VII

"Round about the cauldron go;In the poison'd entrails throw.Toad, that under coldest stone,Days and nights has thirty-oneSwelter'd venom sleeping got,Boil thou first i' the charmed pot!Fillet of a fenny snake,In the cauldron boil and bake;Eye of newt and toe of frog,Wool of bat and tongue of dog,Adder's fork, and blind-worm's sting,Lizard's leg, and owlet's wing,For a charm of powerful trouble,Like a hell-broth boil and bubble.Scale of dragon, tooth of wolf;Witches' mummy; maw and gulf,Of the ravin'd salt-sea shark;Root of hemlock digg'd i' the dark;Liver of blaspheming Jew;Gall of goat, and slips of yew,Silvered in the moon's eclipse;Nose of Turk, and Tartar's lips;Finger of birth-strangled babe,Ditch deliver'd by a drab,—Make the gruel thick and slab;Add thereto a tiger's chaudron,For the ingredients of our cauldron.Cool it with the baboon's blood,Then the charm is firm and good."

From folk-medicine to false and absurd forms of remedial systems, the transition is slight. For present purposes the most instructive of such systematized beliefs is the doctrine of sympathy, of which the most familiar survival is the phrase, "to take a hair of the dog that bit you." The system appeared in various phases and at various times. We find Paracelsus a believer in it in the form of a "weapon salve," which is to be applied to the weapon that caused the wound and thereby to heal the wound; weapon and wound having once been related as cause and effect, this relation is supposed to insure further connection. The system found wide circulation through the efforts of Sir Kenelm Digby. While Sir Kenelm's practices involved bad observation and ignorance of medicine, what gave the method its plausibility and induced the faulty observation was an underlying belief in the argument by analogy. His treatment may be gathered from a story he tells of aMr. Howell, whose hand was cut in an attempt to stop a duel between friends. Sir Kenelm arrives on the scene and asks for anything that had the blood upon it; he is given the garter wherewith the hand was first bound; this he places in a basin of water, when suddenly Mr. Howell, who is unaware of what is going on, experiences a cooling effect and a relief from pain. When the garter is placed before a great fire, Mr. Howell experiences an intense burning in the wound. Still another form of this idea appears in the "sympathetic alphabet," in which each of two friends cuts out a piece of his skin and has it transferred to the other; on this grafted skin an alphabet is tattooed, and when a letter is pricked on the skin of the one friend, the other feels the pain at the corresponding point; and thus intercourse is established. A still more curious form of the doctrine appears in an out-of-the-way pamphlet; its title (a German translation from the French) is "The Thought Telegraph: or the instantaneous communication of thought at any distance, even from one end of the world to the other, by means of a portable machine. The most wonderful invention of our age." The true basis of the method, we are told, depends upon a "sympathetic-galvano, magnetic, mineral, animal, adamitic fluid;" the practice depends upon the alleged discovery of a species of snails, placed in a sympathetic relation, so that ever after their movements are in harmony. Accordingly each operator takes one of the snails and places it upon the alphabet chart; the snail crawls over the chart resting upon certain letters, and the other snail, however far removed, will do just the same, and thus the thought-telegraph willbe established. Like Charles the Second's famous fish, that would not add to the weight of a dish of water in which it was placed, it lacks nothing but truth to be a great invention. Practices of the same general nature are still current; in the Netherlands, the knife that cut one is rubbed with fat in the belief that as the fat dries the wound will heal. The relation may become more remotely analogical and more arbitrary, as when, to cure ague, as many notches are cut in a stick as there have been fits; as the stick dries the ague is to disappear; ruptured children are passed through a split tree, and thus a sympathy is produced between child and tree, so that as the tree heals the child will be cured. A like sympathy is supposed to exist between celestial objects and human events; this is particularly applied to the moon, the moon's growth and wane indicating the fortunate times for growth and decay of earthly things. One must sow grain, cut the hair, and perform sundry other operations with the increase of the moon, to insure increase of growth. The tides are similarly significant, as the ever-pathetic Barkis "going out with the tide" sufficiently illustrates.

