SOLUTION OF THE HYDROSTATIC PROBLEM FOR THE SEA. 1 25 



a sea-pressure of a certain number of decibars. It it be convenient for the calcu- 

 lations we may consider it as taken from the depth expressed by the same number 

 of dynamic meters. 



As a consequence of these approximation rules, it remains indifferent whether 

 depths or pressures have been observed. The four forms of the problem met with 

 in the atmosphere (section 49) are, therefore, in the case of the sea, reduced prac- 

 tically to two, the calculation of the depth corresponding to a given pressure and 

 the calculation of the pressure at a given depth, it being immaterial whether the 

 temperature is registered as functions of pressure or of depth. 



77. Calculation of the Anomalies of Depth and of Pressure. These approxi- 

 mation rules being accepted, the calculation of the integrals (a) and (b) can be 

 made immediately. Taking first the anomaly of depth of the isobaric surfaces, 

 we remember (section 27) that we can write for the anomaly 8 of the specific 

 volume 



8 = 8+8+8+8 +8 T +8 r 



the quantities S s , S r , S, T , 8, p , S T) S^ being tabulated in tables 9H, 10 h, iih, 12 h, 13 h, 

 and 14 H,- respectively, for all occurring values of temperature, salinity, and pressure. 

 By means of these tables and the observed temperatures and salinities we find the 

 values of these quantities and by adding them the values of 8 corresponding to a 

 set of known pressures. Then the value of the integral (z), section 75, is found by 

 a regular process of integration; i. e., we take the average of the successive values of 

 8, multiply by the corresponding difference of pressure, and form the sum from the 

 pressure o at sea-level down to the pressure p. This sum represents the anomaly 

 AD of the dynamic depth of the isobaric surface of pressure p. 



We find the anomaly of pressure Ap in the given dynamic depth D in exactly 

 the same way, writing 



e = . + e T + s r + e,z> + ^d + sT z> 



using tables 17H, 18 h, 19 h, 20 h, 21 h, and 22 h and performing the integration in 

 the same regular way. 



The systematic performance of the calculation is easily understood by examina- 

 tion of the examples worked out below. 



Adding the anomaly of depth AD to the normal value D 35:0)P we get the equi- 

 librium relation in form of depth for a given pressure. Adding the anomalies of 

 specific volume 8 to the normal values a^ aiP we get the actual specific volumes a 

 for given values of the pressure, i. e., the equilibrium relation between pressure 

 and specific volume. 



In the same way the addition of the anomalies of pressure Ap to the normal 

 values _^ 36|0 ,i) gives the equilibrium relation in form of pressures in given dynamic 

 depths, and the addition of the anomalies of density s to the normal densities p 3s ,o,j> 

 gives the actual densities p at given depths, i. e., the equilibrium relation between 

 density and depth. 



