Produced by Chris Curnow, Tom Cosmas, Joseph Cooper, The Internet Archive for some images and the Online Distributed Proofreading Team at http://www.pgdp.net A Quantitative Study of the Nocturnal Migration of Birds BY GEORGE H. LOWERY, JR. University of Kansas Publications Museum of Natural History Volume 3, No. 2, pp. 361-472, 47 figures in text June 29, 1951 University of Kansas LAWRENCE 1951 UNIVERSITY OF KANSAS PUBLICATIONS, MUSEUM OF NATURAL HISTORY Editors: E. Raymond Hall, Chairman; A. Byron Leonard, Edward H. Taylor, Robert W. Wilson UNIVERSITY OF KANSAS Lawrence, Kansas PRINTED BY FERD VOILAND, JR., STATE PRINTER TOPEKA, KANSAS 1951 [Union Label] 23-1020 A Quantitative Study of the Nocturnal Migration of Birds By GEORGE H. LOWERY, JR. CONTENTS Page INTRODUCTION 365 ACKNOWLEDGMENTS 367 PART I. FLIGHT DENSITIES AND THEIR DETERMINATION 370 Lunar Observations of Birds and the Flight Density Concept 370 Observational Procedure and the Processing of Data 390 PART II. THE NATURE OF NOCTURNAL MIGRATION 408 Horizontal Distribution of Birds on Narrow Fronts 409 Density as a Function of the Hour of the Night 413 Migration in Relation to Topography 424 Geographical Factors and the Continental Density Pattern 432 Migration and Meteorological Conditions 453 CONCLUSIONS 469 LITERATURE CITED 470 LIST OF FIGURES Figure Page 1. The field of observation as it appears to the observer 374 2. Determination of diameter of cone at any point 375 3. Temporal change in size of the field of observation 376 4. Migration at Ottumwa, Iowa 377 5. Geographic variation in size of cone of observation 378 6. The problem of sampling migrating birds 380 7. The sampling effect of a square 381 8. Rectangular samples of square areas 382 9. The effect of vertical components in bird flight 383 10. The interceptory potential of slanting lines 384 11. Theoretical possibilities of vertical distribution 388 12. Facsimile of form used to record data in the field 391 13. The identification of co-ordinates 392 14. The apparent pathways of birds seen in one hour 393 15. Standard form for plotting the apparent paths of flight 395 16. Standard sectors for designating flight trends 398 17. The meaning of symbols used in the direction formula 399 18. Form used to compute zenith distance and azimuth of the moon 400 19. Plotting sector boundaries on diagrammatic plots 402 20. Form to compute sector densities 403 21. Determination of the angle [alpha] 404 22. Facsimile of form summarizing sector densities 405 23. Determination of net trend density 406 24. Nightly station density curve at Progreso, Yucatán 407 25. Positions of the cone of observation at Tampico, Tamps 411 26. Average hourly station densities in spring of 1948 414 27. Hourly station densities plotted as a percentage of peak 415 28. Incidence of maximum peak at the various hours of the night in 1948 416 29. Various types of density-time curves 418 30. Density-time curves on various nights at Baton Rouge 422 31. Directional components in the flight at Tampico, Tamps 428 32. Hourly station density curve at Tampico, Tamps 429 33. The nightly net trend of migrations at three stations in 1948 431 34. Stations at which telescopic observations were made in 1948 437 35. Positions of the cone of observation at Progreso, Yucatán 443 36. Hourly station density curve at Progreso, Yucatán 444 37. Sector density representation on two nights at Rosedale, Miss. 451 38. Over-all sector vectors at major stations in spring of 1948 455 39. Over-all net trend of flight directions shown in Figure 38 456 40. Comparison of flight trends and surface weather conditions on April 22-23, 1948 460 41. Winds aloft at 10:00 P. M. on April 22 (CST) 461 42. Comparison of flight trends and surface weather conditions on April 23-24, 1948 462 43. Winds aloft at 10:00 P. M. on April 23 (CST) 463 44. Comparison of flight trends and surface weather conditions on April 24-25, 1948 464 45. Winds aloft at 10:00 P. M. on April 24 (CST) 465 46. Comparison of flight trends and surface weather conditions on May 21-22, 1948 466 47. Winds aloft at 10:00 P. M. on May 21 (CST) 467 INTRODUCTION The nocturnal migration of birds is a phenomenon that long has intrigued zoologists the world over. Yet, despite this universal interest, most of the fundamental aspects of the problem remain shrouded in uncertainty and conjecture. Bird migration for the most part, whether it be by day or by night, is an unseen movement. That night migrations occur at all is a conclusion derived from evidence that is more often circumstantial than it is direct. During one day in the field we may discover hundreds of transients, whereas, on the succeeding day, in the same situation, we may find few or none of the same species present. On cloudy nights we hear the call notes of birds, presumably passing overhead in the seasonal direction of migration. And on stormy nights birds strike lighthouses, towers, and other tall obstructions. Facts such as these are indisputable evidences that migration is taking place, but they provide little basis for evaluating the flights in terms of magnitude or direction. Many of the resulting uncertainties surrounding the nocturnal migration of birds have a quantitative aspect; their resolution hinges on how many birds do one thing and how many do another. If we knew, for instance, how many birds are usually flying between 2 and 3 A. M. and how this number compares with other one-hour intervals in the night, we would be in a position to judge to what extent night flight is sustained from dusk to dawn. If we could measure the number of birds passing selected points of observation, we could find out whether such migration in general proceeds more or less uniformly on a broad front or whether it follows certain favored channels or flyways. This in turn might give us a clearer insight into the nature of the orienting mechanism and the extent to which it depends on visual clues. And, if we had some valid way of estimating the number of birds on the wing under varying weather conditions, we