While in the doctrine of sympathy, the resemblance basal to the analogy is one of relation,—such as the relation of cause and effect, of owner and the object owned, of implement and the action performed by its use,—in the doctrine of seals or signatures, the resemblance is an outward, usually a visible one, of form, color, or the possession of marked peculiarities. Underlying this doctrine seems to be the belief that no object or event is without profound significance forman's welfare. The key to this significance is to be found in a resemblance obvious or remote, actual or ideal. Hence the uses of things are suggested by their appearance. The euphrasia or eyebright is useful in case of sore eyes on account of the bright eye-like spot in its corolla; special virtues are ascribed to the ginseng on account of the resemblance of its roots to a human shape. The granulated roots of the white meadow saxifrage were regarded as efficacious against calculous complaints. The Solomon's-seal is so called on account of the marks in the cross-section of its roots, and is used to seal wounds. Water-soldier, on account of its sword-shaped leaves, was regarded as useful for gunshot wounds. The red rose suggests its use in blood diseases; and yellow flowers were used in jaundice and liver complaints. The walnut was clearly defined for use in mental diseases: for its shape was that of the head, the outer green covering being the pericranium, the hard shell the skull, and the kernel the brain. Old ladies' thistle was for stitches in the side, nettle tea for nettle-rash, hearts'-ease for heart troubles. Plants whose parts resembled teeth were prescribed for toothache, quaking grass against shakes, and so on with consistent illogicality (Dyer). The resemblances here involved are obvious enough; they are just such as underlie popular names of plants and the metaphorical use of terms. They form another illustration of how metaphor and analogy overlap; what we accept as a sufficient suggestion for an appropriate name was by pseudo-science, by folk-lore, or by superstition regarded as sufficiently significant to support a cause-and-effect-like or a teleological relation.This, furthermore, is a line of practice in which modern superstition and savage belief stand on an equal footing; the prescriptions just cited are matched by the operations of the Cherokee, who make "a decoction of the cone-flower for weak eyes because of the fancied resemblance of that plant to the strong-sighted eye of the deer" (Clodd); who carry out the notion more elaborately when they "drink an infusion of the tenacious burrs of the common beggars'-lice, an American species of the genus Desmodium, to strengthen the memory," or to "insure a fine voice, boil crickets and drink the liquor" (Clodd). The "Zulu medicine-man, who takes the bones of the oldest bull or dog of the tribe, giving scrapings of these to the sick, so that their lives may be prolonged to old age," in turn finds a parallel in the seventeenth-century doctors, "who, with less logic, but perchance unconscious humor, gave their patients pulverized mummy to prolong their years" (cited by Clodd). Analogy in savagery, in pseudo-science, and in undeveloped science, in superstition and in survival, are of a nature all compact.

The transition from magic to science was made possible by, and itself illustrates the supplanting of, loose and false reasoning by close and logical thought; the pseudo-sciences represent weak and erroneous inference even more than they embody defective observation or mere ignorance. An over-dependence upon analogy characterizes some portions of them all, and finds its fullest development in astrology, as also in the various forms of alchemy and magic with which it is historically connected. Although this body of thought engaged the energies of many able and famous scholars, wecan look upon it only as a system of resemblances and coincidences, elaborate and complex indeed, but requiring little more than a vivid imagination and a somewhat keen sense for far-fetched analogies. "This investigation," says the astrologer in Rydberg's "Magic of the Middle Ages," "relies on the resemblances of things, for this similarity is derived from a correspondence, and causality is interwoven with correspondence. Thus, for instance, we judge from the resemblance between the splendor of gold and that of the sun, that gold has its celestial correspondence in that luminary and sustains to it a causal relation." Again, "the two-horned beetle bears a causal relation to the moon, which at its increase and wane is also two-horned; and if there were any doubt of this intimate relation between them, it must vanish when we learn that the beetle hides its eggs in the earth for the space of twenty-eight days, or just so long a time as is required for the moon to pass through the zodiac, but digs them up again on the twenty-ninth, when the moon is in conjunction with the sun." (Agrippa, "De Occulta Philosophiæ," i. 24.)

