Popular Science Monthly/Volume 44/April 1894/The Method of Homing Pigeons
By C. F. HODGE, Ph. D.,
ASSISTANT PROFESSOR OF PHYSIOLOGY, CLARK UNIVERSITY.
WHEN Sir John Lubbock rotated a paper disk upon which ants were moving in a given direction and the ants turned so as to maintain their course, it seemed as if they were endowed with some mysterious sense or power of direction, like that of a magnetic needle upon its pivot. When he substituted for the plain disk a circular hat-box, which, as he thought, must constitute for an ant the entire visible universe, and still the ants turned as the box was rotated, the fact seemed proved. Ants must have located within their bodies, and independent of ordinary sensory impressions from the external world, the power of going in any direction they wish. This conclusion is far reaching in its consequences. If ants possess such mysterious power, may it not exist in other, or all, animals? It must be of the nature of a special sense. Where, then, is the sense organ? How should ideas of animal sensation be modified by it?
Many writers would have ceased experimenting at this point, and gone off into chapters of ecstatic hypothesis about this fathomless mystery, this unmistakable "sense of direction" developed to such perfection in so humble a creature. Not so with Lubbock. When he covered the hat-box, then rotated it, the ants did not turn, but were turned with the box; or when he shifted the position of his candles to the opposite side, as he rotated the box, the ants did not turn. And so their action fell from the realm of exquisite mystery to take its place among such commonplaces as that of the sailor steering his course by the lighthouse or the stars, or that of a man guided home by the light of his own camp fire.
A considerable literature, pro and con, has gathered about the subject, in which we find frequent use of such expressions as "direction-sense," "sens de la direction," "sense of orientation," "faculté d'orientation" "instinct of location," "magnetic sense," "Orientierungssinne," "Gefühl der Kardinalrichtungen," and many more. By whatever terms designated, the idea is that animals possess some special sense, some occult faculty, by which, without reference to external objects, they are able to guide their movements aright. This power, it is commonly thought, is not possessed, or only in a rudimentary degree, by civilized man, is more highly developed in savages, and may be found in its perfection in certain migratory animals.
The literature is open to the general criticism that the strange and exceptional is noted, while by far the more important, common, and usual occurrence rarely appears in print; and thus queer stories of dogs and cats, horses, mules, birds, insects, and even men, who are able to point unerringly north, no matter how blindfolded or manipulated, come to predominate. Still, as the methods of animals have come to be studied with scientific
Flight of six pigeons, open cage.
accuracy, these notions have been compelled to flit from one form to another in most lively fashion.
Migratory birds, most careful study has proved, learn their route from "zone to zone," and follow it solely by means of vision. "This," Mr. Wallace says, "is now well ascertained." The work of Sir John Lubbock, of Forel, and the perfectly conclusive experiments of Mr. and Mrs. Peckham, leave no resting place for the idea among insects; and developments in anthropology teach that savages depend solely for directions upon a skillful use of the external signs of Nature.
All this may be true. It still remains an utter impossibility that a homing pigeon can return from a distance of over a thousand miles if unaided by some special "sense of direction." Such a view is rarely held by a practical pigeon fancier. He knows too well how many birds he loses, even with most careful short-distance training. He has observed that his birds, until they have learned the country, generally consume time enough to enable them to hunt over mile by mile a vast area, and that they can do nothing in a fog or snowstorm, or if blindfolded or hooded. Twenty years ago Leonard wrote as follows: "Some writers, chiefly poets and romancers, would have us believe that the carrier pigeon finds his way home from remote places by a kind of instinct; but this is not the case. Its flight is guided by sight alone. When let loose from confinement, it rises to a great height in the air by a series of constantly enlarging circles until it catches sight of some familiar landmark by which to direct its course."
Had "poets and romancers" continued sole occupants of the field, the following notes would have served no other than the private purpose for which they were taken. As it is, a number of attempts have recently been made by men of high scientific attainments to prove theories of "direction-sense" by feats of the homing pigeon. In general, such attempts are made in line with one or the other of two assumptions. According to the one, "direction-sense" is ascribed to some mysterious, direct, and immediate perception or sensation of location or direction in space. More often it is supposed to be a sort of "dead reckoning" which the organism has become able to keep—that is, the animal has come to have a feeling, definite or vague, as to how long, how fast, and which way it has traveled or has been carried. Two papers may be cited as giving possibly the best expositions of these two views. The one by Prof. Exner adduces evidence to prove the "dead-reckoning" theory; the other, by Prof. Caustier, attempts to establish that of immediate perception. Both agree as to the organ—viz., the membranous labyrinth, especially the semicircular canals.
