X and X are depths (feet) of a given isotherm at the be- 



i i + 1 



ginning and end of the ith distance (or time) interval along the 

 track; 7^_ is the depth difference (feet) . When the isotherm is 



falling, the difference is negative. 



From the speed of the ship and depth differences, approxi- 

 mate slopes can be obtained. At a speed of 6 knots, the ship trav- 

 eled 304 feet in each half-minute interval; therefore the dividing of 

 the depth differences by 304 feet gave the slope of the isothermal 

 surface in the direction of the ship's motion. This slope could also 

 be expressed by the angle having this slope for a tangent. 



From 1010 to 1440 consecutive observations of isotherm 

 depths were made on each sample section of Cruise 4. The dis- 

 tributions of depth changes and slopes for each selected isotherm 

 on each 8-12 hour section of the cruise are diagrammed as a 

 cumulative frequency curve of depth changes and slope angle in 

 Appendix A. 



Appendix A shows that half-minute depth changes as great as 

 plus or minus 30 feet were observed over a distance of 304 feet in 

 several of the isotherms. This corresponds to a vertical angle of 

 5°45'. On the other hand 58 per cent of all the adjacent half- 

 minute readings showed changes of less than one foot for the shal- 

 low isotherm, and 51 per cent for the deep isotherm. An example 

 of the S- shaped nature of the cumulative frequency curve (or per 

 cent of observations) is shown in figure 4. 



The change in depth of this 20 °C isotherm may be plus or 

 minus. In figure 4 the 25th and 75th percentile depth changes are 

 -1.3 and +1.4 feet; thus in 50 per cent of the cases the change is 

 less than about 1.35 feet (in absolute value) in a horizontal dis- 

 tance of 304 feet. The 15th and 85th percentile changes occur at 

 -2.3 and +2. 7 feet with 70 per cent of the data in this range. The 

 corresponding vertical angles are less than 0°15' (in absolute 

 value) for the central 50 per cent of the cases and less than 0°28' 

 for the central 70 per cent of the data. This example is a nearly 

 typical case since the median of the absolute values of 44, 000 data 

 samplings is 0°16', and the 70th percentile of the absolute values 

 of slope is 0°30'. 



13 



