Locating the position of a particular sector boundary now becomes a mere matter of substituting the values in the equation (1) and reducing. The computation of the north point for 11 to 12 P. M. in the sample set of data will serve as an example. Since the north point reckoned west from the south point is 180°, its [eta] has a value of 180°. [Illustration: FIG. 19. Method of plotting sector boundaries on the diagrammatic plots. The example employed is the 11:00 to 12:00 P. M. diagram of Figure 15.] tan [theta]_{Npt.} = tan (180° - [psi]_{0}) / cos Z_{0} Substituting values of [psi]_{0} found on the form (Figure 18): tan [theta]_{Npt.} = tan [180° - (-35°)] / cos 50° = tan 215° / cos 50° = .700 / .643 = 1.09 [theta]_{Npt.} = 47°28´ [Illustration: FIG. 20. Form for computing sector densities.] Four angles, one in each quadrant, have the same tangent value. Since, in processing spring data, we are dealing mainly with north sectors, it is convenient to choose the acute angle, in this instance 47° 28´. In doubtful cases, the value of the numerator of the equation (here 215°) applied as an angular measure from 6 o'clock will tell in which quadrant the projected boundary must fall. The fact that projection always draws the boundary closer to the 3-9 line serves as a further check on the computation. [Illustration: FIG. 21. Determinationn of the angle [alpha]] In the same manner, the projected position angles of all the pertinent sector boundaries for a given hour may be calculated and plotted in red pencil with a protractor on the circular diagrams of Figure 15. To avoid confusion in lines, the zones are not portrayed in the black and white reproduction of the sample plot form. They are shown, however, in the shaded enlargement (Figure 19) of the 11 to 12 P. M. diagram. The number of birds recorded for each sector may be ascertained by counting the number of tally marks between each pair of boundary lines and the information may be entered in the columns provided in the plot form (Figure 15). We are now prepared to turn to the form for "Computations of Sector Densities" (Figure 20), which systematizes the solution of the following equation: (220) 60/T (No. of Birds) (cos^2 Z_{0}) D = --------------------------------------- (2) (1 - sin^2 Z_{0} cos^2 [alpha])^0.5 [Illustration: FIG. 22. Facsimile of form summarizing sector densities. The totals at the bottom of each column give the station densities.] [Illustration: FIG. 23. Determination of Net Trend Density.]