It will readily be seen how limitless are the results obtainable with such a system. Each planet becomes associated with a definite part of the body, and an argument such as the following becomes possible: "Since Capricornus, which presided over the knees in the house of Saturn, and all crawling animals are connected with the planet, the fat of snakes is an effective remedy against gout in the knees, especially on Saturday, the day of Saturn" (Rydberg). Tables of correspondences were freely devised showing the representativesof the sun, moon, and five planets among the elements, the microcosm, animals, plants, metals, and stones. Thus Mars was represented in these spheres respectively, by fire, acid juices, beasts of prey, burning, poisonous and stinging plants, iron or sulphuric metals, diamond, jasper, amethyst, and magnet; the vein of analogy lying in the fierce character of the god, whose name the planet bears. This idea of correspondence dominates the queer collection of odds and ends by which the old-time magician worked his charms. "Here," for instance, he would say, "is a plate of lead on which is engraved the symbol of a planet; and beside it a leaden flask containing gall. If I now take a piece of fine onyx marked with the same planet symbol and this dried cypress branch, and add to them the skin of a snake and the feather of an owl, you will need but to look into one of the tables given you to find that I have only collected various things in the elementary world which bear a relation of mutual activity to Saturn, and if rightly combined can attract both the powers of that planet and of the angels with which it is connected" (Rydberg). Mr. Tylor thus ably characterizes the analogies on which such systems are built and the uses to which they are put. "But most of his pseudo-science seems to rest on even weaker and more arbitrary analogies, not of things but of names. Names of stars and constellations, of signs denoting regions of the sky and periods of days and years, no matter how arbitrarily given, are materials which the astrologer can work upon and bring into ideal connection with mundane events. That astronomers should have divided the sun's course into imaginarysigns of the zodiac, was enough to originate astrological rules, that these celestial signs have an actual effect on real earthly rams, bulls, crabs, lions, virgins. A child born under the sign of the lion will be courageous, but one under the crab will not go forward in life; one born under the waterman will be drowned, and so forth.... Again, simply because astronomers chose to distribute among the planets the names of certain deities, the planets thereby acquired the characters of their divine namesakes. Thus it was that the planet Venus became connected with love, Mars with war, Jupiter (whose ♃ in altered shape still heads our physicians' prescriptions) with power and joviality." The various positions of the heavenly bodies at one's birth, interpreted by such wild analogies, readily yield material for the prediction of future careers, vague enough to defy close denial, and bold enough to claim readily foreseeable consequences as striking verifications. Astrology represents the climax of the argument by analogy, fully systematized and calling into play many of the resources of modern learning. What is so clearly represented in astrology appears to a less extent in other pseudo-scientific systems; notably in palmistry and phrenology. It captivates the well-informed as well as the ignorant, it appeals to minds that are strong as well as those that are weak, and emphasizes the pricelessness of our scientific inheritance and the necessity of guarding it by the cultivation of sound logical habits of thought.

It would be pleasant, but unwarranted, to think of these forms of thought as obsolete; human nature ismore deep-seated than learning. "In every department of human thought," says Mr. Clodd, "evidence of the non-persistence of primitive ideas is the exception rather than the rule. Scratch the epiderm of the civilized man, and the barbarian is found in the derm. In proof of which, there are more people who believe in Zadkiel's 'Vox Stellarum' than in the Nautical Almanac; and rare are the households where the 'Book of Dreams' and 'Fortune-Teller' are not to be found in the kitchen. The Singhalese caster of nativities has many representatives in the West, and there may lie profit in the reminder of the shallow depth to which knowledge of the orderly sequence of things has yet penetrated in the many. Societies and serials for the promulgation of astrology exist and flourish among us; Zadkiel boasts his circulation of a hundred thousand, and vaunts the fulfillment of his Delphic prophecies; while the late Astronomer Royal, Sir George Airy, was pestered, as his successor probably is, with requests to work the planets, accompanied by silver wherewith to cross his expert palm." The old astrology finds its descendants in modern fatuous volumes on Heliocentric Astrology, or Kabalistic Astrology, abounding in absurd pseudo-philosophic jargon and science-aping demonstrations, but in reality only the "vulgarest travesty of the old."

