metric depths obtained to the wire length is 

 utilized. Each of these methods is described 

 below. 



3-14 The Depth Difference (L-Z) Method 

 for Determining Accepted Depth. — The L-Z 

 method of determining accepted depth from a 

 given wire depth, L, thermometric depth, Z, 

 and surface wire angle affords a simplified 

 method for evaluating the validity of each 

 thermometric depth and interpolating for the 

 samples taken between these depths. Tlie curve 

 used in tlie evaluation and interpolation closely 

 approximates the actual pattern assumed by 

 the wire during the cast. Each cast taken must 

 be graphed separately. Graph paper of 10 x 10 

 to the K inch or millimeter may be used. The 

 Hydrographic Office uses millimeter graph 

 paper with tlie values for L and L-Z printed 

 thereon (fig. 3-5). The procedure used in 

 constructing the L-Z graph is as follows: 



1. On the vertical side of the graph, lay off 

 the wire depth, i, starting with zero at the 

 upper left corner for the shallow cast and 

 the upper right corner for the deep cast. Use 

 a convenient depth increment for each cast 

 which will allow sufficient space for the max- 

 imum wire depth sampled. 



2. Across the top of the graph lay off the 

 depth difference, L-Z, for each cast. The 

 increments need not be less than one per 

 millimeter and must not be greater than four 

 per millimeter to maintain accuracj'. It is 

 better to use larger graph paper than to reduce 

 the scale if conditions of high wire angle give 

 large Z-Z values. 



3. From the origin (upper left or right 

 corner) construct a line making an angle from 

 the vertical which represents one minus the 

 cosine (1-cosine) of the wire angle. This is 

 done as follows: 



a. From a table of trigonometric functions, 

 find the cosine of the measured wire angle. 

 For example, the cosine of the wire angle 27° 

 is 0.891. 



b. From 1.000 take the cosine. 1.000— 

 0.891=0.109. 



c. Multiply the remainder by 100. 

 0.109X100=10.9 



d. At wire depth of 100 meters plot the 

 value 10.9 as L-Z, and construct a line passing 

 through the origin and this point. This line 

 represents a wire angle of 27° for the scale 

 used. 



4. From the A-sheet tabulate the wire depth, 

 L, for each thermometric depth, Z, and compute 

 the depth difference, L-Z. The values shown 

 on the sample log sheet, figure 14-2, are: 



36 



Tkermo- Depth 

 metric difference 

 Wire depth (L) depth (Z) {L-Z) 



Cast I: 



200 190 10 



300 283 17 



400 385 15 



Cast II: 



600 538 62 



1200 1086 114 



2000 1853 147 



2.300 2153 147 



5. At the wire depths, plot the depth differ- 

 ence values for each cast. Select the best 

 points and draw a smooth curve through them 

 to the origin so that it becomes tangent with 

 the wire angle line. Owing to inaccuracies of 

 wire angle measurement (±5°) the curve may 

 not fair into the wire angle precisely. In 

 such case, plot lines representing angles 5° 

 greater and less than the one measured. The 

 curve must fall between these limits to be 

 valid. The L-Z curve must be studied for 

 errors. From the nature of the plotted curve 

 certain errors should be apparent; for example, 

 no value of L-Z can be negative, nor can the 

 curve have a negative slope because the wire 

 reaches a limiting shape at any depth when it 

 becomes vertical (Pollak, 1950). The curve 

 should be reasonably smooth. If the instru- 

 ment fails to give a correct thermometric depth, 

 the error will be evident and the value should 

 not be used when constructing the curve. 

 This situation appears with the 300-meter- 

 depth bottle in figure 3-5 where, if used, would 

 make a negative curve between 300 and 400 

 meters depth. 



6. From the curve, a new set of L-Z values 

 are taken to determine the accepted depths for 

 every Nansen bottle of the cast. These are 

 taken by interpolation along the arc of the 

 curve. At the wire depth for each sample, 

 take the L-Z from the curve and record this in 

 the Used column of the A-sheet, thus in- 

 dicating on the log sheet the values actually 

 used to determine the accepted depths. Next 

 subtract the Used L-Z from L to get the 

 accepted depth for each sample. Example: 



(L) - (L-Z) = Accepted depth. 

 1500—131 = 1,369 meters. 



3-15 The Depth-Ratio {ZIL) Method of 

 Determining Accepted Depths. — Another 

 method of determining accepted depths consists 

 of plotting the ratio of the thermometric depth 

 to wire depth, ZjL, against wire depth, L, 

 and drawing a smooth curve through these 

 points to the cosine of the wire angle at the 

 surface. This depth-ratio method is sometimes 

 referred to as the cosine method. The pro- 



H. O. 607 