might be able to understand better the nature and development of migration waves so familiar to field ornithologists. These are just random examples suggesting some of the results that may be achieved in a broad field of inquiry that is still virtually untouched--the quantitative study of migratory flights. This paper is a venture into that field. It seeks to evaluate on a more factual basis the traditional ideas regarding these and similar problems, that have been developed largely from circumstantial criteria. It is primarily, therefore, a study of comparative quantities or volumes of migration--or what may be conveniently called flight densities, if this term be understood to mean simply the number of birds passing through a given space in a given interval of time. In the present study, the basic data permitting the numerical expression of such migration rates from many localities under many different sets of circumstances were obtained by a simple method. When a small telescope, mounted on a tripod, is focused on the moon, the birds that pass before the moon's disc may be seen and counted, and their apparent pathways recorded in terms of coördinates. In bare outline, this approach to the problem is by no means new. Ornithologists and astronomers alike have recorded the numbers of birds seen against the moon in stated periods of time (Scott, 1881a and 1881b; Chapman, 1888; Libby, 1889; West, 1896; Very, 1897; Winkenwerder, 1902a and 1902b; Stebbins, 1906; Carpenter, 1906). Unfortunately, as interesting as these observations are, they furnish almost no basis for important generalizations. Most of them lack entirely the standardization of method and the continuity that would make meaningful comparisons possible. Of all these men, Winkenwerder appears to have been the only one to follow up an initial one or two nights of observation with anything approaching an organized program, capable of leading to broad conclusions. And even he was content merely to reproduce most of his original data without correlation or comment and without making clear whether he fully grasped the technical difficulties that must be overcome in order to estimate the important flight direction factor accurately. The present study was begun in 1945, and early results obtained were used briefly in a paper dealing with the trans-Gulf migration of birds (Lowery, 1946). Since that time the volume of field data, as well as the methods by which they can be analyzed, has been greatly expanded. In the spring of 1948, through the cooperation and collaboration of a large number of ornithologists and astronomers, the work was placed on a continent-wide basis. At more than thirty stations (Figure 34, page 437) on the North American continent, from Yucatán to Ontario, and from California to South Carolina, observers trained telescopes simultaneously on the moon and counted the birds they saw passing before its disc. Most of the stations were in operation for several nights in the full moon periods of March, April, and May, keeping the moon under constant watch from twilight to dawn when conditions permitted. They have provided counts representing more than one thousand hours of observation, at many places in an area of more than a million square miles. But, as impressive as the figures on the record sheets are, they, like the published observations referred to above, have dubious meaning as they stand. Were we to compare them directly, station for station, or hour for hour, we would be almost certain to fall into serious errors. The reasons for this are not simple, and the measures that must be taken to obtain true comparisons are even less so. When I first presented this problem to my colleague, Professor William A. Rense, of the Department of Physics and Astronomy at Louisiana State University, I was told that mathematical means exist for reducing the data and for ascertaining the desired facts. Rense's scholarly insight into the mathematics of the problem resulted in his derivation of formulae that have enabled me to analyze on a comparable basis data obtained from different stations on the same night, and from the same station at different hours and on different nights. Astronomical and technical aspects of the problem are covered by Rense in his paper (1946), but the underlying principles are discussed at somewhat greater length in this paper. Part I of the present paper, dealing with the means by which the data were obtained and processed, will explore the general nature of the problem and show by specific example how a set of observations is prepared for analysis. Part II will deal with the results obtained and their interpretation. ACKNOWLEDGMENTS In the pursuit of this research I have received a tremendous amount of help from my colleagues, students, and other friends. In the first place, in order to obtain much of the data on which the study was based, it was necessary to enlist the aid of many persons in various parts of the country and to draw heavily on their time and patience to get all-night telescopic counts of migrating birds. Secondly, the processing of the primary data and its subsequent analysis demanded that I delve into the fields of astronomy and mathematics. Here, from the outset, I have enjoyed the constant and untiring help of Professor W. A. Rense of the Department of Physics and Astronomy at Louisiana State University. Without his collaboration, I would not have been able to do this work, for he not only supplied formulae whereby I was able to make desired computations, but time and again he maneuvered me through my difficulties in the mathematical procedures. Moreover, Professor Rense has manifested a great interest in the ornithological aspect of the problem, and his trenchant advice has been of inestimable value to me. No less am I indebted to my associate, Robert J. Newman, with whom I have spent untold hours discussing the various aspects of the problem. Indeed, most of the concepts that have evolved in the course of this study have grown out of