By way of conclusion it may be helpful to consider certain general truths in the field of anthropology and mental evolution, upon which the illustrations we have been considering have a bearing. We have seen what a widely extended genus the analogical argument compasses;and yet, if we were to include under this head certain closely allied and yet distinguishable forms of thought, it would be much wider still. I refer particularly to the use of metaphor and symbolism, which, like the children's make-believe with their dolls or fairies, is none the less on the boundary line between the real and the fictitious. Myth equally readily passes from the unconscious to the conscious stage, and much of what is plausibly interpreted as an argument by analogy, seems equally well an intentional use of symbolism and myth. That savages, at least in all but the lower stages, appreciate the use of myth is beyond all doubt. Primitive ceremonials, as also primitive explanations of the changes of nature, are full of symbolisms, which involve the same mental habit, whose products in the domain of analogy have been portrayed. This mythological instinct, Mr. Tylor well says, "belongs to that great doctrine of analogy from which we have gained so much of our apprehension of the world around us. Distrusted as it now is by severer science for its misleading results, analogy is to us still a chief means of discovery and illustration, while in earlier grades of education its influence was all but paramount. Analogies which are but fancies to us were to men of past ages reality. They could see the flame licking its yet undevoured prey with tongues of fire, or the serpent gliding along the sword from hilt to point; they could see a live creature gnawing within their bodies in the pangs of hunger; they heard the voices of the hill-dwarfs answering in the echo, and the chariot of the heaven god rattling in thunder over the solid firmament. Men to whom these were living thoughts hadno need of the schoolmaster and his rules of composition, his injunctions to use metaphor cautiously and to take care to make all similes consistent."

The principle that what was once the serious occupation of men becomes in more advanced stages of culture the play of children, or is reduced from seriousness to mere amusement, finds illustrations in the mental as in the material world. The drum, once the serious terrifying instrument of the savage warrior, and the rattle, once the powerful emblem of the medicine man, have become the common toys of children. The bow and arrow are used for skill and sport only. In a similar way the formidable and trusted argument by analogy finds its proper field in riddles and puns. When we put the question, "Why is this object like the other?" we understand that some out-of-the-way and accidental resemblance is asked for, some not very close analogy, that provokes amusement but not belief; in many cases the resemblance is in the name only and degenerates into a pun. In such exercises of fancy we are employing the same faculties that our ancestors used in arriving at the customs and beliefs that we have been considering. The laws governing the progress of industrial arts, of mechanical inventions and social institutions seem thus to find equally ready application to the evolution of habits and customs in the mental world.

From another, and that also a comparative anthropological point of view, the natural history of analogy illustrates, though imperfectly, the evolutionary bond that unites the development of the race from primitive culture to civilization, from infantile helplessness toadult power, and again the dissolution of these processes in disease or their atavistic retention in less progressive strata of society. Significant, even though sporadic, parallelisms have been pointed out in the use of analogy by savages and by children; and far more completely can it be shown that superstitions and pseudo-sciences, folk-lore traditions and popular beliefs show the survival of these same analogical habits of mind, which may be viewed in part as reversions to outgrown conditions of thought, in part as the cropping out, in pathological form, of retarding tendencies which the course of evolution may have repressed but not wholly destroyed. For there is hardly a form of modern superstition, there is hardly a custom sanctioned by the unwritten tradition of the people, but what can be closely duplicated among the customs and beliefs of the untutored savage.

All this impresses us with the enduring qualities of man's barbaric past, the permanent though latent effect of his complete adaptation for thousands of years to a low intellectual environment. "The intrusion of the scientific method," Mr. Clodd aptly comments, "in its application to man's whole nature, disturbed that equilibrium. But this, as yet, only within the narrow area of the highest culture." The earlier and more fundamental psychological factor of humanity is feeling and not thought, or more accurately an incipient rationality, thoroughly suffused with emotional motives; and primitive analogies proceed by a feeling of analogical fitness, and not by an intellectual justification. "The exercise of feeling has been active from the beginning of his history, while thought, speakingcomparatively, has but recently had free play.... Man wondered long chiliads before he reasoned, because feeling travels along the line of least resistance, while thought, or the challenge by inquiry, with its assumption that there may be two sides to a question, must pursue a path obstructed by the dominance of taboo and custom, by the force of imitation, and by the strength of prejudice, passion, and fear."

