To rear the Clotho is not an arduous undertaking; we are not obliged to take the heavy flagstone, on which the dwelling is built, away with us. A very simple operation suffices. I loosen the fastenings with my pocket- knife. The Spider has such stay-at-home ways that she very rarely makes off. Besides, I use the utmost discretion in my rape of the house. And so I carry away the building, together with its owner, in a paper bag.

The flat stones, which are too heavy to move and which would occupy too much room upon my table, are replaced either by deal disks, which once formed part of cheese-boxes, or by round pieces of cardboard. I arrange each silken hammock under one of these by itself, fastening the angular projections, one by one, with strips of gummed paper. The whole stands on three short pillars and gives a very fair imitation of the underrock shelter in the form of a small dolmen. Throughout this operation, if you are careful to avoid shocks and jolts, the Spider remains indoors. Finally, each apparatus is placed under a wire-gauze, bell-shaped cage, which stands in a dish filled with sand.

We can have an answer by the next morning. If, among the cabins swung from the ceilings of the deal or cardboard dolmens, there be one that is all dilapidated, that was seriously knocked out of shape at the time of removal, the Spider abandons it during the night and instals herself elsewhere, sometimes even on the trellis-work of the wire cage.

The new tent, the work of a few hours, attains hardly the diameter of a two-franc piece. It is built, however, on the same principles as the old manor-house and consists of two thin sheets laid one above the other, the upper one flat and forming a tester, the lower curved and pocket-shaped. The texture is extremely delicate: the least trifle would deform it, to the detriment of the available space, which is already much reduced and only just sufficient for the recluse.

Well, what has the Spider done to keep the gossamer stretched, to steady it and to make it retain its greatest capacity? Exactly what our static treatises would advise her to do: she has ballasted her structure, she has done her best to lower its centre of gravity. From the convex surface of the pocket hang long chaplets of grains of sand strung together with slender silken cords. To these sandy stalactites, which form a bushy beard, are added a few heavy lumps hung separately and lower down, at the end of a thread. The whole is a piece of ballast-work, an apparatus for ensuring equilibrium and tension.

The present edifice, hastily constructed in the space of a night, is the frail rough sketch of what the home will afterwards become. Successive layers will be added to it; and the partition-wall will grow into a thick blanket capable of partly retaining, by its own weight, the requisite curve and capacity. The Spider now abandons the stalactites of sand, which were used to keep the original pocket stretched, and confines herself to dumping down on her abode any more or less heavy object, mainly corpses of insects, because she need not look for these and finds them ready to hand after each meal. They are weights, not trophies; they take the place of materials that must otherwise be collected from a distance and hoisted to the top. In this way, a breastwork is obtained that strengthens and steadies the house. Additional equilibrium is often supplied by tiny shells and other objects hanging a long way down.

What would happen if one robbed an old dwelling, long since completed, of its outer covering? In case of such a disaster, would the Spider go back to the sandy stalactites, as a ready means of restoring stability? This is easily ascertained. In my hamlets under wire, I select a fair-sized cabin. I strip the exterior, carefully removing any foreign body. The silk reappears in its original whiteness. The tent looks magnificent, but seems to me too limp.

This is also the Spider's opinion. She sets to work, next evening, to put things right. And how? Once more with hanging strings of sand. In a few nights, the silk bag bristles with a long, thick beard of stalactites, a curious piece of work, excellently adapted to maintain the web in an unvaried curve. Even so are the cables of a suspension-bridge steadied by the weight of the superstructure.

Later, as the Spider goes on feeding, the remains of the victuals are embedded in the wall, the sand is shaken and gradually drops away and the home resumes its charnel-house appearance. This brings us to the same conclusion as before: the Clotho knows her statics; by means of additional weights, she is able to lower the centre of gravity and thus to give her dwelling the proper equilibrium and capacity.

Now what does she do in her softly-wadded home? Nothing, that I know of. With a full stomach, her legs luxuriously stretched over the downy carpet, she does nothing, thinks of nothing; she listens to the sound of earth revolving on its axis. It is not sleep, still less is it waking; it is a middle state where naught prevails save a dreamy consciousness of well-being. We ourselves, when comfortably in bed, enjoy, just before we fall asleep, a few moments of bliss, the prelude to cessation of thought and its train of worries; and those moments are among the sweetest in our lives. The Clotho seems to know similar moments and to make the most of them.