discussions over a four-year period with both Rense and Newman. Whatever merit this work may have may be attributable in no small part to the help these two men have given me. In the preparation of many of the illustrations, I am further obligated to Newman for his excellent creative ideas as well as draftsmanship, and to Miss Helen Behrnes and A. Lowell Wood for their assistance. The mathematical computations required in this study have been laborious and time-consuming. It is estimated that more than two thousand man-hours have gone into this phase of the work alone. Whereas I have necessarily done most of this work, I have received a tremendous amount of help from A. Lowell Wood. Further assistance in this regard came from Herman Fox, Donald Norwood, and Lewis Kelly. The recording of the original field data in the spring of 1948 from the thirty-odd stations in North America involved the participation of more than 200 ornithologists and astronomers. This collaboration attests to the splendid cooperative spirit that exists among scientists. Many of these persons stayed at the telescope, either as observer or as recorder, hours on end in order to get sets of data extending through a whole night. The following were responsible for much of the field data herein used: J. R. Andrews, S. A. Arny, M. Dale Arvey, H. V. Autrey, Charles C. Ayres, Mr. and Mrs. Roy Bailey, Irwin L. Baird, Maurice F. Baker, Rollin H. Baker, Bedortha and Edna Baldwin, Mrs. A. Marguerite Baumgartner, T. A. Becket, Paul Bellington, Donald Bird, Carl Black, Jr., Lea Black, Lytle Blankenship, Mr. and Mrs. J. Stewart Boswell, Bruce Boudreaux, Frank Bray, Mr. and Mrs. Leonard Brecher, Homer Brewer, Mrs. Harvey Broome, Heyward Brown, Floyd Browning, Cyril Broussard, Paul Buress, Ralph M. Burress, Robert Cain, Don Carlos, Mrs. Reba Campbell, Mr. and Mrs. E. Burnham Chamberlain, Laura Chaney, Van B. Chaney, Jr., Edward Clebsch, Mr. and Mrs. Ben B. Coffey, William Cook, Dr. Jack Craven, Hugh C. and William Davis, Katherine Davis, Richard Davis, Richard DeArment, Robert E. Delphia, J. C. Dickinson, Mr. and Mrs. Otto Dietrich, John Dietrich, Clara Dixon, Nina Driven, John J. Duffy, Mr. and Mrs. R. J. Dunbar, Betty Dupre, Bernard E. Eble, Jr., Robert G. Eble, Dr. and Mrs. William H. Elder, C. C. Emory, Davis Emory, Alice H. Farnsworth, James Fielding, William R. Fish, Mr. and Mrs. Myron Ford, W. G. Fuller, Louis Gainey, Dr. Mary E. Gaulden, Mr. and Mrs. John J. Giudice, Lt. L. E. Goodnight, Earl R. Greene, Max Grilkey, W. W. H. Gunn, Noel Maxwell Hall, Jr., A. J. Hanna, Paul Hansen, Harold W. Harry, Joseph Healy, Dorothy Helmer, Mr. and Mrs. John H. Helmer, Philip E. Hoberecht, William D. Hogan, Dr. and Mrs. Joseph C. Howell, E. J. Huggins, Mrs. Walter Huxford, Hugh Iltis, W. S. Jennings, William M. Johnson, William Kasler, Luther F. Keeton, Lawrence C. Kent, W. H. Kiel, L. P. Kindler, Mr. and Mrs. Joseph E. King, Harriet Kirby, E. J. Koestner, Roy Komarek, Ann Knight, Mr. and Mrs. N. B. Langworthy, Mr. and Mrs. C. F. Lard, Prentiss D. Lewis, Ernest Liner, Dr. and Mrs. R. W. Lockwood, Dr. Harvey B. Lovell, William J. Lueck, Don Luethy, James Major, Mr. and Mrs. Russell L. Mannette, Mrs. John B. Mannix, Donald Mary, Dale E. McCollum, Stewart McConnell, Mr. and Mrs. M. L. McCroe, Robert L. McDaniel, Mr. and Mrs. Frank McGill, Thomas Merimer, Mr. and Mrs. I. S. H. Metcalf, Ann Michener, John Michener, T. H. Milby, D. S. Miller, Burt Monroe, Jr., Burt Monroe, Sr., Mrs. R. A. Monroe, Gordon Montague, Duryea Morton, James Mosimonn, Don L. Moyle, Grant Murphy, John T. Murphy, Mrs. H. F. Murphy, Mrs. Hill Myers, Mr. and Mrs. Robert J. Newman, William Nichols, R. A. Norris, Floyd Oaks, Eugene P. Odum, Mrs. E. E. Overton, Lennie E. Pate, Kenneth Patterson, Ralph Paxton, Louis Peiper, Marie Peiper, Mr. and Mrs. Harold S. Peters, Mary Peters, Mr. and Mrs. D. W. Pfitzer, Betty Plice, Max Plice, Lestar Porter, D. R. Power, Kenneth Price, George Rabb, Marge Reese, Wayne L. Reeve, C. L. Riecke, R. D. Ritchie, V. E. Robinson, Beverly J. Rose, Mary Jane Runyon, Roger Rusk, Bernd Safinsley, Mr. and Mrs. Glen C. Sanderson, Lewis L. Sandidge, John Sather, J. Benton Schaub, Evelyn Schneider, Henry W. Setzer, Mr. and Mrs. Walter Shackleton, Mr. and Mrs. Francis P. Shannon, Mr. and Mrs. Charles Shaw, Paul H. Shepard, Jr., Alan C. Sheppard, Mabel Slack, Alice Smith, R. Demett Smith, Jr., Nat Smith, Major and Mrs. Charles H. Snyder, Albert Springs, Dr. and Mrs. Fred W. Stamm, J. S. Steiner, Mrs. Paul Stephenson, Herbert Stern, Jr., Herbert Stoddard, Mr. and Mrs. F. W. Stomm, Charles Strull, Harold P. Strull, Mrs. Fan B. Tabler, Dr. and Mrs. James T. Tanner, S. M. H. Tate, David Taylor, Hall Tennin, Scott Terry, Mr. and Mrs. S. Charles Thacher, Olive Thomas, G. A. Thompson, Jr., Dr. and Mrs. S. R. Tipton, Robert Tucker, Tom Uzzel, Mr. and Mrs. M. G. Vaiden, Richard Vaught, Edward Violante, Brother I. Vincent, Marilyn L. Walker, Mr. and Mrs. Willis Weaver, Mr. and Mrs. W. L. Webb, Margaret M. L. Wehking, W. A. Welshans, Jr., Mrs. J. F. Wernicke, Francis M. Weston, Miss G. W. Weston, Dr. James W. White, John A. White, A. F. Wicke, Jr., Oren Williams, J. L. Wilson III, W. B. Wilson, Dr. and Mrs. Leonard Wing, Sherry Woo, Rodney Wuthnow, Grace Wyatt, Mr. and Mrs. Malcom Young, Mr. and Mrs. A. J. Zimmerman. To the scores of other people who assisted in making these observations I extend my hearty thanks. Drs. E. R. Hall, Edward H. Taylor, and H. B. Hungerford of the University of Kansas have read the manuscript and have made valuable suggestions, as have also Dr. W. H. Gates of Louisiana State University and Dr. Donald S. Farner of the State College of Washington. Dr. Farner has also been of great help, together with Drs. Ernst Mayr, J. Van Tyne, and Ernst Schüz, in suggesting source material bearing on the subject in foreign literature. Dr. N. Wyaman Storer, of the University of Kansas, pointed out a short-cut in the method for determining the altitude and azimuth of the moon, which resulted in much time being saved. For