Fig. 13. The identification of coördinates. These diagrams illustrate how the moon may be envisioned as a clockface, constantly oriented with six o'clock nearest the horizon and completely independent of the rotation of the moon's topographic features.
Fig. 14. The apparent pathways of the birds seen in one hour. The observations are those recorded in the 11:00-12:00 P. M. interval on April 24-25, 1948, at Progreso, Yucatán (see [Table 1]).
Whenever a bird is seen, the exact time must be noted, together with its apparent pathway on the moon. These apparent pathways can be designated in a simple manner. The observer envisions the disc of the moon as the face of a clock, with twelve equally spaced points on the circumference marking the hours ([Figure 13]). He calls the bottommost point 6 o'clock and the topmost, 12. The intervals in between are numbered accordingly. As this lunar clockface moves across the sky, it remains oriented in such a way that 6 o'clock continues to be the point nearest the horizon, unless the moon reaches a position directly overhead. Then, all points along the circumference are equidistant from the horizon, and the previous definition of clock values ceases to have meaning. This situation is rarely encountered in the northern hemisphere during the seasons of migration, except in extreme southern latitudes. It is one that has never actually been dealt with in the course of this study. But, should the problem arise, it would probably be feasible to orient the clock during this interval with respect to the points of the compass, calling the south point 6 o'clock.
When a bird appears in front of the moon, the observer identifies its entry and departure points along the rim of the moon with respect to the nearest half hour on the imaginary clock and informs the recorder. In the case of the bird shown in [Figure 13], he would simply call out, "5 to 10:30." The recorder would enter "5" in the "In" column on the data sheet (see [Figure 12]) and 10:30 in the "Out" column. Other comment, offered by the observer and added in the remarks column, may concern the size of the image, its speed, distinctness, and possible identity. Any deviation of the pathway from a straight line should be described. This information has no bearing on subsequent mathematical procedure, except as it helps to eliminate objects other than birds from computation.
The first step in processing a set of data so obtained is to blue-pencil all entries that, judged by the accompanying remarks, relate to extraneous objects such as insects or bats. Next, horizontal lines are drawn across the data sheets marking the beginning and the end of each even hour of observation, as 8 P. M.-9 P. M., 9 P. M.-10 P. M., etc. The coördinates of the birds in each one-hour interval may now be plotted on separate diagrammatic clockfaces, just as they appeared on the moon. Tick marks are added to each line to indicate the number of birds occurring along the same coördinate. The slant of the tick marks distinguishes the points of departure from the points of entry. [Figure 14] shows the plot for the 11 P. M.-12 P. M. observations reproduced in [Table 1]. The standard form, illustrated in [Figure 15], includes four such diagrams.
Applying the self-evident principle that all pathways with the same slant represent the same direction, we may further consolidate the plots by shifting all coördinates to the corresponding lines passing through the center of the circle, as in [Figure 15]. To illustrate, the 6 to 8, 5 to 9, 3 to 11, and 2 to 12 pathways all combine on the 4 to 10 line. Experienced computers eliminate a step by directly plotting the pathways through center, using a transparent plastic straightedge ruled off in parallel lines.