If I push open the door of the cabin, invariably I find the Spider lying motionless, as though in endless meditation. It needs the teasing of a straw to rouse her from her apathy. It needs the prick of hunger to bring her out of doors; and, as she is extremely temperate, her appearances outside are few and far between. During three years of assiduous observation, in the privacy of my study, I have not once seen her explore the domain of the wire cage by day. Not until a late hour at night does she venture forth in quest of victuals; and it is hardly feasible to follow her on her excursions.

Patience once enabled me to find her, at ten o'clock in the evening, taking the air on the flat roof of her house, where she was doubtless waiting for the game to pass. Startled by the light of my candle, the lover of darkness at once returned indoors, refusing to reveal any of her secrets. Only, next day, there was one more corpse hanging from the wall of the cabin, a proof that the chase was successfully resumed after my departure.

The Clotho, who is not only nocturnal, but also excessively shy, conceals her habits from us; she shows us her works, those precious historical documents, but hides her actions, especially the laying, which I estimate approximately to take place in October. The sum total of the eggs is divided into five or six small, flat, lentiform pockets, which, taken together, occupy the greater part of the maternal home. These capsules have each their own partition-wall of superb white satin, but they are so closely soldered, both together and to the floor of the house, that it is impossible to part them without tearing them, impossible, therefore, to obtain them separately. The eggs in all amount to about a hundred.

The mother sits upon the heap of pockets with the same devotion as a brooding hen. Maternity has not withered her. Although decreased in bulk, she retains an excellent look of health; her round belly and her well-stretched skin tell us from the first that her part is not yet wholly played.

The hatching takes place early. November has not arrived before the pockets contain the young: wee things clad in black, with five yellow specks, exactly like their elders. The new-born do not leave their respective nurseries. Packed close together, they spend the whole of the wintry season there, while the mother, squatting on the pile of cells, watches over the general safety, without knowing her family other than by the gentle trepidations felt through the partitions of the tiny chambers. The Labyrinth Spider has shown us how she maintains a permanent sitting for two months in her guard-room, to defend, in case of need, the brood which she will never see. The Clotho does the same during eight months, thus earning the right to set eyes for a little while on her family trotting around her in the main cabin and to assist at the final exodus, the great journey undertaken at the end of a thread.

When the summer heat arrives, in June, the young ones, probably aided by their mother, pierce the walls of their cells, leave the maternal tent, of which they know the secret outlet well, take the air on the threshold for a few hours and then fly away, carried to some distance by a funicular aeroplane, the first product of their spinning-mill.

The elder Clotho remains behind, careless of this emigration which leaves her alone. She is far from being faded indeed, she looks younger than ever. Her fresh colour, her robust appearance suggest great length of life, capable of producing a second family. On this subject I have but one document, a pretty far-reaching one, however. There were a few mothers whose actions I had the patience to watch, despite the wearisome minutiae of the rearing and the slowness of the result. These abandoned their dwellings after the departure of their young; and each went to weave a new one for herself on the wire net-work of the cage.

They were rough-and-ready summaries, the work of a night. Two hangings, one above the other, the upper one flat, the lower concave and ballasted with stalactites of grains of sand, formed the new home, which, strengthened daily by fresh layers, promised to become similar to the old one. Why does the Spider desert her former mansion, which is in no way dilapidated—far from it—and still exceedingly serviceable, as far as one can judge? Unless I am mistaken, I think I have an inkling of the reason.

The old cabin, comfortably wadded though it be, possesses serious disadvantages: it is littered with the ruins of the children's nurseries. These ruins are so close-welded to the rest of the home that my forceps cannot extract them without difficulty; and to remove them would be an exhausting business for the Clotho and possibly beyond her strength. It is a case of the resistance of Gordian knots, which not even the very spinstress who fastened them is capable of untying. The encumbering litter, therefore, will remain.

If the Spider were to stay alone, the reduction of space, when all is said, would hardly matter to her: she wants so little room, merely enough to move in! Besides, when you have spent seven or eight months in the cramping presence of those bedchambers, what can be the reason of a sudden need for greater space? I see but one: the Spider requires a roomy habitation, not for herself—she is satisfied with the smallest den—but for a second family. Where is she to place the pockets of eggs, if the ruins of the previous laying remain in the way? A new brood requires a new home. That, no doubt, is why, feeling that her ovaries are not yet dried up, the Spider shifts her quarters and founds a new establishment.