supplying climatological data and for guidance in the interpretation thereof, I am grateful to Dr. Richard Joel Russell, Louisiana State University; Commander F. W. Reichelderfer, Chief of the U. S. Weather Bureau, Washington, D. C.; Mr. Merrill Bernard, Chief of the Climatological and Hydrologic Services; and Mr. Ralph Sanders, U. S. Weather Bureau at New Orleans, Louisiana. Acknowledgment is made to Bausch and Lomb Optical Company for the loan of six telescopes for use in this project. Messrs. G. V. Cutler and George Duff of Smith and Johnson Steamship Company, operators of the Yucatán Line, are to be thanked for granting me free passage on the "S. S. Bertha Brøvig" to Progreso, Yucatán, where I made observations in 1945 and 1948. I am also indebted to the Louisiana State University Committee on Faulty Research for a grant-in-aid. PART I. FLIGHT DENSITIES AND THEIR DETERMINATION A. LUNAR OBSERVATIONS OF BIRDS AND THE FLIGHT DENSITY CONCEPT The subject matter of this paper is wholly ornithological. It is written for the zoologist interested in the activities of birds. But its bases, the principles that make it possible, lie in other fields, including such rather advanced branches of mathematics as analytical geometry, spherical geometry, and differential calculus. No exhaustive exposition of the problem is practicable, that does not take for granted some previous knowledge of these disciplines on the part of all readers. There are, however, several levels of understanding. It is possible to appreciate _what_ is being done without knowing _how_ to do it; and it is possible to learn how to carry out the successive steps of a procedure without entirely comprehending _why_. Some familiarity with the concepts underlying the method is essential to a full understanding of the results achieved, and details of procedure must be made generally available if the full possibilities of the telescopic approach are to be realized. Without going into proof of underlying propositions or actual derivation of formulae, I shall accordingly present a discussion of the general nature of the problem, conveyed as much as possible in terms of physical visualization. The development begins with the impressions of the student when he first attempts to investigate the movements of birds by means of the moon. _What the Observer Sees_ Watched through a 20-power telescope on a cloudless night, the full moon shines like a giant plaster hemisphere caught in the full glare of a floodlight. Inequalities of surface, the rims of its craters, the tips of its peaks, gleam with an almost incandescent whiteness; and even the darker areas, the so-called lunar seas, pale to a clear, glowing gray. Against this brilliant background, most birds passing in focus appear as coal-black miniatures, only 1/10 to 1/30 the apparent diameter of the moon. Small as these silhouettes are, details of form are often beautifully defined--the proportions of the body, the shape of the tail, the beat of the wings. Even when the images are so far away that they are pin-pointed as mere flecks of black against the illuminated area, the normal eye can follow their progress easily. In most cases the birds are invisible until the moment they "enter," or pass opposite, the rim of the moon and vanish the instant they reach the other side. The interval between is likely to be inestimably brief. Some birds seem fairly to flash by; others, to drift; yet seldom can their passing be counted in seconds, or even in measureable fractions of seconds. During these short glimpses, the flight paths tend to lie along straight lines, though occasionally a bird may be seen to undulate or even to veer off course. Now and again, in contrast to this typical picture, more eerie effects may be noted. Some of them are quite startling--a minute, inanimate-looking object drifting passively by like a corpuscle seen in the field of a microscope; a gigantic wing brushing across half the moon; a ghost-like suggestion of a bird so transparent it seems scarcely more than a product of the imagination; a bird that pauses in mid-flight to hang suspended in the sky; another that beats its way ineffectually forward while it moves steadily to the side; and flight paths that sweep across the vision in astonishingly geometric curves. All of these things have an explanation. The "corpuscle" is possibly a physical entity of some sort floating in the fluid of the observer's eye and projected into visibility against the whiteness of the moon. The winged transparency may be an insect unconsciously picked up by the unemployed eye and transferred by the _camera lucida_ principle to the field of the telescope. It may be a bird flying very close, so drastically out of focus that the observer sees right through it, as he would through a pencil held against his nose. The same cause, operating less effectively, gives a characteristic gray appearance with hazy edges to silhouettes passing just beneath the limits of sharp focus. Focal distortions doubtless also account for the precise curvature of some flight paths, for this peculiarity is seldom associated with distinct images. Suspended flight and contradictory directions of drift may sometimes be attributable to head winds or cross winds but more often are simply illusions growing out of a two-dimensional impression of a three-dimensional reality. Somewhat more commonplace are the changes that accompany clouds. The moon can be seen through a light haze and at times remains so clearly visible that the overcast appears to be behind, instead of in front of, it. Under these circumstances, birds can still be readily discerned. Light reflected from the clouds may cause the silhouettes to fade somewhat, but they retain sufficient definition to distinguish them from out-of-focus images. On occasion, when white cloud banks lie at a favorable level, they themselves provide a backdrop against which birds can be followed all the way across the field of the telescope, whether or not they directly traverse the main area of