The Washington times. [volume] (Washington [D.C.]) 1902-1939, 1921-08-28
Mystery of the Tides
WHY THE SUN AND MOON AFFECT THEM
DIFFERENTLY

times more mass than the moon.
III II were as near to the earth as
the moon is II would exercise u.s.
100000 times as much tidal force
upon the ocean waters as the
moon does.
But being 400 times farther
away than the moon, what Is the
consequence? Is its tidal force
reduced to 1-400 of what 1t would
be II II were as near as the moon
is? No, that cannot be, for In
that case the tides raised by the
sun would still be $3.50 times as
high as those raised by the moon,
There must be some other law
in operation, and in searching for
1t you may recall the principle OF
inverse squares" to which /
have often referred in these arti-
cles. According to that principle
the attractive force of a body like
the sun varies inversely as the
square OF distance. Let us try this
and see II 1T will help us out.
The square of 400 is 160, 900.
we divide the $500 900, represent
ing the tidal power Of the sun rel
atively to that of the moon when
distance, by 100000. and the quo
tient is nearly 100. which shows us
that we have not yet found the
true law, for the solar tides. in.
stead of being 160 times higher
than the lunar ones, are less than
half as high.
Now II, instead of simply squar-
ing the 400 which represents the
distance OF sun as compared with
the moons distance, we cube ii.
we get 400x400x4O0 equals 64,-
900 900; and this, taken inversely,
shows the actual reduction of the
suns tidal power due to it's greater
distance.
AS far as mass is concerned.
then. the sun is 25,500.000 times
more powerful than the moon in
producing tides. and, as far as dis
lance Is concerned. 1t is 81 900 900
times less powerful.
The final result is that the ef-
fective tidal force Of the moon is
about two and a half times greater
than the suns. The actual pro-
portion is somewhat less than
that, because we have used round
numbers in the calculation, which
slightly exaggerate the suns dis
lance as compared with the moons.
The law that we have just ap-
piled, viz: that the tidal force
varies inversely as the cube Of
the distance OF the attracting body,
is very important one to re-
member.
1t does not contradict. as you
might hastily infer, the general
law that the force of gravitation
rio yv,vy AvaIxv -
the distance, but. on the contrary.
1t grows out OF that law; but I
have not space here to give a
mathematical explanation Of 1t.
Instead. let us glance at some
of its remarkable consequences.
IL the distance of the moon from
the earth should be diminished to
one-half of it's present amount the
height OF the tides would be in
creased eight-fold!
At every flood tide the lower
parts of New York City would be
swept with a wave, or bore, forty
or fifty feet in height.
If, on the other hand. the moon
should suddenly retreat to twice it's
present distance. the lunar tides
would be diminished to one-eighth
OF their actual height, and not only
New York bay, but nearly all the
great harbors of the world. would
become unnavigable for ships Of
heavy burden.
II the moon should approach I,
one-tenth its present distance land
there Is reason to believe that IT
was formerly much nearer than
thap, its tidal force would lie in
creased a thousand-fold. and near.
~ the whole surface of the United
states, from the Atlantic coast "a
the Rocky Mountains, would be in.
undated by tidal waves.
III the planet Jupiter should ap.
proach as near as the moon now
is, the tidal force would suffice TO
raise tidal waves in the open ocean
ten miles high!
The story of the tides, and of
the part that they have PLAYED in
the evolution of the earth. the
moon. and indeed of the whole
universe. is one of the greatest
romances of science.