[Figure 26], representing the average hourly densities for all stations on all nights of observation, demonstrates the over-all effect of these tendencies. Here the highest density is reached in the hour before midnight with indications of flights of great magnitude also in the hour preceding and the hour following the peak interval. The curve ascends somewhat more rapidly than it declines, which fact may or may not be significant. Since there is a great disproportion in the total volume of migration at different localities, the thought might be entertained that a few high magnitude stations, such as Tampico and Progreso, have imposed their own characteristics on the final graph. Fortunately, this idea may be tested by subjecting the data to a second treatment. If hourly densities are expressed as a percentage of the nightly peak, each set of observations, regardless of the number of birds involved, carries an equal weight in determining the character of the over-all curve. [Figure 27] shows that percentage analysis produces a curve almost identical with the preceding one. To be sure, all of the individual curves do not conform with the composite, either in shape or incidence of peak. The extent of this departure in the latter respect is evident from [Figure 28], showing the number of individual nightly station curves reaching a maximum peak in each hour interval. Even this graph demonstrates that maximum densities near midnight represent the typical condition.

Fig. 28. Incidence of maximum peak at the various hours of the night in 1948. "Number of stations" represents the total for all nights of the numbers of station peaks falling within a given hour.

The remarkable smoothness and consistency of the curves shown in Figures [26] and [27] seem to lead directly to the conclusion that the volume of night migration varies as a function of time. Admittedly other factors are potentially capable of influencing the number of birds passing a given station in a given hour. Among these are weather conditions, ecological patterns, and specific topographical features that might conceivably serve as preferred avenues of flight. However, if any of these considerations were alone responsible for changes in the numbers of birds seen in successive intervals, the distribution of the peak in time could be expected to be haphazard. For example, there is no reason to suppose that the cone of observation would come to lie over favored terrain at precisely the hour between eleven and twelve o'clock at so many widely separated stations. Neither could the topographical hypothesis explain the consistently ascending and descending pattern of the ordinates in [Figure 28]. This is not to say that other factors are without effect; they no doubt explain the divergencies in the time pattern exhibited by [Figure 28]. Nevertheless, the underlying circumstances are such that when many sets of data are merged these other influences are subordinated to the rise and fall of an evident time pattern. Stated in concrete terms, the time frequencies shown in the graphs suggest the following conclusions: first, nocturnal migrations are not a continuation of daytime flights; second, nearly all night migrants come to earth well before dawn; and, third, in each hour of the night up until eleven or twelve o'clock there is typically a progressive increase in the number of birds that have taken wing and in each of the hours thereafter there is a gradual decrease. Taken at its face value, the evidence seems to indicate that birds do not begin their night migrations en masse and remain on the wing until dawn and that in all probability most of them utilize less than half of the night.

Interestingly enough, the fact that the plot points in [Figure 26] lie nearly in line tempts one to a further conclusion. The curve behaves as an arithmetic progression, indicating that approximately the same number of birds are leaving the ground in each hour interval up to a point and that afterwards approximately the same number are descending within each hour. However, some of the components making up this curve, as later shown, are so aberrant in this regard that serious doubt is cast on the validity of this generalization.

Because the results of these time studies are unexpected and startling, I have sought to explore other alternative explanations and none appears to be tenable. For example, the notion that the varying flight speeds of birds might operate in some way to produce a cumulative effect as the night progresses must be rejected on close analysis. If birds of varying flight speeds are continuously and evenly distributed in space, a continuous and even flow would result all along their line of flight. If they are haphazardly distributed in space, a correspondingly haphazard density pattern would be expected.

Another explanation might be sought in the purely mathematical effects of the method itself. The computational procedure assumes that the effective area of the sample is extremely large when the moon is low, a condition that usually obtains in the early hours of the evening in the days surrounding the full moon. Actually no tests have yet been conducted to ascertain how far away a silhouette of a small bird can be seen as it passes before the moon. Consequently, it is possible that some birds are missed under these conditions and that the effective field of visibility is considerably smaller than the computed field of visibility. The tendency, therefore, may be to minimize the densities in such situations more than is justified. However, in many, if not most, cases, the plotting of the actual number of birds seen, devoid of any mathematical procedures, results in an ascending and descending curve.

Fig. 29. Various types of density-time curves. (A) Near typical, Ottumwa, April 22-23; (B) random fluctuation, Stillwater, April 23-24; (C) bimodal, Knoxville, April 22-23; (D) sustained peak, Ottumwa, April 21-22; (E) early peak, Oak Grove, May 21-22; (F) late peak, Memphis, April 23-24.

A third hypothesis proposes that all birds take wing at nearly the same time, gradually increase altitude until they reach the mid-point of their night's journey, and then begin a similarly slow descent. Since the field of observation of the telescope is conical, it is assumed that the higher the birds arise into the sky the more they increase their chances of being seen. According to this view, the changes in the density curve represent changes in the opportunity to see birds rather than an increase or decrease in the actual number of migrants in the air. Although measurements of flight altitude at various hours of the night have not been made in sufficient number to subject this idea to direct test, it is hardly worthy of serious consideration. The fallacy in the hypothesis is that the cone of observation itself would be rising with the rising birds so that actually the greatest proportion of birds flying would still be seen when the field of observation is in the supine position of early evening.