U. S. COAST AND GEODETIC SURVEY 
The Tide-Producing Forces 
The tide arises as the result of the attractive forces of sun and moon on the rotating 
earth. The intensity with which a heavenly body attracts a particle of matter on the 
earth varies directly as its mass and inversely as the square of its distance. For the 
solid earth as a whole the distance is obviously to be measured from the center of the 
earth since that is the center of mass of the whole body. But the oceanic waters, 
which may be considered as lying on the surface of the earth, are on the one side of 
the earth nearer the heavenly body and on the other side farther away than the center 
of the earth. The attraction on the waters of the oceans is thus different in intensity 
from the attraction for the solid earth as a whole, and these differences of attraction 
give rise to forces that cause the ocean waters to move relative to the solid earth and 
bring about the tide. These forces are called the tide-producing forces. 
The mathematical development of these forces brings out the fact that the tide- 
producing power of a heavenly body varies directly as its mass and inversely as the 
cube of its distance from the earth. Of the heavenly bodies, only the sun and moon 
need be taken into consideration insofar as the tide on our earth is concerned. For 
the other heavenly bodies are either too small or too far away to bring about any 
appreciable tides on the earth. The sun has a mass about 27,000,000 times as great 
as that of the moon but it is 389 times as far away from the earth. Hence the tide- 
producing power of the sun is to that of the moon as 27,000,000 is to (389)* or somewhat 
less than half. The moon is thus the principal tide-producing body. 
When the relative motions of the earth, moon and sun are introduced into the 
equations, it is found that the tide-producing forces of sun and moon group themselves 
into three classes: (a) Those having a period of approximately half a day, which are 
therefore called the semidiurnal or semidaily forces; (6) those having a period of approx- 
imately one day, known as the diurnal or daily forces; (c) those having a period of half 
a month or more, known as the long-period forces. 
The tide-producing forces are distributed in a regular manner over the earth, 
varying with latitude. But the response of the various oceans and seas to these forces 
differs, depending on the hydrographic features of the basins of the different oceans 
and seas. As a result, the tides as they actually occur differ markedly at different 
places but with no apparent relation to latitude. 
The principal tide-producing forces are the semidiurnal forces. These forces go 
through two complete cycles in a tidal day, and it is because of the predominance of 
these semidaily forces that there are at most places two complete tidal cycles, and 
therefore two high and two low waters in a tidal day. 
Tidal Currents 
In its rise and fall the tide is accompanied by a horizontal forward and backward 
movement of the water called the tidal current. The two movements—the vertical 
rising and falling of the tide and the horizontal forward and backward movement of 
the tidal current—are intimately related, forming parts of the same phenomenon 
brought about by the tidal forces of sun and moon. 
It is necessary, however, to distinguish clearly between tide and tidal current, 
for the relation between the two is not a simple one nor is it everywhere the same. 
