From these equations, and if *T*_{m} is taken at 4 x 10^{8} years, the following
conclusions are reached:

(a) The value of the gravitational constant, *g* now expressed in metres
per second square as 9.80665, had more nearly the value 9.80667 in
Newton's time and will have the value 9.80663 in the year 2250.

(b) The radius of the earth is diminishing by nearly 4 mm. per
year.

(c) During the geological period known as the Cambrian the earth had
about two-and-a-half times its present mass and its radius was about
13.5 per cent. greater than now.

(d) During the time, two thousand million years ago, when the first
known sedimentary rocks were laid down the mass of the earth had thirty-two times its present value and the radius was more than three times as
great as it is now.

(e) At the time when these sedimentary rocks were laid down water
boiled at 140^{o}C. Its great weight must have caused it to have an enormous
scouring action on rocks. Sedimentation must have been a much more
rapid process than it is now.

(f) If it were not for the slowing down effect of the tides, the continuous
decrease in the earth's radius of gyration would lead to a continuous increase in its angular velocity. It follows that tides dissipate more energy
than has hitherto been supposed.

The astronomical, geological and biological consequences of this slow
but unceasing reduction in the earth's mass and volume must be significant.
If my theory that the half-life of matter is finite is true, it must therefore
provide extensive and rewarding fields for new research by experts in these
three disciplines. This appendix is not a suitable place for considering in
detail the nature of this research, but it is worthwhile to consider some
samples of the problems that continuous extinction raises in each of these
disciplines.

The astronomical field seems to be the least promising of the three, for
the astronomical changes that would result from shrinking of the earth
are likely to be the least easy to detect.

One such change would be the earth's hold on the moon, which must
be steadily loosening as *g* decreases. It has already been mentioned in
Appendix C. Another would be the increase in angular velocity that must
accompany reduction in the earth's radius of gyration. As just mentioned,
this speeding-up of the earth's rotation must go some way towards counter-acting the slowing-down effect of the tides. But I cannot think of any
astronomical observations precise enough to detect the predicted changes
in *g* and in the radius of gyration.

These changes would affect the exact times when eclipses occur. One
can calculate these times very accurately for past eclipses on the assumption that the earth's mass was no greater then that it is now and could
then compare the result with historical records. If observations thousands
of years ago had been as precise as they are today, one might be able to
discover from a discrepancy between the calculated and the observed
moments whether the earth's mass has changed or not.

But to be sure one would also have to disentangle the two effects that
influence the length of the day: tides, which tend to make the day grow
longer, and contraction, which tends to make it grow shorter. For this
one would have to know accurately how much energy is dissipated by
tides and this is, in fact, hardly possible to estimate. The conclusion is,
I am afraid, that precise astronomical observation and calculations are too
recent and knowledge of some of the relevant quantities too incomplete,
for the gradual shrinking of the earth to have an observable effect in
astronomy.