The square root of the mean of the squares of corrected differences was then 

 calculated to provide an index of comparison for corresponding data aggregates. 

 The root mean square values obtained ranged from about .09° to .15° Fahrenheit 

 for the samples analyzed. 



Corresponding data aggregates were then computer processed for 

 regression point sets using different values for ST. An index of comparison 

 was computed for corresponding regression sets, based upon differences 

 between interpolated temperatures at corresponding five meter intervals 

 corrected for trace slope. It was reasoned that if it is appropriate to fit 

 straight line segments to a digital BT, then for some values of 8T the index 

 of comparison would be less than the index of comparison for the original data 

 aggregates. Moreover, the index of comparison would tend to diminish to a 

 minimum for values of ST representing the thickness of the stylus trace. It was 

 found that for values of ST in the neighborhood 0.2° Fahrenheit, the differences 

 between the regression sets were somewhat less than the differences between the 

 original data aggregates. For values of ST in the neighborhood 0,3° Fahrenheit, 

 the index of comparison for corresponding regression sets ranged in value for 

 about 0.06°, a minimum for the data samples and ST values tested, to .15° 

 Fahrenheit. The most conclusive results were pbtained for profiles with smooth 

 gradients and slight hysteresis (Figure 8) and the least conclusive results were 

 obtained for irregular profiles (Figure 9). On the basis of these experiments 

 it was concluded that the most appropriate choice for ST was probably about 

 0.3° Fahrenheit (0.16° Celsius), or about .015 inches on the plane of the 

 standard scale bathythermograph, 



G. Measure of "Appropriateness of Fit" 



It was considered advisable to provide a measure of the appropriateness 

 of fit of a regression line over the interval of regression. Accordingly, a 

 subroutine was used in the regression program to calculate the root mean of 

 the squares of differences between temperature data in the interval between 

 regression points and interpolated temperature values at corresponding depths 

 on the regression line. These values were not corrected for the slope of the 

 line. It was assumed that the user of the BT data would be more interested in 

 estimating the reliability of temperatures in a profile than the probable departure 

 of a point from a straight line on the bathythermogram. It follows that the RMS 

 values for the profile interval between adjacent regression points will tend to 

 increase with increasing slope angles and decrease to a minimum for a vertical 

 trace (slope angle zero). If the user is interested in relating these RMS values 

 to departures from a straight line in the plane of the bathythermogram he may 

 use the relationship: 



14 