The facts observed are confined to this change of dwelling. I regret that other interests and the difficulties attendant upon a long upbringing did not allow me to pursue the question and definitely to settle the matter of the repeated layings and the longevity of the Clotho, as I did in that of the Lycosa.

Before taking leave of this Spider, let us glance at a curious problem which has already been set by the Lycosa's offspring. When carried for seven months on the mother's back, they keep in training as agile gymnasts without taking any nourishment. It is a familiar exercise for them, after a fall, which frequently occurs, to scramble up a leg of their mount and nimbly to resume their place in the saddle. They expend energy without receiving any material sustenance.

The sons of the Clotho, the Labyrinth Spider and many others confront us with the same riddle: they move, yet do not eat. At any period of the nursery stage, even in the heart of winter, on the bleak days of January, I tear the pockets of the one and the tabernacle of the other, expecting to find the swarm of youngsters lying in a state of complete inertia, numbed by the cold and by lack of food. Well, the result is quite different. The instant their cells are broken open, the anchorites run out and flee in every direction as nimbly as at the best moments of their normal liberty. It is marvellous to see them scampering about. No brood of Partridges, stumbled upon by a Dog, scatters more promptly.

Chicks, while still no more than tiny balls of yellow fluff, hasten up at the mother's call and scurry towards the plate of rice. Habit has made us indifferent to the spectacle of those pretty little animal machines, which work so nimbly and with such precision; we pay no attention, so simple does it all appear to us. Science examines and looks at things differently. She says to herself:

'Nothing is made with nothing. The chick feeds itself; it consumes or rather it assimilates and turns the food into heat, which is converted into energy.'

Were any one to tell us of a chick which, for seven or eight months on end, kept itself in condition for running, always fit, always brisk, without taking the least beakful of nourishment from the day when it left the egg, we could find no words strong enough to express our incredulity. Now this paradox of activity maintained without the stay of food is realized by the Clotho Spider and others.

I believe I have made it sufficiently clear that the young Lycosae take no food as long as they remain with their mother. Strictly speaking, doubt is just admissible, for observation is needs dumb as to what may happen earlier or later within the mysteries of the burrow. It seems possible that the repleted mother may there disgorge to her family a mite of the contents of her crop. To this suggestion the Clotho undertakes to make reply.

Like the Lycosa, she lives with her family; but the Clotho is separated from them by the walls of the cells in which the little ones are hermetically enclosed. In this condition, the transmission of solid nourishment becomes impossible. Should any one entertain a theory of nutritive humours cast up by the mother and filtering through the partitions at which the prisoners might come and drink, the Labyrinth Spider would at once dispel the idea. She dies a few weeks after her young are hatched; and the children, still locked in their satin bed-chamber for the best part of the year, are none the less active.

Can it be that they derive sustenance from the silken wrapper? Do they eat their house? The supposition is not absurd, for we have seen the Epeirae, before beginning a new web, swallow the ruins of the old. But the explanation cannot be accepted, as we learn from the Lycosa, whose family boasts no silky screen. In short, it is certain that the young, of whatever species, take absolutely no nourishment.

Lastly, we wonder whether they may possess within themselves reserves that come from the egg, fatty or other matters the gradual combustion of which would be transformed into mechanical force. If the expenditure of energy were of but short duration, a few hours or a few days, we could gladly welcome this idea of a motor viaticum, the attribute of every creature born into the world. The chick possesses it in a high degree: it is steady on its legs, it moves for a little while with the sole aid of the food wherewith the egg furnishes it; but soon, if the stomach is not kept supplied, the centre of energy becomes extinct and the bird dies. How would the chick fare if it were expected, for seven or eight months without stopping, to stand on its feet, to run about, to flee in the face of danger? Where would it stow the necessary reserves for such an amount of work?

The little Spider, in her turn, is a minute particle of no size at all. Where could she store enough fuel to keep up mobility during so long a period? The imagination shrinks in dismay before the thought of an atom endowed with inexhaustible motive oils.