There is nothing impossible about Exner's explanation. All animals, by the processes going on in their bodies, must have some notion of time. This would give the "how long" element in the problem. The "how fast" might be given by such an instrument
Flight of six pigeons, covered cage.
as we find in the otoliths resting on the sensory hairs of the maculæ acousticæ; these hairs bending under the weight more or less, according to rate of movement. The "which way" could easily be indicated by a bending of the sensory hairs of the cristæ acousticæ as the liquid in the semicircular canals is thrown this way or that by angular deviation of line of motion. Experimental test of the theory is impossible, since, after injury of a single semicircular canal, the birds refuse to fly at all. It must rest, therefore, upon facts obtained from observation of habits and methods employed by homing pigeons. If it is true, there should appear some relation between the flight of a bird home and the course by which it has been carried to the place of liberation. It should either tend to retrace its course or to follow a straight line home. However, the writer has not been able to record a single fact which points in this direction.
Graver objections must be admitted to obtain against the theory of M. Caustier, tinted as it is by the "electro-magnetic" romancing of the French hypnotists. He tells us of the bird, endowed with "une nature eminemment électrique," of "l'électricité de l'air," of "magnetisme terrestre," of "l'action physiologique du magnétisme," and the like. This means that pigeons can sense currents of atmospheric electricity or terrestrial magnetism in such a manner as to be guided by them; and this can hardly stand even as passing theory, while it remains so thoroughly proved by the experiments of Hermann, and these have been confirmed with powerful dynamos in at least two laboratories in this country, that the magnetic field has not the least physiological influence ("nicht die geringste Wirkung") upon the action of any tissue or sense organ or upon the animal as a whole.
But what say homing pigeons for themselves?
Of first importance to the study of a homing instinct is the method which an animal employs to mark or locate its home. On leaving a new camp for a day's hunt in the Bad Lands, a man naturally turns about and makes a mental note of prominent buttes in the vicinity. This butte with three pine trees on top is just to the left of the gulch where the tents are pitched. "I can tell it as far as I can see it," and he strikes out. Why may not other animals adopt a similar method? Concerning bees, Thompson has observed that, "if the position of a hive be changed, the bees for the first day take no distant flights till they have thoroughly scrutinized every object in its neighborhood." This would seem to indicate a rational method of procedure.
Upon their arrival in Madison, Wis., from Worcester, Mass., the pigeons were kept confined in a large loft which had but one window, and this happened to be upon the side next another barn close by, so that it afforded no view of the surrounding country. This arrangement was accidental at the time, but served very well a subsequent purpose. Five of the birds were "youngsters," and had never been liberated anywhere. On January 30 (1892), six months after their arrival, I let out these young birds one at a time, and with my wife to assist, and with spyglass, watch, and note-book at hand, we studied every act of each of the birds as long as we could keep them in sight. Since they all adopted precisely the same method of locating their loft, a description of one case will suffice.
A black Antwerp, let out at 4 p. m., flew to the ridge of a house eighty yards to the northwest, and sat for fifteen minutes, turning first this way, then that; looking eagerly the whole time; neck stretched out and head not still for a moment. This pigeon happened to alight on the north side of a chimney which came up through the ridge of the house. Its position was so close to the chimney that with stretching its neck as far as possible in both directions a considerable sector of the landscape must have been hidden from view. A few minutes after it alighted I recorded the remark, "If it is really in earnest about seeing everything in the neighborhood, it ought to go around to the other side of that chimney." Its first move, after fifteen minutes of looking, was a simple flit around the chimney. Here it stood for five minutes longer, looking attentively the whole time. It then flew a hundred yards south to the peak of a higher house, where six minutes more were given to observation from this new position. It next flew to a small, low house a hundred yards north. Here it remained scarcely a minute, whence it flew a hundred yards southeast to the peak of the highest house in the vicinity, where eight minutes more were devoted to observation. It now struck out to the southwest over a hill and grove and was lost to view until ten minutes past five, when it alighted on the loft. This flight may have been for the purpose of exploration and location, it probably was, in part at least; but leaving that out of the account, the bird spent thirty-five minutes doing nothing but look at its surroundings. The others consumed about the same time in the same way. In this we find the power to return laid in the painstaking visual localization of the home spot. One of the old birds, which escaped by accident, acted in a very different manner. After a few rapid circles, he flew straight for Madison and was not seen for three days; when, failing to find his old home in Worcester, he returned to the loft.
