e.
I may indeed remark, that the question as to what becomes of all the
radiant energy which the millions of suns in the universe are daily
discharging offers a problem apparently not easy to solve; but we need
not discuss the matter at present, we are only going to trace out the
vicissitudes of our own system; and whatever other changes that system
may exhibit, the fact is certain that the total quantity of energy it
contains is declining.
Of the two endowments of energy and of moment of momentum originally
conferred on our system the moment of momentum is the entailed estate.
No matter how the bodies may move, no matter how their actions may
interfere with one another, no matter how this body is pulled one way
and the other body that way, the conservation of moment of momentum is
not imperilled, nor, no matter what losses of heat may be experienced
by radiation, could the store of moment of momentum be affected. The
only conceivable way in which the quantity of moment of momentum in
the solar system could be tampered with is by the interference of some
external attracting body. We know, however, that the stars are all
situated at such enormous distances, that the influences they can
exert in the perturbation of the solar system are absolutely
insensible; they are beyond the reach of the most delicate
astronomical measurements. Hence we see how the endowment of the
system with moment of momentum has conferred upon that system a
something which is absolutely inalienable, even to the smallest
portion.
Before going any further it would be necessary for me to explain more
fully than I have hitherto done the true nature of the method of
estimating moment of momentum. The moment of momentum consists of two
parts: there is first that due to the revolution of the bodies around
the sun; there is secondly the rotation of these bodies on their axes.
Let us first think simply of a single planet revolving in a circular
orbit around the sun. The momentum of that planet at any moment may be
regarded as the product of its mass and its velocity; then the moment
of momentum of the planet in the case mentioned is found by
multiplying the momentum by the radius of the path pursued. In a more
general case, where the planet does not revolve in a circle, but
pursued an elliptic path, the moment of momentum is to be found by
multiplying the planet's velocity and its mass into the perpendicular
from the sun on the direction in which the
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