The survey of the argument by analogy brings home the conviction that there are forms of mental action, psychological tendencies or thought-habits, characteristic of undeveloped stages of human mentality; that these appear in versatile and instructive variety; and, more important still, that they furnish glimpses of the workings of a great progressive law, visible in the shifting of importance attached to the argument by analogy, and in its gradual subordination to, and ultimate retirement in favor of the sturdy principles of inductive logic. We are thus led to appreciate the means by which error is converted into truth, the slow and painful steps by which the logic of the sciences is unfolded and mastered. When Lord Chesterfield relates that the people expected a fatal issue of the king's illness, because the oldest lion in the tower, of about the same age as the king, had just died, he cannot help commenting upon the wildness and caprice of the human mind; but Mr. Tylor more judiciously remarks, "Indeed the thought was neither wild nor capricious; it was simply such an argument by analogy as the educated world has at length painfully learned to be worthless, but which it is not too much to declare would to this day carry considerable weight to theminds of four-fifths of the human race." Analogy has doubtless lost the prestige of olden time; but the remains of effete and misleading forms of thought, upheld by a feeling of their analogical plausibility, continue to survive, and may at any time, when cloaked in a modern garb, regain their former efficiency, and feed the contagion of some new fad or pseudo-science; while superstition, like poverty, we shall always have with us, so long as there are social and intellectual distinctions amongst men. In the light of the natural history survey of analogy, these phenomena appear in their true significance, testifying at once to the inherent progress, despite reversions, and to the underlying unity of constitution and purpose, through which these phenomena acquire their deeper and more human interest.

Hamlet.My father,—methinks, I see my father.Horatio.O, where, my lord?Hamlet.In my mind's eye, Horatio.

It is a commonplace taught from nursery to university that we see with our eyes, hear with our ears, and feel with our fingers. This is the truth, but not the whole truth. Indispensable as are the sense organs in gaining an acquaintance with the world in which we live, yet they alone do not determine how extensive or how accurate that acquaintance shall be. There is a mind behind the eye and the ear and the finger-tips which guides them in gathering information, and gives value and order to the exercise of the senses. This is particularly true of vision,—the most intellectual of all the senses, the one in which mere acuteness of the sense organ counts least and the training in observation counts most. The eagle's eye sees farther, but our eyes tell us vastly more of what is seen.

The eye may be compared to a photographic camera, with its eyelid cap, its iris shutter, its lens, and its sensitive plate,—the retina; when properly adjusted for distance and light, the image is formed on the retina as on the glass plate, and the picture is taken. So far the comparison is helpful; but while the camera takes a picture whenever and wherever the plate happens tobe exposed, the complete act of seeing requires some coöperation on the part of the mind. The retina may be exposed a thousand times and take but few pictures; or perhaps it is better to say that the pictures may be taken, but remain undeveloped and evanescent. The pictures that are developed are stacked up, like the negatives in the photographer's shop, in the pigeon-holes of our mental storerooms,—some faded and blurred, some poorly arranged or mislaid, some often referred to and fresh prints made therefrom, and some quite neglected.

In order to see, it is at once necessary that the retina be suitably exposed toward the object to be seen, and that the mind be favorably disposed to the assimilation of the impression. True seeing, observing, is a double process, partly objective or outward—the thing seen and the retina,—and partly subjective or inward—the picture mysteriously transferred to the mind's representative, the brain, and there received and affiliated with other images. Illustrations of such seeing with the "mind's eye" are not far to seek. Wherever the beauties and conformations of natural scenery invite the eye of man, does he discover familiar forms and faces; the forces of nature have rough-hewn the rocks, but the human eye detects and often creates the resemblances. The stranger to whom such curiosities of form are first pointed out often finds it difficult to discover the resemblance, but once seen, the face or form obtrudes itself in every view, and seems the most conspicuous feature in the outlook. The flickering fire furnishes a fine background for the activity of the mind's eye, and against this it projects the forms andfancies which the leaping flames and the burning embers from time to time suggest. Not all see these fire-pictures readily, for our mental eyes differ more from one another than the physical ones, and perhaps no two persons see the same picture in quite the same way. It is not quite true, however, as many have held, that in waking hours we all have a world in common, but in dreams each has a world of his own; for our waking worlds are made different by the differences in what engages our interest and our attention. It is true that our eyes when open are opened very largely to the same views, but by no one observer are all these views, though visible, really seen.

