. Further investigation 
and reflection haye confirmed this inference, and I believe we may now accept with 
entire confidence the result reached at Berlin in November, 1889. 
In the first investigation Poincaré begins with the Jacobian ellipsoid of three unequal 
axes, and imagines it shrinking in such a way as to remain homogeneous, and yet gain 
constantly in velocity of axial rotation. When the oblateness has become about 2 he 
finds that the equilibrium in this form becomes unstable, and the mass tends to become 
a dumb-bell with unequal bulbs—an unsymmetrical pear-shaped figure which I have 
called the Anioid. As the contraction continues the whole evidently ruptures into two 
comparable masses, and the smaller will then revolve orbitally about the larger. If 
* RESEARCHES ON THE EVOLUTION OF THE STELLAR SystmMs, Vol. I: On the Universality of the Law of Grav- 
tution and on the Orbits and General Characteristics of Binary Stars (Tue Nichols Press, Lynn, Mass., 1896). 