We must needs, therefore, appeal to the immaterial, in particular to heat- rays coming from the outside and converted into movement by the organism. This is nutrition of energy reduced to its simplest expression: the motive heat, instead of being extracted from the food, is utilized direct, as supplied by the sun, which is the seat of all life. Inert matter has disconcerting secrets, as witness radium; living matter has secrets of its own, which are more wonderful still. Nothing tells us that science will not one day turn the suspicion suggested by the Spider into an established truth and a fundamental theory of physiology.



APPENDIX: THE GEOMETRY OF THE EPEIRA'S WEB

I find myself confronted with a subject which is not only highly interesting, but somewhat difficult: not that the subject is obscure; but it presupposes in the reader a certain knowledge of geometry: a strong meat too often neglected. I am not addressing geometricians, who are generally indifferent to questions of instinct, nor entomological collectors, who, as such, take no interest in mathematical theorems; I write for any one with sufficient intelligence to enjoy the lessons which the insect teaches.

What am I to do? To suppress this chapter were to leave out the most remarkable instance of Spider industry; to treat it as it should be treated, that is to say, with the whole armoury of scientific formulae, would be out of place in these modest pages. Let us take a middle course, avoiding both abstruse truths and complete ignorance.

Let us direct our attention to the nets of the Epeirae, preferably to those of the Silky Epeira and the Banded Epeira, so plentiful in the autumn, in my part of the country, and so remarkable for their bulk. We shall first observe that the radii are equally spaced; the angles formed by each consecutive pair are of perceptibly equal value; and this in spite of their number, which in the case of the Silky Epeira exceeds two score. We know by what strange means the Spider attains her ends and divides the area wherein the web is to be warped into a large number of equal sectors, a number which is almost invariable in the work of each species. An operation without method, governed, one might imagine, by an irresponsible whim, results in a beautiful rose-window worthy of our compasses.

We shall also notice that, in each sector, the various chords, the elements of the spiral windings, are parallel to one another and gradually draw closer together as they near the centre. With the two radiating lines that frame them they form obtuse angles on one side and acute angles on the other; and these angles remain constant in the same sector, because the chords are parallel.

There is more than this: these same angles, the obtuse as well as the acute, do not alter in value, from one sector to another, at any rate so far as the conscientious eye can judge. Taken as a whole, therefore, the rope-latticed edifice consists of a series of cross-bars intersecting the several radiating lines obliquely at angles of equal value.

By this characteristic we recognize the 'logarithmic spiral.' Geometricians give this name to the curve which intersects obliquely, at angles of unvarying value, all the straight lines or 'radii vectores' radiating from a centre called the 'Pole.' The Epeira's construction, therefore, is a series of chords joining the intersections of a logarithmic spiral with a series of radii. It would become merged in this spiral if the number of radii were infinite, for this would reduce the length of the rectilinear elements indefinitely and change this polygonal line into a curve.

To suggest an explanation why this spiral has so greatly exercised the meditations of science, let us confine ourselves for the present to a few statements of which the reader will find the proof in any treatise on higher geometry.

The logarithmic spiral describes an endless number of circuits around its pole, to which it constantly draws nearer without ever being able to reach it. This central point is indefinitely inaccessible at each approaching turn. It is obvious that this property is beyond our sensory scope. Even with the help of the best philosophical instruments, our sight could not follow its interminable windings and would soon abandon the attempt to divide the invisible. It is a volute to which the brain conceives no limits. The trained mind, alone, more discerning than our retina, sees clearly that which defies the perceptive faculties of the eye.

The Epeira complies to the best of her ability with this law of the endless volute. The spiral revolutions come closer together as they approach the pole. At a given distance, they stop abruptly; but, at this point, the auxiliary spiral, which is not destroyed in the central region, takes up the thread; and we see it, not without some surprise, draw nearer to the pole in ever-narrowing and scarcely perceptible circles. There is not, of course, absolute mathematical accuracy, but a very close approximation to that accuracy. The Epeira winds nearer and nearer round her pole, so far as her equipment, which, like our own, is defective, will allow her. One would believe her to be thoroughly versed in the laws of the spiral.

I will continue to set forth, without explanations, some of the properties of this curious curve. Picture a flexible thread wound round a logarithmic spiral. If we then unwind it, keeping it taut the while, its free extremity will describe a spiral similar at all points to the original. The curve will merely have changed places.

