FIELDS OF FORCE AND OF MASS IN THE SEA. 135 



sea's surface. This layer will then till out the deepenings where the physical sur- 

 face of the sea is lower than the ideal sea-level. This being done, we can transport 

 all verticals so as to begin at the ideal sea-level. The charts will then represent a 

 certain pressure along true level surfaces, namely, that which added to the 

 pressure along the ideal sea-level would give the true pressure. The indeter- 

 minate element, then, will be the pressure existing along the ideal sea-level under 

 the defined conditions. 



Whichever interpretation we choose for the isobaric charts, the indetermination 

 due to our ignorance of the true topography of physical sea-level will remain. But 

 quite independently of this, the charts giving the differences of pressure from one 

 surface to another will give a full representation of the distribution of density in the 

 standard layers. 



83. Change of Topographic into Isobaric Charts. An isobaric chart for the 

 depth of a certain number of dynamic meters will be exceedingly like the topo- 

 graphic chart of an isobaric surface of the same number of decibars. In the same 

 manner, the chart of pressure differences between two level surfaces will be 

 exceedingly like the chart of mutual topography of the two corresponding isobaric 

 surfaces. If, therefore, the topographic charts be drawn, we can derive the corre- 

 sponding isobaric charts from them, no independent calculation of pressures at 

 given depths being required. 



To change a chart of mutual topography of isobaric surfaces into one of pressure 

 differences between the corresponding levels, table 23 h, which changes densities 

 into corresponding specific volumes, can be used with satisfactory exactitude. 

 This is evident at once if we remember that the charts of mutual topography repre- 

 sent the average specific volume in the isobaric sheets, and those of pressure 

 differences the average density in the level sheets. If, therefore, the water were 

 under exactly the same pressure in the isobaric and the corresponding level sheets, 

 this table would change with perfect exactitude the required differences of pressure 

 between the level surfaces into the corresponding vertical distances between the 

 isobaric surfaces, or vice versa. Now, corresponding isobaric and level sheets are 

 not exactly at the same depth, and, therefore, not exactly under the same pressure. 

 But the difference is too small to produce any visible error on the charts drawn 

 according to the directions appended to the table. 



We then consider the problem of changing the topographic chart of an iso- 

 baric surface into the isobaric chart in the corresponding level surface. Of course, 

 the method of doing this will be independent of the question whether the given 

 chart represents true topograph)' or only relative topography referred to an initial 

 surface of an unknown topography. But in the latter case the resulting isobaric 

 chart will be one of corresponding incompleteness, as explained above (section 81). 

 For simplicity we make our developments as if always true topographies, true level 

 surfaces, and true pressures were under consideration. 



Given the isobaric surface of pressure p, represented topographically by the 

 level curves of depth, Z>,, D t , . . . D n ; further, the level D, in which the cor- 