This characteristic of vision often serves as a source of amusement. The puzzle picture with its tantalizing face, or animal, or what not, hidden in the trees, or fantastically constructed out of heterogeneous elements that make up the composition, is to many quite irresistible. We turn it about in all directions, wondering where the hidden form can be, scanning every detail of the picture, until suddenly a chance glimpse reveals it, plainly staring us in the face. When several persons are engaged in this occupation, it is amusing to observe how blind each is to what the others see; their physical eyes see alike, but their mental eyes reflect their own individualities.

Of the many thousands of persons who handle our silver dollar, but few happen to observe the lion's head which lies concealed in the representation of the familiar head of Liberty; frequently even a careful examination fails to detect this hidden emblem of British rule; but, as before, when once found, it is quiteobvious (Fig. 1).[10]For similar reasons it is a great aid in looking for an object to know what to look for; to be readily found, the object, though lost to sight, should be to memory clear. Searching is a mental process similar to the matching of a piece of fabric in texture or color, when one has forgotten the sample and must rely upon the remembrance of its appearance. If the recollection is clear and distinct, recognition takes place when the judgment decides that what the physical eye sees corresponds to the image in the mind's eye; with an indistinct mental image the recognition becomes doubtful or faulty. The novice in the use of the microscope experiences considerable difficulty in observing the appearance which his instructor sees and describes, and this because his conception of the object to be seen is lacking in precision. Hence his training in the use of the microscope is distinctly aided by consulting the illustrations in the textbook, for they enable his mental eye to realize the pictures which it should entertain. He may be altogether too much influenced by the pictures thus suggested to his mental vision, and draw what is really not under his microscope at all; much as the young arithmetician will manage to obtain the answer which the book requires even at the cost of a resort to veryunmathematical processes. For training in correct and accurate vision it is necessary to acquire an alert mental eye, that observes all that is objectively visible, but does not permit the subjective to add to or modify what is really present.

Fig. 1.—In order to see the lion's head, look at the above cut upside down, and the head will be discovered facing the left, as above outlined. It is clearer on the coin itself than in this representation.

Fig. 2.—These letters should not be seen at all until they have been observed at a distance of eight to twelve feet. An interesting method of testing the activity of the mind's eye with these letters is described in the text.

Fig. 2a.

Fig. 2b.

Fig. 3.—For description, see text, page 282.

