conclusions suggested are of a provisional nature. Yet, compared with
similar procedures in its field, flight density study is a highly
objective method, and a relatively reliable one. In no other type of
bird census has there ever been so near a certainty of recording _all_
of the individuals in a specified space, so nearly independently of
the subjective interpretations of the observer. The best assurance of
the essential soundness of the flight density computations lies in the
coherent results and the orderly patterns that already emerge from the
analyses presented in Part II.
B. OBSERVATIONAL PROCEDURE AND THE PROCESSING OF DATA
At least two people are required to operate an observation
station--one to observe, the other to record the results. They should
exchange duties every hour to avoid undue eye fatigue. Additional
personnel are desirable so that the night can be divided into shifts.
Essential materials and equipment include: (1) a small telescope;
(2) a tripod with pan-tilt or turret head and a mounting cradle;
(3) data sheets similar to the one illustrated in Figure 12. Bausch
and Lomb or Argus spotting scopes (19.5 x) and astronomical telescopes
up to 30- or 40-power are ideal. Instruments of higher magnification
are subject to vibration, unless very firmly mounted, and lead to
difficulties in following the progress of the moon, unless powered by
clockwork. Cradles usually have to be devised. An adjustable lawn chair
is an important factor in comfort in latitudes where the moon reaches
a point high overhead.
[Illustration: FIG. 12. Facsimile of form used to record
data in the field. One sheet of the actual observations
obtained at Progreso, Yucatan, on April 24-25, 1948, is
reproduced here. The remainder of this set of data, which is
to be used throughout the demonstration of procedures, is
shown in Table 1.]
[Transcription of Figure 12's Data]
ORIGINAL DATA SHEET
DATE 24-25 April 1948 LOCALITY Progreso, Yucatan
OBSERVERS Harold Harry; George H. Lowery
WEATHER Moderate to strong "trade" winds along coast, slightly
N of E. Moon emerged above low cloud bank at 8:26.
INSTRUMENT B. & L. 19.5 Spotting Scope; image erect
REMARKS Observation station located 1 mile from land, over Gulf of
Mexico, at end of new Progreso wharf
-----------+------+-------+----------------------------------------
TIME | IN | OUT | REMARKS
-----------+------+-------+----------------------------------------
C.S.T | | |
8:26 | -- | -- | observations begin; H.H. observing
50 | 4:30 | 9 | slow; small
56 | 3 | 10 | medium size
9:00 | 2 | 10:30 | very small
11 | 5 | 9:30 | moderately fast
25 | 5 | 10 | very small; rather slow
26 | 3 | 11 | " "
36 | 5 | 10 | medium size
40 | 3 | 10 | " "
43 | 5:30 | 9 | " "
46 | 3:30 | 10 | small
56 | 4:30 | 10 | medium size
9:58-10:00 | -- | -- | time out to change observers; G.L. at
10:05 | 4:30 | 11:30 | scope small
06 | 3 | 11 |
12 | 5 | 8 | very small
25 | 5 | 12 | very fast; small
30 | 4 | 10 | small
32 | 4 | 11 | "
32 | 2 | 11 | "
33 | 5 | 11 | "
33 | 4 | 1 | "
33 | 5:30 | 11 | "
35 | 4:30 | 10 | swallow-like
36 | 5 | 1:30 |
As much detail as possible should be entered in the space provided at
the top of the data sheet. Information on the weather should include
temperature, description of cloud cover, if any, and the direction
and apparent speed of surface winds. Care should be taken to specify
whether the telescope used has an erect or inverted image. The entry
under "Remarks" in the heading should describe the location of the
observation station with respect to watercourses, habitations, and
prominent terrain features.
The starting time is noted at the top of the "Time" column, and the
observer begins the watch for birds. He must keep the disc of the moon
under unrelenting scrutiny all the while he is at the telescope. When
interruptions do occur as a result of changing positions with the
recorder, re-adjustments of the telescope, or the disappearance of the
moon behind clouds, the exact duration of the "time out" must be set
down.