The next experiments were directed to determining the course taken by a pigeon in his return flight. The method employed is essentially the same as that used by Sir John Lubbock with the ants. The pigeons were taken to a convenient distance and liberated, and tracings of their flight were dotted oft' upon a chart of
Three successive flights of pigeon No. 2.
———— First flight, May 29.
the country. About fifty such, tracings were taken, of which a few of the more instructive are reproduced below.
A few days of freedom were allowed, in order that the birds might more exactly locate their loft; then all were again confined in preparation for the following experiments for nearly four months.
On May 29th six pigeons were caught at random and carried in a cage, the top and sides of which were made of open-mesh wire netting to allow free vision, to the top of a hill about half a mile southeast of "home." The birds were liberated singly, and the course flown by each in returning to loft may be seen by a glance at Fig. 1. At the same time, six other birds, also taken without selection, were carried to the same place in a basket closely wrapped in a heavy black shawl. Tracings of their homeward flights are reproduced in Fig. 2.
By comparing the two figures may be seen the influence of vision upon directness of return flight. In Fig. 1, five of the birds are seen to start toward home at once; one, a young bird out of the loft for the first time, flies in the wrong direction a short distance, turns sharply about, and alights upon the first house on the line toward home. Three pigeons fly home without preliminary circling. Fig. 2 shows not a single direct course. Two begin circling in the wrong direction. One of these persists in his false bent to the extent of searching over the whole city of Madison. In the case of Fig. 1, the birds, most of them, see home very soon and fly directly to it. Fig. 2 shows more of the method which a pigeon adopts in covering unknown territory.
By comparing successive tracings of the same bird, may be seen the effect of education—i. e., improvement in good birds, failure to improve in poor ones. The first is well shown in Fig. 3, the three different lines representing three successive flights of pigeon No. 2. As this is a typical case, let us follow its development a moment. No. 2 has been carried from the loft in a covered basket to the hill half a mile distant. Not having any idea as to which direction he has been taken, he naturally starts out the wrong way. His first thought, if I may so speak, is to look around for some familiar object. So at a he turns about and is occupied with looking over the landscape, while he describes a number of semicircles back and forth around the place of starting. He evidently sees nothing until his widening circles bring him over a group of buildings around a farmhouse at b. Among these is a red barn, and close to the loft is a red house. This looks quite like home, and he swoops down toward it. On closer examination, however, he fails to discover the familiar barn, the pigeonholes, and alighting board. After making four circles low down over and among these buildings, he rises high in the air again to take another look. All to the south and west are lake and marsh and woods, with but few farmhouses visible. Toward the north he sees a cluster of houses—South Madison. He looks them over in the same way. From c he catches sight of another
Three successive flights of pigeon No. 5.
———— First flight, May 29.
red barn at d, and goes to inspect it. Failing to find anything here, he must look farther. He has just come from the west. To the south and east are nothing but lake and woods again. To the north lies the densely settled portion of Madison. Possibly he sees the red brick courthouse near the State Capitol. He flies thither, but on reaching the city nothing looks familiar, and he spends little time in circling over it. He is soon lost to view at X. His course thus far measures about ten miles; time, a trifle over eight minutes. He was liberated at four o'clock, and after being lost at x he was next seen as he swooped down from the west to settle upon the roof of the loft at 5.10. As it is almost certain that he flew continuously, this leaves sixty minutes unaccounted for, and at a moderate estimate fifty miles of search-line not drawn upon the chart. Were it possible to fill this in, how much "sense of direction" should we need to invoke to account for his finding home? He has flown certainly eleven miles, almost as surely sixty, to find a good-sized barn half a mile away.
