Fig. 16. Standard sectors for designating flight trends. Each zone covers a span of 22½°. The N6 and N8, the N5 and N7, and their south complements, where usually few birds are represented, can be combined and identified as N6-8 and N5-7, etc.
Several methods may be used to find the projection of the sector boundaries on the plot diagrams of [Figure 15]. Time may be saved by reference to graphic tables, too lengthy for reproduction here, showing the projected reading in degrees for every boundary, at every position of the moon; and a mechanical device, designed by C. M. Arney, duplicating the conditions of the original projection, speeds up the work even further. Both methods are based on the principle of the following formula:
| tan θ = tan (η - ψ) / cos Z0 | (1) |
Fig. 17. The meaning of symbols used in the direction formula.
The symbols have these meanings:
θ is the position angle of the sector boundary on the lunar clock, with positive values measured counterclockwise from 12 o'clock, negative angles clockwise ([Figure 17A]).
η is the compass direction of the sector boundary expressed in degrees reckoned west from the south point ([Figure 17B]).
Z0 is the zenith distance of the moon's center midway through the hour of observation, that is, at the half hour. It represents the number of degrees of arc between the center of the moon and a point directly over the observer's head ([Figure 17C]).
ψ is the azimuth of the moon midway through the hour of observation, measured from the south point, positive values to the west, negative values to the east ([Figure 17D]).