136 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



responding isobaric chart should be drawn; and the series of pressures, p x , p 2 , 

 . . . p u , for which the isobaric curves should be drawn. The problem is to find 

 the situations of these curves from the known situations of the level curves 

 D iy D 2 , . . . That is, we shall find the depth D x of a point on the isobaric surface 

 p, vertically below which we have the given pressure p n at the level surface D. 



In the first approximation we may consider the water as homogeneous along 

 every vertical, while its density may vary from vertical to vertical. Under this 

 supposition we have simple proportionality along every vertical between dynamic 

 depth and pressure, thus 



D - D i 



But now D and p represent corresponding pressures and depths in the sense 

 defined. Thus numerically we may write D instead of p, and consequently 



D 2 



W A = j n 



This formula is easily tabulated for all depths D at which we wish to draw isobaric 

 charts, and for all pressures p n which may occur at these depths. 



The numbers thus tabulated will, however, be slightly erroneous, because the 

 water between the isobaric and the corresponding level surface is not homogeneous, 

 there being a slight increase of density downward as a consequence of the com- 

 pression. The amount of this error is easily found in the case of sea-water of 

 35 / 00 salinity and o C. For in this case we have tabulated both the depths at 

 given pressures and the pressures in given depths (tables 7 h and 15 h). From 

 these we find the true D r , and thus the error involved in the use of the formula (a) 

 in the case of " normal " sea-water. From this the correction in all other cases is 

 easily found. For evidently the error will be proportional to the distance between 

 the isobaric and the corresponding level surface. This distance is zero for water of 

 unit density, and otherwise proportional to the excess of the density above unity. 



Table 24H of our Hydrographic Tables is calculated in this way by the formula 

 (a), with addition of the always very small corrections obtained in the manner 

 described from tables 7 h and 15 h. The practical use of the tables is easily seen 

 from the appended examples. 



Evidently these tables also enable us to solve the inverse problem to change 

 isobaric charts for given levels into topographic charts for the corresponding 

 isobaric surfaces. 



84. Vertical Sections. As we did in the case with the atmosphere, so we can 

 draw diagrams containing the profile curves either of isobaric and isosteric surfaces 

 or of equipotential and isopycnic surfaces. This will, however, present a practical 

 difficulty. Since the deviations of the different profile-curves from the horizontal 

 course are so minute, extreme exaggeration of the vertical dimensions in compari- 

 son with the horizontal would be required to make them visible. 



