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., Tc^ M g — where g is the rate 

 of change of motion (acceleration) ot a falling body. Work is con- 

 sideration of a force and length; w = lc L, but substituting for h its 

 value ML T-^, we get ic = ML- T-~. Work may also be spoken of 

 in other fonns as energy or potential — ^viz, the ability to do work. 

 There is another force which enters h3"drodynamics — namely, pres- 

 sure — and it is defined as a force with respect to an area, or 



p = Y^= ML-^T~^. The pressure at any depth in the sea is equal 



to the weight of a column of water of unit depth h with respect to unit 

 area, or p = qgh. But substituting q= 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 wnll 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. 