The result of education is seen in his subsequent flights. A week later he flies home from the same hill in less than a minute. Two weeks later still he flies from the university almost as straight as though he did have a "sense of direction." Upon the question of education, however, we must compare Fig. 3 with similar tracings of another bird. No. 5, given in Fig. 4. In the first trial No. 5 (continuous line. Fig. 4) succeeds in reaching home from the open cage without much difficulty. Liberated from a boat on Lake Monona for a second trial, he flies wildly (the broken line seen in Fig. 4). This tracing gives an index to the harum-scarum character of the bird. Unlike No. 2, which looks over the likely places carefully and then moves on. No. 5 is careless, has no confidence in his ability, and consequently looks the same ground over and over again (see 1, 2, and 3, Fig. 4). At a he flies out to the familiar hill, and thence does strike out in the right direction (b, Fig. 4) and goes close to home (c), but stupidly fails to recognize it, and flies back to the boat again for a fresh start. No. 5 shows no improvement with education. When carried to the hill for a third trial (dotted line. Fig. 4), he circles for a moment, and then seeing the red barn by the farmhouse, he starts off the wrong way. This bird, with eleven others, is subsequently sent away six miles, and he alone of the twelve fails to return. No doubt there are stupid pigeons as well as stupid men.
Two points of some little interest from their bearing upon comparative psychology may be mentioned in this connection. The first is the definite reaction to color which the pigeons unquestionably gave. Until they had completed their education so far as to know the landscape pretty well, and had learned that there are many red houses and barns in the world, a red building was enough to determine their flight with almost mathematical precision. The second point is one which the Peckhams have noted with reference to wasps—viz., if wasps are taken away from their nests and liberated over water, they fly toward the nearest land, although their nest is in the opposite direction. In liberating the pigeons from the boat this reaction was tested a great many times and never failed.
The tracings speak too plainly for themselves to require further comment. If any are able to extract "direction-sense consolation" out of them, they are entirely welcome to it.
The criticism naturally arises at this point that the pigeons are not trying to find home at all. They may be flying for pleasure or exercise. Two things may be said in reply: First, theories of "direction-sense" have been based upon the air-line course which a pigeon has been supposed to take, "after getting his bearings," from place of liberation to loft. This, as we have seen, comes only after training. In the second place, after a little observation, it is easy to distinguish from the sportive cavortings for pleasure the eager darting flight of search.
If, however, they fail to give evidence of "direction-sense," may not such tracings show something of even greater importance? All animals, from amoeba to man, spend a good share of their time searching for something or other. May there not be a fundamental logic of search as universal as the search itself? Naturally, if this is so, those animals whose life depends most closely upon finding the objects of their search would come to have the power and the logic of search most highly developed. We may then ask. What is the path or curve of logical search? It could hardly be a straight line, since the effort necessary to search must have a tendency to cause any animal to search over nearest ground first, inasmuch as turning or looking around is easier than moving the body ahead as far as the animal is able to see or feel ahead. We see this exemplified in the circling of hawks and the circling of dogs when starting out to cover a field. It could not be a circle, however, in case of an animal with memory to avoid covering the same ground twice.
To test the matter experimentally, a number of people kindly drew for the writer the path each would take to find an object, the proximity or direction of which is unknown. The object is supposed to lie upon a uniform field. Types of the curves handed in are given in Figs. 5 to 8. Undoubtedly the logical curve is the one submitted by Prof. Story (Fig. 5). It will be recognized to be a peculiar spiral, the involute of a circle, the characteristic of which is that the convolutions are always the same distance apart. This distance will be, of course, twice the distance at which the object is visible. The curve given by the majority is drawn in Fig. 6. This is a shade less ideal. The searcher, supposing him to be at the center, first looks around as far as he can see, then goes straight out twice the distance at which the object is visible, and begins following circles, each one being twice the visible distance from every other. A number of rectilinear figures were
received, types of which are reproduced in Figs. 7 and 8. These are a stage above the fundamentally logical. They clearly belong to the realm of the practical. We might call them "Yankee" search curves. They are practical, of course, because it is easier to follow a straight line than a curve.
A simple experiment was next devised, in which a person actually sets out to find a red tennis ball on a grassy lawn, his steps being plotted while lie is making the search. The ball was placed in all cases so that it could be seen from a distance of ten steps and at a uniform distance forty steps from the center stake, in order that the tracings of different persons could be compared as to time and length of course traversed. Fig. 9.
No attempt was made to do more than was necessary to obtain a suggestion which might serve to indicate the logic and method of the pigeons. In all only sixteen tracings were taken, and this number includes one experiment on a shepherd dog. Of the whole number, ten conform more or less closely to Prof. Story's curve. Three of the best of these are reproduced in Fig. 9. Two correspond evidently to the circular type (Fig. 6). These are given in Fig. 10, together with the only one which is in any degree rectangular, the "Yankee" type, and this was not made by a Yankee at all, but by an Irish boy twelve years of age. Three of the curves are hardly susceptible of logical classification.