Jacques Bernouilli, {42} to whom geometry owes this magnificent theorem, had engraved on his tomb, as one of his proudest titles to fame, the generating spiral and its double, begotten of the unwinding of the thread. An inscription proclaimed, 'Eadem mutata resurgo: I rise again like unto myself.' Geometry would find it difficult to better this splendid flight of fancy towards the great problem of the hereafter.

There is another geometrical epitaph no less famous. Cicero, when quaestor in Sicily, searching for the tomb of Archimedes amid the thorns and brambles that cover us with oblivion, recognized it, among the ruins, by the geometrical figure engraved upon the stone: the cylinder circumscribing the sphere. Archimedes, in fact, was the first to know the approximate relation of circumference to diameter; from it he deduced the perimeter and surface of the circle, as well as the surface and volume of the sphere. He showed that the surface and volume of the last- named equal two-thirds of the surface and volume of the circumscribing cylinder. Disdaining all pompous inscription, the learned Syracusan honoured himself with his theorem as his sole epitaph. The geometrical figure proclaimed the individual's name as plainly as would any alphabetical characters.

To have done with this part of our subject, here is another property of the logarithmic spiral. Roll the curve along an indefinite straight line. Its pole will become displaced while still keeping on one straight line. The endless scroll leads to rectilinear progression; the perpetually varied begets uniformity.

Now is this logarithmic spiral, with its curious properties, merely a conception of the geometers, combining number and extent, at will, so as to imagine a tenebrous abyss wherein to practise their analytical methods afterwards? Is it a mere dream in the night of the intricate, an abstract riddle flung out for our understanding to browse upon?

No, it is a reality in the service of life, a method of construction frequently employed in animal architecture. The Mollusc, in particular, never rolls the winding ramp of the shell without reference to the scientific curve. The first-born of the species knew it and put it into practice; it was as perfect in the dawn of creation as it can be to-day.

Let us study, in this connection, the Ammonites, those venerable relics of what was once the highest expression of living things, at the time when the solid land was taking shape from the oceanic ooze. Cut and polished length-wise, the fossil shows a magnificent logarithmic spiral, the general pattern of the dwelling which was a pearl palace, with numerous chambers traversed by a siphuncular corridor.

To this day, the last representative of the Cephalopoda with partitioned shells, the Nautilus of the Southern Seas, remains faithful to the ancient design; it has not improved upon its distant predecessors. It has altered the position of the siphuncle, has placed it in the centre instead of leaving it on the back, but it still whirls its spiral logarithmically as did the Ammonites in the earliest ages of the world's existence.

And let us not run away with the idea that these princes of the Mollusc tribe have a monopoly of the scientific curve. In the stagnant waters of our grassy ditches, the flat shells, the humble Planorbes, sometimes no bigger than a duckweed, vie with the Ammonite and the Nautilus in matters of higher geometry. At least one of them, Planorbis vortex, for example, is a marvel of logarithmic whorls.

In the long-shaped shells, the structure becomes more complex, though remaining subject to the same fundamental laws. I have before my eyes some species of the genus Terebra, from New Caledonia. They are extremely tapering cones, attaining almost nine inches in length. Their surface is smooth and quite plain, without any of the usual ornaments, such as furrows, knots or strings of pearls. The spiral edifice is superb, graced with its own simplicity alone. I count a score of whorls which gradually decrease until they vanish in the delicate point. They are edged with a fine groove.

I take a pencil and draw a rough generating line to this cone; and, relying merely on the evidence of my eyes, which are more or less practised in geometric measurements, I find that the spiral groove intersects this generating line at an angle of unvarying value.

The consequence of this result is easily deduced. If projected on a plane perpendicular to the axis of the shell, the generating lines of the cone would become radii; and the groove which winds upwards from the base to the apex would be converted into a plane curve which, meeting those radii at an unvarying angle, would be neither more nor less than a logarithmic spiral. Conversely, the groove of the shell may be considered as the projection of this spiral on a conic surface.

Better still. Let us imagine a plane perpendicular to the aids of the shell and passing through its summit. Let us imagine, moreover, a thread wound along the spiral groove. Let us unroll the thread, holding it taut as we do so. Its extremity will not leave the plane and will describe a logarithmic spiral within it. It is, in a more complicated degree, a variant of Bernouilli's 'Eadem mutata resurgo:' the logarithmic conic curve becomes a logarithmic plane curve.