illumination. _Types of Data Obtained_ The nature of the observations just described imposes certain limitations on the studies that can be made by means of the moon. The speed of the birds, for instance, is utterly beyond computation in any manner yet devised. Not only is the interval of visibility extremely short, but the rapidity with which the birds go by depends less on their real rate of motion than on their proximity to the observer. The identification of species taking part in the migration might appear to offer more promise, especially since some of the early students of the problem frequently attempted it, but there are so many deceptive elements to contend with that the results cannot be relied upon in any significant number of cases. Shorn of their bills by the diminution of image, foreshortened into unfamiliar shape by varying angles of perspective, and glimpsed for an instant only, large species at distant heights may closely resemble small species a few hundred feet away. A sandpiper may appear as large as a duck; or a hawk, as small as a sparrow. A goatsucker may be confused with a swallow, and a swallow may pass as a tern. Bats, however, can be consistently recognized, if clearly seen, by their tailless appearance and the forward tilt of their wings, as well as by their erratic flight. And separations of nocturnal migrants into broad categories, such as seabirds and passerine birds, are often both useful and feasible. It would be a wonderful convenience to be able to clock the speed of night-flying birds accurately and to classify them specifically, but neither of these things is indispensable to the general study of nocturnal migration, nor as important as the three kinds of basic data that _are_ provided by telescopes directed at the moon. These concern:--(1) the direction in which the birds are traveling; (2) their altitude above the earth; (3) the number per unit of space passing the observation station. Unfortunately none of these things can be perceived directly, except in a very haphazard manner. Direction is seen by the observer in terms of the slant of a bird's pathway across the face of the moon, and may be so recorded. But the meaning of every such slant in terms of its corresponding compass direction on the plane of the earth constantly changes with the position of the moon. Altitude is only vaguely revealed through a single telescope by the size and definition of images whose identity and consequent real dimensions are subject to serious misinterpretation, for reasons already explained. The number of birds per unit of space, seemingly the easiest of all the features of migration to ascertain, is actually the most difficult, requiring a prior knowledge of both direction and altitude. To understand why this is so, it will be necessary to consider carefully the true nature of the field of observation. _The Changing Field of Observation_ Most of the observations used in this study were made in the week centering on the time of the full moon. During this period the lunar disc progresses from nearly round to round and back again with little change in essential aspect or apparent size. To the man behind the telescope, the passage of birds looks like a performance in two dimensions taking place in this area of seemingly constant diameter--not unlike the movement of insects scooting over a circle of paper on the ground. Actually, as an instant's reflection serves to show, the two situations are not at all the same. The insects are all moving in one plane. The birds only appear to do so. They may be flying at elevations of 500, 1000, or 2000 feet; and, though they give the illusion of crossing the same illuminated area, the actual breadth of the visible space is much greater at the higher, than at the lower, level. For this reason, other things being equal, birds nearby cross the moon much more swiftly than distant ones. The field of observation is not an area in the sky but a volume in space, bounded by the diverging field lines of the observer's vision. Specifically, it is an inverted cone with its base at the moon and its vertex at the telescope. Since the distance from the moon to the earth does not vary a great deal, the full dimensions of the Great Cone determined by the diameter of the moon and a point on the earth remain at all times fairly constant. Just what they are does not concern us here, except as regards the angle of the apex (roughly 1/2°), because obviously the effective field of observation is limited to that portion of the Great Cone below the maximum ceiling at which birds fly, a much smaller cone, which I shall refer to as the Cone of Observation (Figure 1). [Illustration: FIG. 1. The field of observation, showing its two-dimensional aspect as it appears to the observer and its three-dimensional actuality. The breadth of the cone is greatly exaggerated.] [Illustration: FIG. 2. Method for determining the diameter of the cone at any point. The angular diameter of the moon may be expressed in radians, or, in other words, in terms of lengths of arc equivalent to the radius of a circle. In the diagram, the arc between C and E, being equivalent to the radius CO, represents a radian. If we allow the arc between A and B to be the diameter of the moon, it is by astronomical calculation about .009 radian, or .009 CO. This ratio will hold for any smaller circle inscribed about the center O; that is, the arc between A´B´ equals .009 C´O. Thus the width of the cone of observation at any point, expressed in degrees of arc, is .009 of the axis of the cone up to that point. The cone is so slender that the arc between A and B is essentially equal to the chord AB. Exactly the same consideration holds true for the smaller circle where the chord A´B´ represents part of the flight ceiling.] The problem of expressing the number of passing birds in terms of a definite quantity of space is fundamentally one of finding out the critical dimensions of this smaller cone. The diameter at any distance from the observer may be determined with