A point of interest in this connection attaches to the dotted line in Fig. 9. This represents the path of L. W., the university carpenter, a man sixty-five years old, who had worked at his trade of straight lines and right angles for forty-five years. I had expected a typical rectangular curve. Instead he gave an ideal spiral. After finding the ball, however, he volunteered the following suggestive remark: "After I got started, I thought, if I was going to do it again, I would go at it on the square. I started out," he added, "before I thought." Thus instinctive logic won the day against forty-five years of special training.
If instinctive, however, this logic should be found almost as well developed in children as in adults. Accordingly, spicing the ball with candy or a small coin, several experiments were tried upon children from three to twelve years of age. In general the above statement was supported; but two of the number, aged respectively three and six, failed to show anything like the amount of search-logic possessed by most of the pigeons or the shepherd dog. One of these, the devious path of a bright six-year-old Irish girl, is reproduced in Fig. 12. Lubbock's ants might be pardoned for smiling should they chance to see this tracing.
The search line of an intelligent dog is given in Fig. 11. His eyes were covered, but he evidently had a strong impression that the ball had been thrown in the direction I happened to be facing. Resemblance between this and tracings of a number of the pigeons is quite evident.
The bearing of the above upon the problem of search as exhibited by the homing pigeon requires no detailed statement. In a word, the pigeon uses a logic of search which is common to animals generally, and there is no evidence that he employs anything else. His power of rapid and prolonged flight makes it possible for him to spin his search lines over vast areas and so carry them beyond our vision and lift them into the realm of mystery.
In such cases the time consumed furnishes an important check. Of a large number of birds sent away by rail for longer flights, not one made the return trip in less time than would have enabled him to fly on the involute of a circle from the place of liberation. This refers to "first flights." The best time made was twenty-six miles in five hours and nine minutes. Three other Fig. 10.
One thing which causes the search lines of the pigeons to swerve from the ideal curve of search upon a uniform field is that the field in their case is never uniform. A house of any kind, especially a red building, or, upon the lake, nearness to land, furnish elements of greater probability and determine search in that direction. To obtain an ideal curve for a uniform surface it would be necessary to liberate the pigeon on a Dakota prairie or in mid-ocean, where no break in the landscape is visible even from an altitude of a thousand feet. It is not, however, difficult Fig. 11.
It may seem to some that in denying a "sense of direction" and affirming a logic is like jumping from the frying pan into the fire. The only thing to be said on this point is that we do find evidence for search-logic and no evidence for "direction-sense." And further, in the one case we explain the phenomena by something fundamental in animal life, which we do know something about; whereas on "sense-direction" grounds we are explaining the partially known by the absolutely unknown.
An instance of quite a different sort from the above stood in the writer's mind as almost conclusive proof of sense-direction powers for a number of years. It may be briefly stated as follows:
A large Maltese tomcat once joined, on his own invitation, an evening rowing party on one of the Wisconsin lakes. It was a sultry summer night, as dark as a moonless night can be. Not a breath of air was stirring. We rowed nearly due north, straight out toward the middle of the lake, which is something over two miles wide. For some time Tom purred and made himself generally agreeable from one end of the boat to the other; but at last he grew restless and extremely anxious to get home. He would climb out to the end of the boat and, stretching his head toward home, mew almost continuously. We amused ourselves for some time by turning the boat slowly round and round, first one way then the other, to see if we could throw Tom off his bearings; but all to no effect. Whether right side, left side, bow or stern, Tom was always on the part of the boat nearest home, and straining as far as he could in that direction. Fully a mile from any shore, how could he tell which shore was which? But few lights were visible, the lake is thickly wooded, and the cottages stand well back among the trees. Not one in the party could recognize the lights of our own group of cottages. And no one but myself and cat had any idea which way to go for home. For my part, I had kept an eye out for the north star. But what did Tom do for his bearings? Could it be that through such inky darkness he could see enough of the shore to distinguish anything on it? This was easily tested. Taking a heavy blanket
shawl, which was serving as cushion, we wrapped Tom up in a number of thicknesses of it and one of the party held him in her lap while the boat was slowly turned around. This was of no use. On being released Tom started, with never a mistake and without the slightest hesitation, toward the end of the boat nearest home. To make doubly sure that vision was impossible, Tom was wrapped up and gently held flat in the bottom of the boat. This made no difference. Whether the boat was turned by a single stroke, as on a pivot, or rowed slowly around in a circle, the result was always the same. Tom went, without hesitation, invariably to the end or side of the boat nearest home.