A similar geometry is found in the other shells with elongated cones, Turritellae, Spindle-shells, Cerithia, as well as in the shells with flattened cones, Trochidae, Turbines. The spherical shells, those whirled into a volute, are no exception to this rule. All, down to the common Snail-shell, are constructed according to logarithmic laws. The famous spiral of the geometers is the general plan followed by the Mollusc rolling its stone sheath.

Where do these glairy creatures pick up this science? We are told that the Mollusc derives from the Worm. One day, the Worm, rendered frisky by the sun, emancipated itself, brandished its tail and twisted it into a corkscrew for sheer glee. There and then the plan of the future spiral shell was discovered.

This is what is taught quite seriously, in these days, as the very last word in scientific progress. It remains to be seen up to what point the explanation is acceptable. The Spider, for her part, will have none of it. Unrelated to the appendix-lacking, corkscrew-twirling Worm, she is nevertheless familiar with the logarithmic spiral. From the celebrated curve she obtains merely a sort of framework; but, elementary though this framework be, it clearly marks the ideal edifice. The Epeira works on the same principles as the Mollusc of the convoluted shell.

The Mollusc has years wherein to construct its spiral and it uses the utmost finish in the whirling process. The Epeira, to spread her net, has but an hour's sitting at the most, wherefore the speed at which she works compels her to rest content with a simpler production. She shortens the task by confining herself to a skeleton of the curve which the other describes to perfection.

The Epeira, therefore, is versed in the geometric secrets of the Ammonite and the Nautilus pompilus; she uses, in a simpler form, the logarithmic line dear to the Snail. What guides her? There is no appeal here to a wriggle of some kind, as in the case of the Worm that ambitiously aspires to become a Mollusc. The animal must needs carry within itself a virtual diagram of its spiral. Accident, however fruitful in surprises we may presume it to be, can never have taught it the higher geometry wherein our own intelligence at once goes astray, without a strict preliminary training.

Are we to recognize a mere effect of organic structure in the Epeira's art? We readily think of the legs, which, endowed with a very varying power of extension, might serve as compasses. More or less bent, more or less outstretched, they would mechanically determine the angle whereat the spiral shall intersect the radius; they would maintain the parallel of the chords in each sector.

Certain objections arise to affirm that, in this instance, the tool is not the sole regulator of the work. Were the arrangement of the thread determined by the length of the legs, we should find the spiral volutes separated more widely from one another in proportion to the greater length of implement in the spinstress. We see this in the Banded Epeira and the Silky Epeira. The first has longer limbs and spaces her cross- threads more liberally than does the second, whose legs are shorter.

But we must not rely too much on this rule, say others. The Angular Epeira, the Paletinted Epeira and the Cross Spider, all three more or less short-limbed, rival the Banded Epeira in the spacing of their lime- snares. The last two even dispose them with greater intervening distances.

We recognize in another respect that the organization of the animal does not imply an immutable type of work. Before beginning the sticky spiral, the Epeirae first spin an auxiliary intended to strengthen the stays. This spiral, formed of plain, non-glutinous thread, starts from the centre and winds in rapidly-widening circles to the circumference. It is merely a temporary construction, whereof naught but the central part survives when the Spider has set its limy meshes. The second spiral, the essential part of the snare, proceeds, on the contrary, in serried coils from the circumference to the centre and is composed entirely of viscous cross-threads.

Here we have, following one after the other merely by a sudden alteration of the machine, two volutes of an entirely different order as regards direction, the number of whorls and intersection. Both of them are logarithmic spirals. I see no mechanism of the legs, be they long or short, that can account for this alteration.

Can it then be a premeditated design on the part of the Epeira? Can there be calculation, measurement of angles, gauging of the parallel by means of the eye or otherwise? I am inclined to think that there is none of all this, or at least nothing but an innate propensity, whose effects the animal is no more able to control than the flower is able to control the arrangement of its verticils. The Epeira practises higher geometry without knowing or caring. The thing works of itself and takes its impetus from an instinct imposed upon creation from the start.

The stone thrown by the hand returns to earth describing a certain curve; the dead leaf torn and wafted away by a breath of wind makes its journey from the tree to the ground with a similar curve. On neither the one side nor the other is there any action by the moving body to regulate the fall; nevertheless, the descent takes place according to a scientific trajectory, the 'parabola,' of which the section of a cone by a plane furnished the prototype to the geometer's speculations. A figure, which was at first but a tentative glimpse, becomes a reality by the fall of a pebble out of the vertical.