[Illustration: FIG. 13. The identification of cooerdinates.
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.]
[Illustration: 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, Yucatan (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 cooerdinates 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 cooerdinate. 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 cooerdinates 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.
[Illustration: FIG. 15. Standard form for plotting the
apparent paths of flight. On these diagrams the original
cooerdinates, exemplified by Figure 14, have been moved to
center. In practice the sector boundaries are drawn over the
circles in red pencil, as shown by the white lines in Figure
19, making it possible to count the number of birds falling
within each zone. These numbers are then tallied in the
columns at the lower right of each hourly diagram.]
TABLE 1.--Continuation of Data in Figure 12, Showing Time
and Readings of Observations on 24-25 April 1948,
Progreso, Yucatan
==============================+==============================
Time In Out | Time In Out
------------------------------+------------------------------
10:37-10:41 Time out | 11:15 8 9:30
10:45 5:30 10 | 11:16 4 11
6 9 | 5 9
5:30 10 | 11:17 5 11:30
10:46 6 8 | 11:18 5 12
3:30 11 | 6 11:30
5 12 | 11:19 5:30 11:30
10:47 3:15 1 | 11:20 6 10
6 8:30 | 3 12
5:45 11:45 | 5 12
5 10 | 11:21 5:45 11
10:48 6 9:45 | 5 11
10:50 5:30 11 | 11:23 5 12
10:51 4 11 | 11:25 5 10:30
10:52 4 2 | 6 11
5:30 11 | 6 12
10:53 5:30 11:30 | 11:27 6 10
5 11 | 11:28 6 11:30
10:55 5 12 | 5:30 12:30
5 11 | 11:29 6 11:30
10:56 6 10 | 4 12
10:58 4:30 11:30 | 6:30 10:30
5:45 11:45 | 6 11
10:59 6:30 10:30 | 11:30 3 10
11:00 3:30 12 | (2 birds at once)
6:30 11 | 11:31 5 10:30
(2 birds at once) | 5:30 10:30
11:03 6 11 | 11:32 6 11:30
11:04 3 12 | 11:33 7:30 9:30
5 12 | 4 10:30
11:05 6 10 | 6 11:30
5 11 | 8 9:30
11:06 6 10:30 | 11:35 7 10
11:07 3 10 | 4:30 1
11:08 6 11 | 11:38 6:30 11
11:10 7 9:30 | 11:40 5:30 12
11:11 5 9:15 | 11:42 4 2
11:13 5 12 | 5 12
11:14 6:30 10 | 6 10
5:30 1 | 4 2
4 12 | 5 12
------------------------------+------------------------------
Table 1.--_Concluded_
==============================+==============================
Time In Out | Time In Out
------------------------------+------------------------------
11:44 8 9:30 | 8 10:15
7 11 | 12:16 3:30 1:30
6 10 | 8 11
11:45 5 12 | 12:23 7 1:30
6 10:30 | 6 12:30
5:45 11 | 12:36 8 11
4 12 | 12:37 7:30 1
11:46 7 11 | 12:38 7 12:30
6 12 | 12:40 8 1
11:47 8 10 | 12:45 7:30 1
11:48 6 10 | 12:47 5:30 1
11:49 6:30 10:30 | 12:48 7 1
11:51 8 10 | 12:52 5:30 1:30
8 10 | 12:54-12:55 Time out
8 10 | 12:56 8 10:45
8 10 | 12:58 5:30 1:30
6 10 | 7 1:30
8 10 | 7 2
6 11 | 12:59 5 3
7 12 | 1:00-1:30 Time out
11:52 5 1 | 1:37 8 12
11:54 7 11 | 1:38 8 12
6 12:30 | 1:48 7 1
11:55 5 12 | 7 1
11:56 7 10 | 1:51 5:30 11
5 12 | 1:57 8 1
11:58 8 11 | 2:07 7 2
11:59 5:30 12 | 2:09 9 12
12:00-12:03 Time out | 2:10 8 1
12:03 5:30 11:30 | 2:17 9 12
12:04 8 11 | 2:21 6 2
12:07 6 12:30 | 2:30 5:30 3:15
7:30 1 | 2:32 8 2
12:08 5 10:30 | 2:46 7 1
12:09 5:30 1 | 3:36 9 2
7:30 2 | 3:39 8:30 2
12:10 6:30 12:45 | 3:45 6 4
12:13 8 11 | 3:55 9 2
12:14 7 1 | 4:00 8 3
12:15 7 12:30 | 4:03 9 2
7:15 1:30 | 4:30 Closed station
------------------------------+------------------------------
We now have a concise picture of the apparent pathways of all the
birds recorded in each hour of observation. But the cooerdinates do not
have the same meaning as readings of a horizontal clock on the earth's
surface, placed in relation to the points of the compass. They are