Members of the party were blindfolded and required to guess whether the boat was turned or allowed to stand still, or was rowed in a straight line or in a circle; and it was an even chance whether they guessed right or wrong. Tom had a far better head for direction than any of us.
It was suggested that possibly a gentle current of air might be serving Tom as a direction-constant. This, however, could hardly have penetrated the shawl, and certainly not when in the bottom of the boat. Still, might not such a current be conveying odors imperceptible to man, but not to a cat? None of our number could feel the slightest breath of air on our faces, and even with the moistened finger held above the head, it was impossible to detect any flow of air. Might not then a wake of odor hanging in the air over our course serve as the needed direction-constant? This could hardly be, since we had rowed about so much that anything of the sort must have become thoroughly diffused.
Sight, smell, and touch would thus seem to be inadequate to explain the feat. Hearing still remains. But not a sound from any shore broke the silence. No town or city was near to furnish a roar, hum, or series of sounds of any sort. We could hear no bands of music, nor even the occasional bark of a dog. For minutes at a time we could hear absolutely no sound. And yet, may it not be that Tom heard every note some Tabby was making on the shore a mile away? If we were dealing with a sense as delicate as this, further experiment was useless. We had no means of stopping Tom's ears, and no microphone with which to explore the darkness for sounds inaudible to our ears.
The above explanation is open to serious objections. The chief of these, aside from such acuteness of hearing, is the fact that at no moment during the hour or more we were experimenting with him did Tom show the least doubt as to his direction. The auditory constant, therefore, must have been uninterrupted, and supposing it to have been the mewing of some cat, or cats, we all know what the possibilities are. At the time, the writer was quite convinced to the contrary, but several years afterward an incident occurred which threw the balance of probability strongly toward the side of the auditory explanation.
While hunting deer in Montana, I once lay on the top of a hill watching a doe as she kept guard while her two fawns were feeding. The three deer were in about the middle of a level grassy plain fully half a mile from where I lay. I focused my field glasses on the group, and soon became much interested in the alertness of the doe. Not for an instant did she show the slightest relaxation of attention. Generally, under such circumstances, a deer is seen to sniff the air in every direction, but this time no air was stirring, and the main feature of the watching was the constant movement of the long ears. At a slight noise, occasioned by my change of position, a noise not even noticed by myself, I was surprised to see the doe start, turn about, and point her ears in my direction. After a minute's silence, her attention was attracted elsewhere, and this time I made the lowest possible "ahem!" Again both ears and head were directed toward me. And so in turn for an hour, I tried all manners of slight sounds, low whistles, snapping the fingers, tapping my rifle stock, scraping the grass with my foot; all were followed, with the precision of the response of a strychnized frog, with the attent turning of the ears in my direction. The writer at that time was not familiar with any special apparatus for the purpose, and so can give no exact measure of the sounds employed. I can only say, however, that they were so slight that, if a deer could hear them half a mile away over a grassy plain, it might be an easy matter for a cat to hear a moderately loud "mew" a mile away, over the surface of water on a still night.
It is not rare to find great differences in keenness of sense among different men. These differences become emphasized by use, as we find in the sight of the sailor or savage, or in the touch of the blind. There is every reason why we should expect to find such differences much more pronounced between different species of animals. So marked, in fact, do they appear that the temptation has always been to declare them differences in kind. Before doing this, we ought to make a beginning, at least, to learn the possibilities of the senses as they exist in different animals. So far as the writer has gone in this direction, he is content to conclude that they are using the ordinary senses, highly refined, it may be, by generations of development; and the every-day logic which tells man and animal alike that the shortest path between two points is a straight line.
In the course of his journeyings in the Pamirs, the Earl of Dunmore came upon a beautifully clear sheet of water, out of which the Yambulak River flows. It is surrounded on three sides by stupendous cliffs, rising sheer up two thousand feet from the water's edge, with one huge glacier standing out in bold relief in the middle of them, "which doubtless," he says, "gave the water the most beautiful emerald hue I ever saw." The altitude of the lake is 15,800 feet, and the summit of the Yambulak Pass beyond it is 16,530 feet high.