enough accuracy for our purposes simply by multiplying the distance by .009, a convenient approximation of the diameter of the moon, expressed in radians (see Figure 2). One hundred feet away, it is approximately 11 inches; 1000 feet away, nine feet; at one mile, 48 feet; at two miles, 95 feet. Estimating the effective length of the field of observation presents more formidable difficulties, aggravated by the fact that the lunar base of the Great Cone does not remain stationary. The moon rises in the general direction of east and sets somewhere in the west, the exact points where it appears and disappears on the horizon varying somewhat throughout the year. As it drifts across the sky it carries the cone of observation with it like the slim beam of an immense searchlight slowly probing space. This situation is ideal for the purpose of obtaining a random sample of the number of birds flying out in the darkness, yet it involves great complications; for the size of the sample is never at two consecutive instants the same. The nearer the ever-moving great cone of the moon moves toward a vertical position, the nearer its intersection with the flight ceiling approaches the observer, shortening, therefore, the cone of observation (Figure 3). The effect on the number of birds seen is profound. In extreme instances it may completely reverse the meaning of counts. Under the conditions visualized in Figure 3, the field of observation at midnight is only one-fourth as large as the field of observation earlier in the evening. Thus the twenty-four birds seen from 7 to 8 P. M., represent not twice as many birds actually flying per unit of space as the twelve observed from 11:30 to 12:30 A. M., but only half the amount. Figure 4, based on observations at Ottumwa, Iowa, on the night of May 22-23, shows a similar effect graphically. Curve A represents the actual numbers of birds per hour seen; Curve B shows the same figures expressed as flight densities, that is, corrected to take into account the changing size of the field of observation. It will be noted that the trends are almost exactly opposite. While A descends, B rises, and _vice-versa_. In this case, inferences drawn from the unprocessed data lead to a complete misinterpretation of the real situation. [Illustration: FIG. 3. Temporal change in the effective size of the field of observation. The sample sections, A and B, represent the theoretical densities of flight at 8:20 and 12:00 P. M., respectively. Though twice as many birds are assumed to be in the air at midnight when the moon is on its zenith (Z) as there were at the earlier hour, only half as many are visible because of the decrease in size of the cone of observation.] [Illustration: FIG. 4. Migration at Ottumwa, Iowa, on the night of May 22-23, 1948. Curve A is a graphic representation of the actual numbers of birds seen hourly through the telescope. Curve B represents the same figures corrected for the variation in the size of the cone of observation. The dissimilarity in the two curves illustrates the deceptive nature of untreated telescopic counts.] Nor does the moon suit our convenience by behaving night after night in the same way. On one date we may find it high in the sky between 9 and 10 P. M.; on another date, during the same interval of time, it may be near the horizon. Consequently, the size of the cone is different in each case, and the direct comparison of flights in the same hour on different dates is no more dependable than the misleading comparisons discussed in the preceding paragraph. The changes in the size of the cone have been illustrated in Figure 3 as though the moon were traveling in a plane vertical to the earth's surface, as though it reached a point directly over the observer's head. In practice this least complicated condition seldom obtains in the regions concerned in this study. In most of the northern hemisphere, the path of the moon lies south of the observer so that the cone is tilted away from the vertical plane erected on the parallel of latitude where the observer is standing. In other words it never reaches the zenith, a point directly overhead. The farther north we go, the lower the moon drops toward the horizon and the more, therefore, the cone of observation leans away from us. Hence, at the same moment, stationed on the same meridian, two observers, one in the north and one in the south, will be looking into different effective volumes of space (Figure 5). [Illustration: FIG. 5. Geographical variation in the size of the cone of observation. The cones A and B represent the effective fields of observation at two stations situated over 1,200 miles apart. The portions of the great cones included here appear nearly parallel, but if extended far enough would be found to have a common base on the moon. Because of the continental scale of the drawing, the flight ceiling appears as a curved surface, equidistant above each station. The lines to the zenith appear to diverge, but they are both perpendicular to the earth. Although the cones are shown at the same instant in time, and have their origin on the same meridian, the dimensions of B are less than one-half as great as those of A, thus materially decreasing the opportunity to see birds at the former station. This effect results from the different slants at which the zenith distances cause the cones to intersect the flight ceiling. The diagram illustrates the principle that northern stations, on the average, have a better chance to see birds passing in their vicinity than do southern stations.] As a further result of its inclination, the cone of observation, seldom affords an equal opportunity of recording birds that are flying in two different directions. This may be most easily understood by considering what happens on a single flight level. The plane parallel to the earth representing any such flight level intersects the slanting cone, not in a circle, but in an ellipse. The proportions of this ellipse are very variable. When the moon is high, the intersection