The importance of the mind's eye in ordinary vision is also well illustrated in cases in which we see or seem to see what is not really present, but what for one cause or another it is natural to suppose is present. A very familiar instance of this process is the constant overlooking of misprints—false letters, transposed letters, and missing letters—unless these happen to be particularly striking. We see only the general physiognomy of the word, and the detailed features are supplied from within; in this case it is the expected that happens. In a series of experiments by ProfessorMünsterberg a word was briefly shown, while just before a certain idea or train of thought was suggested. Under these circumstances the word shown was often misread in accordance with the suggested idea; if the idea of future is suggested, part may be read as past; if vegetable is the suggested line of thought, fright may be read as fruit, and so on. Reading is thus done largely by the mental eye; and entire words, obviously suggested by the context, are sometimes read in, when they have been accidentally omitted. This is more apt to occur with the irregular characters used in manuscript than in the more distinct forms of the printed alphabet, and is particularly frequent in reading over what one has himself written. In reading proof, however, we are eager to detect misprints, and this change in attitude helps to make them visible. It is very difficult to illustrate this process intentionally, because the knowledge that one's powers of observation are about to be tested places one on one's guard, and thus suppresses the natural activity of the mind's eye and draws unusual attention to objective details. Let the reader at this point hold the page at some distance off—say, eight or twelve feet—and draw an exact reproduction of the letters shown in Fig. 2. He should not look at Fig. 2 at close range nor read further in the text until this has been done; andperhapshe may find that he has introduced strokes which were not present in the original. If this is not the case, let him try the test upon those who are ignorant of its nature, and he will find that most persons will supply light lines to complete the contours of the letters, which in the original are suggested but not really present; theoriginal outline, Fig. 2a, becomes something like Fig. 2b, and so on for the rest of the letters. The physical eye sees the former, but the mental eye sees the latter. I tried this experiment with a class of some thirty University students of Psychology, and, although they were disposed to be quite critical and suspected somekind of an illusion, only three or four drew the letters correctly; all the rest filled in the imaginary light contours; some even drew them as heavily as the real strokes. I followed this by an experiment of a similar character. I placed upon a table a figure (Fig. 3) made of light cardboard, fastened to blocks of wood at the base, so that the pieces would easily stand upright. The middle piece, which is rectangular and higher than the rest, was placed a little in front of the rest of the figure. The students were asked to describe precisely what they saw; and with one exception they all described, in different words, a semicircular piece of cardboard with a rectangular piece in front of it. In reality there was no half-circle of cardboard, but only portions of two quarter-circles with the portion back of the middle piece omitted. The students, of course, were well aware that their physical eyes could not see what was behind the middle cardboard, but they inferred, quite naturally, that the two side pieces were parts of one continuous semicircle. This they saw, so far as they saw it at all, with their mind's eye.

Fig. 4.—The black and white portions of this design are precisely alike; but the effect of looking at the figure as a pattern in black upon a white background, or as a pattern in white upon a black background is quite different, although the difference is not easily described.

There is a further interesting class of illustrations in which a single outward impression changes its character according as it is viewed as representing one thing or another. In a general way we see the same thing all the time, and the image on the retina does not change. But as we shift the attention from one portion of the view to another, or as we view it with a different mental conception of what the figure represents, it assumes a different aspect, and to our mentaleye becomes quite a different thing. A slight but interesting change takes place if we view Fig. 4 first with the conception that the black is the pattern to be seen and the white the background, and again try to see the white as the pattern against a black background. I give a further illustration of such a change in Fig. 5. In our first and natural view of this we focus the attention upon the black lines and observe the familiar illusion, that the four vertical black bands seem far from parallel. That they are parallel can be verified by measurement, or by covering up all of the diagram except the four main bands. But if the white part of the diagram be conceived as the design against a black background, then the design is no longer the same, and with this change the illusion disappears, andthe four bands seem parallel, as they really are. It may require a little effort to bring about this change, but it is marked when once realized.

Fig. 5.—When this figure is viewed as a black pattern on a white background, the four main vertical black bands seem far from parallel; when it is viewed as a white pattern on a black background the pattern is different and the illusion disappears (or nearly so), and the four black bands as well as the five white ones seem more nearly parallel.

A curious optical effect, which in part illustrates the change in appearance under different aspects, is reproduced in Fig. 6. In this case the enchantment of distance is necessary to produce the transformation. Viewed at the usual reading distance, we see nothing but an irregular and meaningless assemblage of black and white blotches. At a distance of not less than fifteen to eighteen feet, however, a man's head appearsquite clearly. Also observe that after the head has once been realized it becomes possible to obtain suggestions of it at nearer distances.

Fig. 6.—This is a highly enlarged reproduction taken from a half-tone process print of Lord Kelvin. It appeared in thePhotographic Times.

