Nevertheless, her preference is for the corpse: furred beast and feathered beast, reptile and fish, indifferently. Together with the greenbottles, she is sedulous in her attendance on my pans. Daily she visits my snakes, takes note of the condition of each of them, savors them with her proboscis, goes away, comes back, takes her time and at last proceeds to business. Still, it is not here, amid the tumult of callers, that I propose to follow her operations. A lump of butcher's meat laid on the window sill, in front of my writing table, will be less offensive to the eye and will facilitate my observations.

Two flies of the genus Sarcophaga frequent my slaughter yard: Sarcophaga carnaria and Sarcophaga haemorrhoidalis, whose abdomen ends in a red speck. The first species, which is a little larger than the second, is more numerous and does the best part of the work in the open air shambles of the pans. It is this fly also who, at intervals and nearly always alone, hastens to the bait exposed on the windowsill.

She comes up suddenly, timidly. Soon she calms herself and no longer thinks of fleeing when I draw near, for the dish suits her. She is surprisingly quick about her work. Twice over—buzz! Buzz!—the tip of her abdomen touches the meat; and the thing is done: a group of vermin wriggles out, releases itself and disperses so nimbly that I have no time to take my lens and count then accurately. As seen by the naked eye, there were a dozen of them. What has become of them? One would think that they had gone into the flesh, at the very spot where they were laid, so quickly have they disappeared. But that dive into a substance of some consistency is impossible to these newborn weaklings. Where are they? I find them more or less everywhere in the creases of the meat; singly and already groping with their mouths. To collect them in order to number them is not practicable, for I do not want to damage them. Let us be satisfied with the estimate made at a rapid glance: there are a dozen or so, brought into the world in one discharge of almost inappreciable length.

Those live grubs, taking the place of the usual eggs, have long been known. Everybody is aware that the flesh flies bring forth living maggots, instead of laying eggs. They have so much to do and their work is so urgent! To them, the instruments of the transformation of dead matter, a day means a day, a long space of time which it is all important to utilize. The greenbottle's eggs, though these are of very rapid development, take twenty-four hours to yield their grubs. The flesh flies save all this time. From their matrix, laborers flow straightway and set to work the moment they are born. With these ardent pioneers of sanitation, there is no rest attendant upon the hatching, there is not a minute lost.

The gang, it is true, is not a numerous one; but how often can it not be renewed! Read Reaumur's description of the wonderful procreating machinery boasted by the Flesh flies. It is a spiral ribbon, a velvety scroll whose nap is a sort of fleece of maggots set closely together and each cased in a sheath. The patient biographer counted the host: it numbers, he tells us, nearly twenty thousand. You are seized with stupefaction at this anatomical fact.

How does the gray fly find the time to settle a family of such dimensions, especially in small packets, as she has just done on my window sill? What a number of dead dogs, moles and snakes must she not visit before exhausting her womb! Will she find them? Corpses of much size do not abound to that extent in the country. As everything suits her, she will alight on other remains of minor importance. Should the prize be a rich one, she will return to it tomorrow, the day after and later still, over and over again. In the course of the season, by dint of packets of grubs deposited here, there and everywhere, she will perhaps end by housing her entire brood. But then, if all things prosper, what a glut, for there are several families born during the year! We feel it instinctively: there must be a check to these generative enormities. Let us first consider the grub. It is a sturdy maggot, easy to distinguish from the greenbottle's by its larger girth and especially by the way in which its body terminates behind. There is here a sudden breaking off, hollowed into a deep cup. At the bottom of this crater are two breathing holes, two stigmata with amber-red tips. The edge of the cavity is fringed with half a score of pointed, fleshy festoons, which diverge like the spikes of a coronet. The creature can close or open this diadem at will by bringing the denticulations together or by spreading them out wide. This protects the air holes which might otherwise be choked up when the maggot disappears in the sea of broth. Asphyxia would supervene, if the two breathing holes at the back became obstructed. During the immersion, the festooned coronet shuts like a flower closing its petals and the liquid is not admitted to the cavity.

Next follows the emergence. The hind part reappears in the air, but appears alone, just at the level of the fluid. Then the coronet spreads out afresh, the cup gapes and assumes the aspect of a tiny flower, with the white denticulations for petals and the two bright red dots, the stigmata at the bottom, for stamens. When the grubs, pressed one against the other, with their heads downwards in the fetid soup, make an unbroken shoal, the sight of those breathing cups incessantly opening and closing, with a little clack like a valve, almost makes one forget the horrors of the charnel yard. It suggests a carpet of tiny Sea anemones. The maggot has its beauties after all.

It is obvious, if there be any logic in things, that a grub so well-protected against asphyxiation by drowning must frequent liquid surroundings. One does not encircle one's hindquarters with a coronet for the sole satisfaction of displaying it. With its apparatus of spokes, the Grey Fly's grub informs us of the dangerous nature of its functions: when working upon a corpse, it runs the risk of drowning. How is that? Remember the grubs of the greenbottle, fed on hard-boiled white of egg. The dish suits them; only, by the action of their pepsin, it becomes so fluid that they die submerged. Because of their hinder stigmata, which are actually on the skin and devoid of any defensive machinery, they perish when they find no support apart from the liquid.