The same speculations take up the parabola once more, imagine it rolling on an indefinite straight line and ask what course does the focus of this curve follow. The answer comes: The focus of the parabola describes a 'catenary,' a line very simple in shape, but endowed with an algebraic symbol that has to resort to a kind of cabalistic number at variance with any sort of numeration, so much so that the unit refuses to express it, however much we subdivide the unit. It is called the number e. Its value is represented by the following series carried out ad infinitum:

e = 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + 1/(1*2*3*4*5) + etc

If the reader had the patience to work out the few initial terms of this series, which has no limit, because the series of natural numerals itself has none, he would find:

e=2.7182818...

With this weird number are we now stationed within the strictly defined realm of the imagination? Not at all: the catenary appears actually every time that weight and flexibility act in concert. The name is given to the curve formed by a chain suspended by two of its points which are not placed on a vertical line. It is the shape taken by a flexible cord when held at each end and relaxed; it is the line that governs the shape of a sail bellying in the wind; it is the curve of the nanny-goat's milk- bag when she returns from filling her trailing udder. And all this answers to the number e.

What a quantity of abstruse science for a bit of string! Let us not be surprised. A pellet of shot swinging at the end of a thread, a drop of dew trickling down a straw, a splash of water rippling under the kisses of the air, a mere trifle, after all, requires a titanic scaffolding when we wish to examine it with the eye of calculation. We need the club of Hercules to crush a fly.

Our methods of mathematical investigation are certainly ingenious; we cannot too much admire the mighty brains that have invented them; but how slow and laborious they appear when compared with the smallest actualities! Will it never be given to us to probe reality in a simpler fashion? Will our intelligence be able one day to dispense with the heavy arsenal of formulae? Why not?

Here we have the abracadabric number e reappearing, inscribed on a Spider's thread. Let us examine, on a misty morning, the meshwork that has been constructed during the night. Owing to their hygrometrical nature, the sticky threads are laden with tiny drops, and, bending under the burden, have become so many catenaries, so many chaplets of limpid gems, graceful chaplets arranged in exquisite order and following the curve of a swing. If the sun pierce the mist, the whole lights up with iridescent fires and becomes a resplendent cluster of diamonds. The number e is in its glory.

Geometry, that is to say, the science of harmony in space, presides over everything. We find it in the arrangement of the scales of a fir-cone, as in the arrangement of an Epeira's limy web; we find it in the spiral of a Snail-shell, in the chaplet of a Spider's thread, as in the orbit of a planet; it is everywhere, as perfect in the world of atoms as in the world of immensities.

And this universal geometry tells us of an Universal Geometrician, whose divine compass has measured all things. I prefer that, as an explanation of the logarithmic curve of the Ammonite and the Epeira, to the Worm screwing up the tip of its tail. It may not perhaps be in accordance with latter-day teaching, but it takes a loftier flight.



FOOTNOTES

{1} A small or moderate-sized spider found among foliage.—Translator's Note.

{2} Leon Dufour (1780-1865) was an army surgeon who served with distinction in several campaigns and subsequently practised as a doctor in the Landes. He attained great eminence as a naturalist.—Translator's Note.

{3} The Tarantula is a Lycosa, or Wolf-spider. Fabre's Tarantula, the Black-bellied Tarantula, is identical with the Narbonne Lycosa, under which name the description is continued in Chapters iii. to vi., all of which were written at a considerably later date than the present chapter.—Translator's Note.

{4} Giorgio Baglivi (1669-1707), professor of anatomy and medicine at Rome.—Translator's Note.

{5} 'When our husbandmen wish to catch them, they approach their hiding- places, and play on a thin grass pipe, making a sound not unlike the humming of bees. Hearing which, the Tarantula rushes out fiercely that she may catch the flies or other insects of this kind, whose buzzing she thinks it to be; but she herself is caught by her rustic trapper.'

{6} Provencal for the bit of waste ground on which the author studies his insects in the natural state.—Translator's note.

{7} 'Thanks to the Bumble-bee.'

{8} Like the Dung-beetles.—Translator's Note.

