PRINCIPLES OF HYDROSTATICS. 47 



(II) Principle of the Unit-Sheets. As is immediately seen, equation (a), 

 section 35, takes the changed form 



() A - A = - P m (4>2 ~ <M 



and thus for an equipotential unit-sheet, <f> 2 < being equal to unity, 



(*) A -A --ft. 



Therefore: 



/ Me s/a/g of equilibrium the number representing the mean density of the 

 fluid in an equipotential unit-sheet also represents the number of isobaric 

 unit-sheets contained in the equipotential unit-sheet. 



39. Determination of the Pressures at Given Heights or Depths. The 



principle of the unit-sheets in its first form led to the method of barometric 

 measurements of heights or of manometric measurements of depths (section 36). 

 In its second form it leads to the solution of the inverse problem, namely, the 

 determination of the pressure at given heights or depths. The m.t.s. isobaric unit- 

 sheet represents the difference of pressure of 1 centibar. The number of such 

 sheets contained in the equipotential unit-sheet therefore gives the difference of 

 pressure in centibars between the surfaces limiting the equipotential unit-sheet. 

 Adding these differences of pressure from level surface to level surface, we can 

 determine the pressure at any level if it be known in an initial level. Performing it 

 practically we may as above make use of other units of pressure and of gravity 

 potential than those of the m.t.s. system. 



Taking the same examples as above, there will be no difference so long as we 

 consider pure incompressible water at maximum of density. The density being 

 unity, the increase of pressure for each dynamic meter of depth will be 1 decibar, 

 and the number representing the depth in dynamic meters will represent at the 

 same time the sea-pressure expressed in decibars. As a second example we shall 

 determine the pressure in given depths in sea-water of 35 /oo salinity and oC. 

 The hydrographical table 16 h gives the density of this water at all depths for 

 intervals of 1 dynamic decameter. Forming the mean value of two and two suc- 

 cessive numbers in this table, we get the average density of the sea-water in 

 equipotential unit-sheets of 1 dynamic decameter, i. e., the increase of pressure in 

 bars from level surface to level surface. Adding these increases of pressure from 

 sea-level downwards, we get the sea-pressure expressed in bars at all dynamic 

 depths for intervals of 1 dynamic decameter. Then, on returning to the smaller 

 units, the dynamic meter and decibar, these pressures are given in table 15 h in 

 our Hydrographic Tables. The equilibrium relation between dynamic depth and 

 pressure contained in this table is intrinsically the same as that contained in table 

 7 H. Graphically we arrive at the same representation from both tables, given 

 by the first vertical of fig. 1. The third vertical represents the relations between 

 dynamic depth and density contained in table 16 h. 



40. Integral Forms of the Equation of Equilibrium. In equations (c), sec- 

 tion 34, and (c), section 37, the increase of potential d<f> and the increase of pressure 



