932 BULLETIN OF THE BUREAU OF FISHERIES 



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 9^^ = 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 estabhsh 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 ordy 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 simphfied. 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 