{9} Like the Solitary Wasps.—Translator's Note.

{10} Such as the Hairy Ammophila, the Cerceris and the Languedocian Sphex, Digger-wasps described in other of the author's essays.—Translator's Note.

{11} The desnucador, the Argentine slaughterman whose methods of slaying cattle are detailed in the author's essay entitled, The Theory of Instinct.—Translator's Note.

{12} A family of Grasshoppers.—Translator's Note.

{13} A genus of Beetles.—Translator's Note.

{14} A species of Digger-wasp.—Translator's Note.

{15} The Cicada is the Cigale, an insect akin to the Grasshopper and found more particularly in the South of France.—Translator's Note.

{16} The generic title of the work from which these essays are taken is Entomological Memories, or, Studies relating to the Instinct and Habits of Insects.—Translator's Note.

{17} A species of Grasshopper.—Translator's Note.

{18} An insect akin to the Locusts and Crickets, which, when at rest, adopts an attitude resembling that of prayer. When attacking, it assumes what is known as 'the spectral attitude.' Its forelegs form a sort of saw-like or barbed harpoons. Cf. Social Life in the Insect World, by J. H. Fabre, translated by Bernard Miall: chaps. v. to vii.— Translator's Note.

{19} .39 inch.— Translator's Note.

{20} These experiments are described in the author's essay on the Mason Bees entitled Fragments on Insect Psychology.—Translator's Note.

{21} A species of Wasp.—Translator's Note.

{22} In Chap. VIII. of the present volume.—Translator's Note.

{23} Jules Michelet (1798-1874), author of L'Oiseau and L'Insecte, in addition to the historical works for which he is chiefly known. As a lad, he helped his father, a printer by trade, in setting type.—Translator's Note.

{24} Chapter III. of the present volume.—Translator's Note.

{25} A species of Dung-beetle. Cf. The Life and Love of the Insect, by J. Henri Fabre, translated by Alexander Teixeira de Mattos: chap. v.—Translator's Note.

{26} A species of Beetle.—Translator's Note.

{27} Cf. Insect Life, by J. H. Fabre, translated by the author of Mademoiselle Mori: chaps. i. and ii.; The Life and Love of the Insect, by J. Henri Fabre, translated by Alexander Teixeira de Mattos: chaps. i. to iv.—Translator's Note.

{28} Chapter II.—Translator's Note.

{29} .39 inch.—Translator's Note.

{30} The Processionaries are Moth-caterpillars that feed on various leaves and march in file, laying a silken trail as they go.—Translator's Note.

{31} The weekly half-holiday in French schools.—Translator's Note.

{32} Cf. Social Life in the Insect World, by J. H. Fabre, translated by Bernard Miall: chap. xiv.—Translator's Note.

{33} Cf. Insect Life, by J. H. Fabre, translated by the author of Mademoiselle Mori: chap. v.—Translator's Note.

{34} The Scolia is a Digger-wasp, like the Cerceris and the Sphex, and feeds her larvae on the grubs of the Cetonia, or Rose-chafer, and the Oryctes, or Rhinoceros Beetle. Cf. The Life and Love of the Insect, by J. Henri Fabre, translated by Alexander Teixeira de Mattos: chap. xi.—Translator's Note.

{35} Cf. Social Life in the Insect World, by J. H. Fabre, translated by Bernard Miall. chap. xiii., in which the name is given, by a printer's error, as Philanthus aviporus.—Translator's Note.

{36} Or Bird Spiders, known also as the American Tarantula.—Translator's Note.

{37} .059 inch.—Translator's Note.

{38} The Ichneumon-flies are very small insects which carry long ovipositors, wherewith they lay their eggs in the eggs of other insects and also, more especially, in caterpillars. Their parasitic larvae live and develop at the expense of the egg or grub attacked, which degenerates in consequence.—Translator's Note.

{39} One of the largest families of Beetles, darkish in colour and shunning the light.—Translator's Note.

{40} The Iulus is one of the family of Myriapods, which includes Centipedes, etc.—Translator's Note.

{41} A species of Land-snail.—Translator's Note.

{42} Jacques Bernouilli (1654-1705), professor of mathematics at the University of Basel from 1687 to the year of his death. He improved the differential calculus, solved the isoperimetrical problem and discovered the properties of the logarithmic spiral.—Translator's Note.

THE END