Harrisburg telegraph. [volume] (Harrisburg, Pa.) 1879-1948, 1919-05-14
SEEMING MAGIC OF
TIDES EXPLAINED
By GARRETT P. sERvIss

II dllIdCllOu VI TIC lHOOh Is
the main cause of the rise and fall
of the surface of the ocean, and a
given point on the earth will pass the
moon but once in a lunar day of "a
hours and SO minutes, please explain
how there come to be two titles in a
lunar day. J. F., Newport News"
This seems to perplex a great number
of people, and as repeated verbal ex-
plantations apparently fail to attain
their aim, have drawn the accompany
ing diagram in the hope that, with its
aid, the puzzle may be cleared up.
First, let us recall the fact that the
force of gravitational attraction varies
inversely with the distance, i. e., as the
distance increases the force decreases.
The variation is inversely as the square
of the distance, but that is detail
which, for our present purpose, we may
ignore.
Now, turning to the diagram, let the
solid circle represent the circumference
of the earth, while the straight line
drawn through it's center shows the di-
rection of the pull of the moon, which
is supposed to be off toward the right.
as indicated by the arrowhead on the
line.
Let the llllle Circles at lHe uSuTeS
a." "2" and "3" stand for three par
ticles, two of which are on opposite
sides of the earth with respect to the
moon, while the other is at the earth's
center. The particles are, then, at
equal distances apart.
Now, to begin, let us disregard the
earth and consider the three particles as
il they were Independent, simply being
arranged at equal intervals on a straight
line running through the moon. From
the law of gravitation stated above 1t
is evident that the moon will draw par
ticle "2,' and also that it will draw
particle "2" with greater force than
particle "3."
Let us represent the effect of these
variations in the attraction by the posi-
tions of the letters "a" "B" and &C."
"A' shows how far the particle al" is
drawn, "B" how far the particle 49,"
and &C" how far the particle 49," the
the respective distances varying with the
force, which dimnishes as the distance
from the moon increases.
If you will take a scale and mea-
sure the diagram you will find that the
line from "A" to &C" is longer than
that from 81" to 49," because "a" is
now farther from "B" than 81" was
from &C." and "B'' farther from &C"
than "2" was from 80"
The point is to see how one single
force, always pulling in the same drec-
ton, but weakening with distance, can
at the same time widen the distance
between the nearest particle and the
middle one, likewise between the mid
die particle and the farthest one. This
being made evident by the diagram, let
baol nd ha orfI
as represented by the solid circle. The
particle "2" is at the center of the earth
nearest the moon, and "3" is on the sur
face farthest from the moon.
Now comes another fact about gravi-
tation to be taken into account. New
ton proved that spherical body, such
as the earth virtually is, attracts and
is attracted just the same as il it's en-
tire mass were concentrated in a point
at it's center. In other words, when con-
sidering the moons pull upon the solid
body of the earth, we have only to con-
Germ ourselves with the force at the
earth's center That determines the ef-
feet of the pull upon the earth as a
whole.
This being so, we see that the amount
by which the moons attraction moves
the solid globe of the earth is denoted
by the distance from "2" to "B" in the
diagram, "B" being the new position of
the center. the dotted circle now repre-
sents the position of the earth. But. if
we suppose the particles "1'' and "3"
to be particles of water in the ocean.
which being liquid can move freely, in
it's different parts. instead of being rig
idly bound like the solid earth, we see
how, in the sape way as 81" is raised
above the surface at "a" by being more
drawn than the solid globe as a whole.
so "3" is, so to speak, left behind at
&C" by being less drawn than the whole
globe. And that is the whole mystery