merely projections of the birds' courses. An equation is available for
reversing the effect of projection and discovering the true directions
of flight. This formula, requiring thirty-five separate computations
for the pathways reproduced in Figure 12 alone, is far too-consuming
for the handling of large quantities of data. A simpler procedure is
to divide the compass into sectors and, with the aid of a reverse
equation, to draw in the projected boundaries of these divisions on
the circular diagrams of the moon. A standardized set of sectors, each
22-1/2 deg. wide and bounded by points of the compass, has been evolved
for this purpose. They are identified as shown in Figure 16. The zones
north of the east-west line are known as the North, or N, Sectors, as
N_{1}, N_{2}, N_{3}, etc. Each zone south of the east-west line bears
the same number as the sector opposite, but is distinguished by the
designation S.
[Illustration: FIG. 16. Standard sectors for designating
flight trends. Each zone covers a span of 22-1/2 deg.. The N_{6}
and N_{8}, the N_{5} and N_{7}, and their south complements,
where usually few birds are represented, can be combined and
identified as N_{6-8} and N_{5-7}, 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 [theta] = tan ([eta] - [psi]) / cos Z_{0} (1)
[Illustration: FIG. 17. The meaning of symbols used in the
direction formula.]
The symbols have these meanings:
[theta] 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).
[eta] is the compass direction of the sector boundary expressed in
degrees reckoned west from the south point (Figure 17B).
Z_{0} 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).
[psi] 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).
[Illustration: FIG. 18. Form used in the computation of the
zenith distance and azimuth of the moon.]
The angle [eta] for any sector boundary can be found immediately by
measuring its position in the diagram (Figure 16). The form (Figure 18)
for the "Computation of Zenith Distance and Azimuth of the Moon"
illustrates the steps in calculating the values of Z_{0} and [psi]_{0}.
From the American Air Almanac (Anonymous, 1945-1948), issued annually
by the U. S. Naval Observatory in three volumes, each covering four
months of the year, the Greenwich Hour Angle (GHA) and the declination
of the moon may be obtained for any ten-minute interval of the date in
question. The Local Hour Angle (LHA) of the observation station is
determined by subtracting the longitude of the station from the GHA.
Reference is then made to the "Tables of Computed Altitude and Azimuth,"
published by the U. S. Navy Department, Hydrographic Office (Anonymous,
1936-1941), and better known as the "H.O. 214," to locate the altitude
and azimuth of the moon at the particular station for the middle of the
hour during which the observations were made. The tables employ three
variables--the latitude of the locality measured to the nearest degree,
the LHA as determined above, and the declination of the moon measured
to the nearest 30 minutes of arc. Interpolations can be made, but this
exactness is not required. When the latitude of the observation
station is in the northern hemisphere, the H.O. 214 tables entitled
"Declinations Contrary Name to Latitude" are used with south
declinations of the moon, and the tables "Declinations Same Name as
Latitude," with north declinations. In the sample shown in Figure 15,
the declination of the moon at 11:30 P. M., midway through the 11 to
12 o'clock interval, was S 20 deg. 22'. Since the latitude of Progreso,
Yucatan is N 21 deg. 17', the "Contrary Name" tables apply to this hour.
