7 
unity then we see that the force is equal to the acceleration. The 
force per unit mass is called the accelerating force. The most com- 
mon natural force is that of gravity, and is expressed, of course, like 
other forces, in relation to a mass—e. g., k= M g—-where g is the rate 
of change of motion (acceleration) of a falling body. Work is con- 
sideration of a force and length; w=k L, but substituting for & its 
value MLT-?, we get w= ML?T-*. Work may also be spoken of 
in other forms as energy or potential—viz, the ability to do work. 
There is another force which enters hydrodynamics—namely, pres- 
sure—and it is defined as a force with respect to an area, or 
p=h= ML-'T-?. The pressure at any depth in the sea is equal 
to the weight of a column of water of unit depth / with respect to unit 
area, or p=qgh. But substituting g= ML, g=LT~, and h=L, we 
get p= ML"'T~. 
The distribution in space of the value of the variables in the sea— 
viz., gravity, pressure, and specific volume—may be represented by 
a series of equiscalar surfaces. Those of gravity are known as equi- 
potential surfaces; those of pressure are called isobaric surfaces; and 
those of specific volume, isosteric surfaces. The space between two 
successive equiscalar surfaces is called an equiscalar sheet. If we 
construct the equiscalar surfaces for unit differences in numerical 
value of the quantities in question, then we obtain unit scalar sheets. 
For example, the differences between equiscalar surfaces of poten- 
tial corresponds to equiscalar units of work. 
GRAVITY 
Let us contemplate this force apart and alone with respect espe- 
cially to the envelope of water which surrounds the earth. We may 
imagine that all the equipotential surfaces throughout an ocean’s 
mass are level, then the surface of such a sea must also be exactly 
level, and a line to the center of the earth, with an attractive force to 
that point, called gravity, will plumb exactly perpendicular. Every- 
where in such a sea gravity will exert a pull at right angles to the 
equiscalar surfaces, and the sea surface itself will be an example of a 
level equipotential plane. Such a motionless state is represented by 
Figure 3, (a), page 8. For the purposes of measuring and coordinating 
the accelerating force exerted by gravity in the hydrosphere, we shall 
endeavor to construct a series of concentric equipotential spheroid 
surfaces, each one separated by equipotential unit sheets. The thick- 
ness of such sheets will vary with the latitude, and in our particular 
subject (the sea) with the depth. The fundamental basis for fixing 
the relative position of equipotential surfaces in the sea, rests, of 
course, upon the presence of an attractive force which exists between 
the earth and the water masses on it. 