on the plane is nearly circular; when the moon is low, the ellipse becomes greatly elongated. Often the long axis may be more than twice the length of the short axis. It follows that, if the long axis happens to lie athwart the northward direction of flight and the short axis across the eastward direction, we will get on the average over twice as large a sample of birds flying toward the north as of birds flying toward the east. In summary, whether we wish to compare different stations, different hours of the night, or different directions during the same hour of the night, no conclusions regarding even the relative numbers of birds migrating are warranted, unless they take into account the ever-varying dimensions of the field of observation. Otherwise we are attempting to measure migration with a unit that is constantly expanding or contracting. Otherwise we may expect the same kind of meaningless results that we might obtain by combining measurements in millimeters with measurements in inches. Some method must be found by which we can reduce all data to a standard basis for comparison. _The Directional Element in Sampling_ In seeking this end, we must immediately reject the simple logic of sampling that may be applied to density studies of animals on land. We must not assume that, since the field of observation is a volume in space, the number of birds therein can be directly expressed in terms of some standard volume--a cubic mile, let us say. Four birds counted in a cone of observation computed as 1/500 of a cubic mile are not the equivalent of 500 × 4, or 2000, birds per cubic mile. Nor do four birds flying over a sample 1/100 of a square mile mathematically represent 400 birds passing over the square mile. The reason is that we are not dealing with static bodies fixed in space but with moving objects, and the objects that pass through a cubic mile are not the sum of the objects moving through each of its 500 parts. If this fact is not immediately apparent, consider the circumstances in Figures 6 and 7, illustrating the principle as it applies to areas. The relative capacity of the sample and the whole to intercept bodies in motion is more closely expressed by the ratio of their perimeters in the case of areas and the ratio of their surface areas in the case of volumes. But even these ratios lead to inaccurate results unless the objects are moving in all directions equally (see Figure 8). Since bird migration exhibits strong directional tendencies, I have come to the conclusion that no sampling procedure that can be applied to it is sufficiently reliable short of handling each directional trend separately. [Illustration: FIG. 6. The problem of sampling migrating birds. The large square in the diagram may be thought of as a square mile on the earth's surface, divided into four equal smaller squares. Birds are crossing over the area in three directions, equally spaced, so that each of the subdivisions is traversed by three of them. We might be tempted to conclude that 4 × 3, or 12, would pass over the large square. Actually there are only seven birds involved all told. Obviously, the interceptive potential of a small square and a larger square do not stand in the same ratio as their areas.] For this reason, the success of the whole quantitative study of migration depends upon our ability to make directional analyses of primary data. As I have already pointed out, the flight directions of birds may be recorded with convenience and a fair degree of objectivity by noting the slant of their apparent pathways across the disc of the moon. But these apparent pathways are seldom the real pathways. Usually they involve the transfer of the flight line from a horizontal plane of flight to a tilted plane represented by the face of the moon, and so take on the nature of a projection. They are clues to directions, but they are not the directions themselves. For each compass direction of birds flying horizontally above the earth, there is one, and only one, slant of the pathway across the moon at a given time. It is possible, therefore, knowing the path of a bird in relation to the lunar disc and the time of the observation, to compute the direction of its path in relation to the earth. The formula employed is not a complicated one, but, since the meaning of the lunar coördinates in terms of their corresponding flight paths parallel to the earth is constantly changing with the position of the moon, the calculation of each bird's flight separately would require a tremendous amount of time and effort. [Illustration: FIG. 7. The sampling effect of a square. In Diagram A eight evenly distributed birds are flying from south to north, and another four are proceeding from east to west. Three appear in each of the smaller squares. Thus, if we were to treat any of these smaller sections as a directly proportionate sample of the whole, we would be assuming that 3 × 16, or 48, birds had traversed the square mile--four times the real total of 12. If we consider the paths separately as in Diagram B, we see quite clearly what is wrong. Every bird crosses four plots the size of the sample and is being computed into the total over and over a corresponding number of times. Patently, just as many south-north birds cross the bottom tier of squares as cross the four tiers comprising the whole area. Just as many west-east birds traverse one side of the large square as cross the whole square. In other words, the inclusion of additional sections _athwart_ the direction of flight involves the inclusion of additional birds proceeding in that direction, while the inclusion of additional sections _along_ the direction does not. The correct ratio of the sample to the whole would seem to be the ratio of their perimeters, in this case the ratio of one to four. When this factor of four is applied to the problem it proves correct: 4 × 3 (the number of birds that have been seen in the sample square) equals 12 (the exact number of birds that could be seen in the square mile).] [Illustration: FIG. 8. Rectangular samples of square areas. In Diagram A, where as many birds are flying from west to east as are flying from south to north, the perimeter ratio (three to eight) correctly expresses the number of birds that have traversed the whole area relative to the number that have passed through the sample. But in Diagram B, where all thirty-two birds are flying from south to north, the correct ratio is the ratio of the base of the sample to the base of the total area (one to four), and use of the perimeter ratio would lead to an inaccurate result (forty-three instead of thirty-two birds). Perimeter ratios do not correctly express relative interceptory potential, unless the shape of the sample is the same as the shape of the whole, or unless the birds are flying in all directions equally.] Whatever we do, computed individual flight directions must be frankly recognized as approximations. Their anticipated inaccuracies are not the result of defects in the mathematical procedure employed. This is rigorous. The difficulty lies in the impossibility of reading the slants of the pathways on the moon precisely and in the three-dimensional nature of movement through space. The observed coördinates of birds' pathways across the moon are the projected product of two component angles--the compass direction of the flight and its slope off the horizontal, or gradient. These two factors cannot be dissociated by any technique yet developed. All we can do is to compute what a bird's course would be, if it were flying horizontal to the earth during the interval it passes before the moon. We cannot reasonably assume, of course, that all nocturnal migration takes place on level planes, even though the local distractions so often associated with sloping flight during the day are minimized in the case of migrating birds proceeding toward a distant destination in darkness. We may more safely suppose, however, that deviations from the horizontal are random in nature, that it is mainly a matter of chance whether the observer happens to see an ascending segment of flight or a descending one. Over a series of observations, we may expect a fairly even distribution of ups and downs. It follows that, although departures from the horizontal may distort individual directions, they tend to average out in the computed trend of the mean. The working of this principle applied to the undulating flight of the Goldfinch (_Spinus_) is illustrated in Figure 9. [Illustration: FIG. 9. The effect of vertical components in bird flight. The four diagrams illustrate various effects that might result if a bird with an undulating flight, such as a Goldfinch, flew before a moon 45° above the horizon. In each case the original profile of the pathways, illustrated against the dark background, is flattened considerably as a result of projection. In the situation shown in Diagram A, where the high point of the flight line, GHJ, occurs within the field of the telescope, it is not only obvious that a deviation is involved, but the line GJ drawn between the entry and departure points coincides with the normal coördinates of a bird proceeding on a horizontal plane. In Diagrams B and C, one which catches an upward segment of flight, and the other, a downward segment, the nature of the deviation would not be detectable, and an incorrect direction would be computed from the coördinates. Over a series of observations, including many Goldfinches, one would expect a fairly even distribution of ups and downs. Since the average between the coördinate angles in Diagrams B and C, +19° and -19°, is the angle of the true coördinate, we have here a situation where the errors tend to compensate. In Diagram D, where the bird is so far away that several undulations are encompassed within the diameter of the field of view, the coördinate readings do not differ materially from those of a straight line.] Since _individually_ computed directions are not very reliable in any event, little is to be lost by treating the observed pathways in groups. Consequently, the courses of all the birds seen in a one-hour period may be computed according to the position of the moon at the middle of the interval and expressed in terms of their general positions on the compass, rather than their exact headings. For this latter purpose, the compass has been divided into twelve fixed sectors, 22-1/2 degrees wide. The trends of the flight paths are identified by the mid-direction of the sector into which they fall. The sectoring method is described in detail in the section on procedures. [Illustration: Fig. 10. The interceptory potential of slanting lines. The diagram deals with one direction of flight and its incidence across lines of six different slants, lines of identical length oriented in six different ways. Obviously, the number of birds that cross a line depends not only on the length of the line, but also on its slant with respect to the flight paths.] The problem remains of converting the number of birds involved in each directional trend to a fixed standard of measurement. Figure 7A contains the partial elements of a solution. All of the west-east flight paths that cross the large square also cross one of its mile-long sides and suggest the practicability of expressing the amount of migration in any certain direction in terms of the assumed quantity passing over a one-mile line in a given interval of time. However, many lines of that length can be included within the same set of flight paths (Figure 10); and the number of birds intercepted depends in part upon the orientation of the line. The 90° line is the only one that fully measures the amount of flight per linear unit of front; and so I have chosen as a standard an imaginary mile on the earth's surface lying at right angles to the direction in which the birds are traveling. _Definitions of Flight Density_ When the count of birds in the
{'title': 'A Quantitative Study of the Nocturnal Migration of Birds by Jr. George H. Lowery', 'source': 'Project Gutenberg', 'lang': 'en'}