932 
BULLETIN OF THE BUEEAU OF FISHEKIES 
The practical application of this theorem to hydrographic problems thus hinges 
on the selection of suitable unit values for thickness and for pressure; the selection 
of such was not the least of Bjerknes’s contributions to dynamic oceanography. 
The force responsible for dynamic currents in the sea is that of gravity — not 
the capacity for work inherent in the water itself because of its mass. Consequently, 
the unit of height (or thickness) used in hydrodynamic calculations must not only 
stand in a linear relationship to the unit of pressure, but it must also be a direct 
measure of the potential force of gravity, which accelerates all falling bodies equally, 
irrespective of their mass. The gravity potential set free when a unit mass of 
water flows down a sloping surface is the product of two arguments— (1) the 
vertical difference in height and (2) the accelerating force of gravity. The latter 
being about 9.8 meters per second, the dynamic value of 1 meter of linear height 
must (in the meter-ton-second system) be stated as 9.8 units. Thus, gravity 
performs one unit of work in ^- = 0.102 meters, so that one dynamic decimeter = 
0.102 meters, or one dynamic meter=1.02 common meters. For the reason just 
stated this relationship between dynamic and common linear measure is constant, 
no matter what the density of the water under study may be. 
It is not practical to make direct instrumental measurement of the pressure below 
the surface of the sea; this can be deduced only from measurements of the temper- 
ature and salinity, and these must be taken at predetermined depths. 
To calculate the thickness of a column of water that will exert any given pres- 
sure — say 100 units — the first step then is to establish the specific volume. This 
decreases in the sea with depth; consequently, to learn the mean specific volume it 
is necessary to determine the value not only for the top but also at the bottom of 
the column. If we could know before hand how deep it would be necessary to lower 
our instruments in order to do this— in other words, if the pressure unit of thickness 
could correspond to the ordinary linear measure — evidently the procedure would 
be vastly simplified. Strictly speaking, this is impossible because the linear value 
of this pressure unit must vary with the specific volume of the water. In practice, 
however, as Bjerknes and Sandstrom and Helland-Hansen (1903) have explained, this 
objection vanishes because the specific volume of the water varies only so very slightly 
with depth that the value will be given for the bottom of the chosen pressure column 
if the readings are taken within a few meters of it, whether shoaler or deeper. 
Consequently, if a pressure unit can be found, which shall nearly (even if not 
quite) correspond to the ordinary linear measure, we can learn the specific volume 
where the pressure is, say, 100 units, simply by measuring the specific volume at a 
depth of 100 meters. The selection of such a unit we owe to Bjerknes, who proposed 
the “ bar” to be equal to the pressure exerted by 10 dynamic meters (or 10.2 common 
meters) of fresh water, not under compression, and at the temperature of its maximum 
density. By the theorem stated on page 931, that pressure is the product of linear 
height, specific gravity, and acceleration of gravity, the “bar” will then equal 9.9 
meters of salt water 35 per mille in salinity and 0° in temperature, so that a decibar 
is virtually 1 meter of sea water. For the reasons just stated, if the salinity and 
temperature be taken at any chosen number of meters below the surface this will give 
the specific volume where the pressure is that same number of decibars. Thus, if in 