Because the H.O. 214 expresses the vertical position of the moon in
terms of its altitude, instead of its zenith distance, a conversion is
required. The former is the number of arc degrees from the horizon to
the moon's center; therefore Z_{0} is readily obtained by subtracting
the altitude from 90 deg.. Moreover, the azimuth given in the H.O. 214 is
measured on a 360 deg. scale from the north point, whereas the azimuth
used here ([psi]_{0}) is measured 180 deg. in either direction from the south
point, negative values to the east, positive values to the west. I
have designated the azimuth of the tables as Az_{n} and obtained the
desired azimuth ([psi]_{0}) by subtracting 180 deg. from Az_{n}. The sign
of [psi]_{0} may be either positive or negative, depending on whether
or not the moon has reached its zenith and hence the meridian of the
observer. When the GHA is greater than the local longitude (that is,
the longitude of the observation station), the azimuth is positive.
When the GHA is less than the local longitude, the azimuth is
negative.
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 deg., its [eta] has a value of
180 deg..
[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 deg. - [psi]_{0}) / cos Z_{0}
Substituting values of [psi]_{0} found on the form (Figure 18):
tan [theta]_{Npt.} = tan [180 deg. - (-35 deg.)] / cos 50 deg.
= tan 215 deg. / cos 50 deg. = .700 / .643 = 1.09
[theta]_{Npt.} = 47 deg.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 deg. 28'. In doubtful cases, the value of the numerator of the equation
(here 215 deg.) 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.]
Some of the symbols and factors, appearing here for the first time,
require brief explanation. D stands for Sector Density. The constant,
220, is the reciprocal of the quotient of the angular diameter of the
moon divided by 2. T is Time In, arrived at by subtracting the total
number of minutes of time out, as noted for each hour on the original
data sheets, from 60. "No. of Birds" is the number for the sector and
hour in question as just determined on the plot form. The symbol
[alpha] represents the angle between the mid-line of the sector and
the azimuth line of the moon. The quantity is found by the equation:
[alpha] = 180 deg. - [eta] + [psi]_{0} (3)
The symbol [eta] here represents the position of the mid-line of the
sector expressed in terms of its 360 deg. compass reading. This equation
is illustrated in Figure 21. The values of [eta] for various zones are
given in the upper right-hand corner of the form (Figure 20). The
subsequent reductions of the equations, as they appear in the figure
for four zones, are self-explanatory. The end result, representing the
sector density, is entered in the rectangular box provided.
After all the sector densities have been computed, they are tabulated
on a form for the "Summary of Sector Densities" (Figure 22). By
totaling each vertical column, sums are obtained, expressing the
Station Density or Station Magnitude for each hour.
An informative way of depicting the densities in each zone is to plot
them as lines of thrust, as in Figure 23. Each sector is represented
by the directional slant of its mid-line drawn to a length expressing
the flight density per zone on some chosen scale, such as 100 birds
per millimeter. Standard methods of vector analysis are then applied
to find the vector resultant. This is done by considering the first
two thrust lines as two sides of an imaginary parallelogram and using
a drawing compass to draw intersecting arcs locating the position of
the missing corner. In the same way, the third vector is combined
with the invisible resultant whose distal end is represented by the
intersection of the first two arcs. The process is repeated
successively with each vector until all have been taken into
consideration. The final intersection of arcs defines the length and
slant of the Vector Resultant, whose magnitude expresses the Net Trend
Density in terms of the original scale.
The final step in the processing of a set of observations is to plot
on graph paper the nightly station density curve as illustrated by
Figure 24.
[Illustration: FIG. 24. Nightly station density curve at
Progreso, Yucatan, on April 24-25, 1948.]