A much larger class of ambiguous diagrams consists of those which represent by simple outlines familiar geometrical forms or objects. We cultivate such a use of our eyes, as indeed of all our faculties, as will on the whole lead to the most profitable results. As a rule, the particular impression is not so important as what it represents. Sense-impressions are simply the symbols or signs of things or ideas, and the thing or the idea is more important than the sign. Accordingly, we are accustomed to interpret lines, wheneverwe can, as the representations of objects. We are well aware that the canvas or the etching or the photograph before us is a flat surface in two dimensions, but we see the picture as the representation of solid objects in three dimensions. This is the illusion of pictorial art. So strong is this tendency to view lines as the symbols of things, that if there is the slightest chance of so viewing them, we invariably do so; for we have a great deal of experience with things that present their contours as lines, and very little with mere lines or surfaces. If we view outlines only, without shading or perspective or anything to definitely suggest what is foreground and what background, itbecomes possible for the mind to supply these details and see foreground as background, andvice versa.

Fig. 7.—This drawing may be viewed as the representation of a book standing on its half-opened covers as seen from the back of the book; or as the inside view of an open book showing the pages.

Fig. 8.—When this figure is viewed as an arrow, the upper or feathered end is apt to seem flat; when the rest of the arrow is covered, the feathered end may be made to project or recede like the book-cover in Fig. 7.

Fig. 9.—The smaller square may be regarded as either the nearer face of a projecting figure or as the more distant face of a hollow figure.

Fig. 10.—This represents an ordinary table-glass,—the bottom of the glass and the entire rear side, except the upper portion, being seen through the transparent nearer side, and the rear apparently projecting above the front. But it fluctuates in appearance between this and a view of the glass in which the bottom is seen directly, partly from underneath, thewholeof the rear side is seen through the transparent front, and the front projects above the back.

Fig. 11.—In this scroll the left half may at first seem concave and the right convex; it then seems to roll or advance like a wave, and the left seems convex and the right concave, as though the trough of the wave had become the crest, andvice versa.

A good example to begin with is Fig. 7. These outlines will probably suggest at first view a book, or better a book-cover, seen with its back toward you and its sides sloping away from you; but it may also be viewed as a book opened out towards you and presenting to you an inside view of its contents. Should the change not come readily, it may be facilitated by thinking persistently of the appearance of an open book in this position. The upper portion of Fig. 8 is practically the same as Fig. 7, and if the rest of the figure be covered up, it will change as did the book cover; when, however, the whole figure is viewed as an arrow, a new conception enters, and the apparently solid book cover becomes theflatfeathered part of the arrow. Look at the next figure (Fig. 9), which represents in outline a truncated pyramid with a square base.Is the smaller square nearer to you, and are the sides of the pyramid sloping away from you toward the larger square in the rear? Or are you looking into the hollow of a truncated pyramid with the smaller square in the background? Or is it now one and now the other, according as you decide to see it? Here (Fig. 12) is a skeleton box which you may conceive as made of wires outlining the sides. Now the front, or side nearest to me, seems directed downward and to the left; again, it has shifted its position and is no longer the front, and the side which appears to be the front seems directed upward and to the right. The presence of the diagonal line makes the change more striking: in one position it runs from the left-handrearupper corner to the right-handfrontlower corner; while in the other it connects the left-handfrontupper corner with the right-handrearlower corner.

Figs. 12, 12a, 12b.—The two methods of viewing Fig. 12 are described in the text. Figs. 12aand 12bare added to make clearer the two methods of viewing Fig. 12. The heavier lines seem to represent the nearer surface. Fig. 12amore naturally suggests the nearer surface of the box in a position downward and to the left, and Fig. 12bmakes the nearer side seem to be upward and to the right. But in spite of the heavier outlines of the one surface, it may be made to shift positions from foreground to background, although not so readily as in Fig. 12.

Fig. 14 will probably seem at first glimpse to be the view of a flight of steps which one is about to ascend from right to left. Imagine it, however, to be aview of the under side of a series of steps; the view representing the structure of overhanging solid masonwork seen from underneath. At first it may be difficult to see it thus, because the view of steps which we are about to mount is a more natural and frequent experience than the other; but by staring at it with the intention of seeing it differently the transition will come, and often quite unexpectedly.

Fig. 13.—Each member of this frieze represents a relief ornament, applied upon the background, which in cross-section would be an isosceles triangle with a large obtuse angle, or a space of similar shape hollowed out of the solid wood or stone. In running the eye along the pattern, it is interesting to observe how variously the patterns fluctuate from one of these aspects to the other.

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