D. Kirkwood on certain Harmonies of the Solar System. 7 
dence, therefore, apart from the reason assigned by my analogy, 
is unquestionably in favor of a long period of rotation. 
It is easily shown that the equality between the angular ve- 
locities of rotation and orbital revolution, which obtains in the 
secondary systems, is not incompatible with the law of rotation, 
When the volumes of the primary planets had the same ratio to 
their spheres of attraction as those of the satellites now have to 
theirs, the former were still in a state of vapor, their masses ex- 
tending beyond the present orbits of the secondaries, and not 
having reached, in all probability, the limits of equality between 
the two angular velocities in their respective cases. Had 
satellites, at the corresponding epoch in their history, been equally 
are, so that any increase in rotary velocity would not have been 
prevented or arrested by solidification, the same law would 
doubtless have obtained in the secondary systems. 
I have believed, however, almost from the time of its first 
announcement, that the statement of my analogy requires some 
modification. If it be the expression of a physical law, it must 
depend on the relation between the primitive momentum of ro- 
tation and that of orbital revolution. Now the time of rotation 
have been had the entire mass condensed in a single body. 
suzzth, the mass of Jupiter being 1. The sum of the masses of 
: : 
tion of the rotary velocities of these planets from the precipitation 
of their secondaries may be wholly negle he mass of 
made for the earth and moon shows that the precipitation of even 
this mass upon the planet would shorten the period of rotation 