The flesh fly's maggots, though incomparable liquefiers, know nothing of this peril, even in a puddle of carrion broth. Their bulky hind part serves as a float and keeps the air holes above the surface. When, for further investigation, they must needs go under completely, the anemone at the back shuts and protects the stigmata. The grubs of the gray fly are endowed with a life buoy because they are first class liquefiers, ready to incur the danger of a ducking at any moment.

When high and dry on the sheet of cardboard where I place them to observe them at my ease, they move about actively, with their breathing rose widespread and their stigmata rising and falling as a support. The cardboard is on my table, at three steps from an open window, and lit at this time of day only by the soft light of the sky. Well, the maggots, one and all of them, turn in the opposite direction to the window; they hastily, madly take to flight.

I turn the cardboard round, without touching the runaways. This action makes the creatures face the light again. Forthwith, the troop stops, hesitates, takes a half turn and once more retreats towards the darkness. Before the end of the racecourse is reached, I again turn the cardboard. For the second time, the maggots veer round and retrace their steps. Repeat the experiment as often as I will, each time the squad wheels about in the opposite direction to the window and persists in avoiding the trap of the revolving cardboard.

The track is only a short one: the cardboard measures three hand's breadths in length. Let us give more space. I settle the grubs on the floor of the room; with a hair pencil, I turn them with their heads pointing towards the lighted aperture. The moment they are free, they turn and run from the light. With all the speed whereof their cripple's shuffle allows, they cover the tiled floor of the study and go and knock their heads against the wall, twelve feet off, skirting it afterwards, some to the right and some to the left. They never feel far enough away from that hateful illuminated opening.

What they are escaping from is evidently the light, for, if I make it dark with a screen, the troop does not change its direction when I turn the cardboard. It then progresses quite readily towards the window; but, when I remove the screen, it turns tail at once.

That a grub destined to live in the darkness, under the shelter of a corpse, should avoid the light is only natural; the strange part is its very perception. The maggot is blind. Its pointed fore part, which we hesitate to call a head, bears absolutely no trace of any optical apparatus; and the same with every other part of the body. There is nothing but one bare, smooth, white skin. And this sightless creature, deprived of any special nervous points served by ocular power, is extremely sensitive to the light. Its whole skin is a sort of retina, incapable of seeing, of course, but able, at any rate, to distinguish between light and darkness. Under the direct rays of a searching sun, the grub's distress could be easily explained. We ourselves; with our coarse skin, in comparison with that of the maggot, can distinguish between sunshine and shadow without the help of the eyes. But, in the present case, the problem becomes singularly complicated. The subjects of my experiment receive only the diffused light of the sky, entering my study through an open window; yet this tempered light frightens them out of their senses. They flee the painful apparition; they are bent upon escaping at all costs.

Now what do the fugitives feel? Are they physically hurt by the chemical radiations? Are they exasperated by other radiations, known or unknown? Light still keeps many a secret hidden from us and perhaps our optical science, by studying the maggot, might become the richer by some valuable information. I would gladly have gone farther into the question, had I possessed the necessary apparatus. But I have not, I never have had and of course I never shall have the resources which are so useful to the seeker. These are reserved for the clever people who care more for lucrative posts than for fair truths. Let us continue, however, within the measure which the poverty of my means permits.

When duly fattened, the grubs of the flesh flies go underground to transform themselves into pupae. The burial is intended, obviously, to give the worm the tranquillity necessary for the metamorphosis. Let us add that another object of the descent is to avoid the importunities of the light. The maggot isolates itself to the best of its power and withdraws from the garish day before contracting into a little keg. In ordinary conditions, with a loose soil, it goes hardly lower than a hand's breadth down, for provision has to be made for the difficulties of the return to the surface when the insect, now full grown, is impeded by its delicate fly wings. The grub, therefore, deems itself suitably isolated at a moderate depth. Sideways, the layer that shields it from the light is of indefinite thickness; upwards, it measures about four inches. Behind this screen reigns utter darkness, the buried one's delight. This is capital.

What would happen if, by an artifice, the sideward layer were nowhere thick enough to satisfy the grub? Now, this time, I have the wherewithal to solve the problem, in the shape of a big glass tube, open at both ends, about three feet long and less than an inch wide. I use it to blow the flame of hydrogen in the little chemistry lessons which I give my children.

I close one end with a cork and fill the tube with fine, dry, sifted sand. On the surface of this long column, suspended perpendicularly in a corner of my study, I install some twenty Sarcophaga grubs, feeding them with meat. A similar preparation is repeated in a wider jar, with a mouth as broad as one's hand. When they are big enough, the grubs in either apparatus will go down to the depth that suits them. There is no more to be done but to leave them to their own devices.

The worms at last bury themselves and harden into pupae. This is the moment to consult the two apparatus. The jar gives me the answer which I should have obtained in the open fields. Four inches down, or thereabouts, the worms have found a quiet lodging, protected above by the layer through which they have passed and on every side by the thickness of the vessel's contents. Satisfied with the site, they have stopped there.

It is a very different matter in the tube. The least buried of the pupae are half a yard down. Others are lower still; most of them even have reached the bottom of the tube and are touching the cork stopper, an insuperable barrier. These last, we can see, would have gone yet deeper if the apparatus had allowed them. Not one of the score of grubs has settled at the customary halting place; all have traveled farther down the column, until their strength gave way. In their anxious flight, they have dug deeper and ever deeper.

What were they flying from? The light. Above them, the column traversed forms a more than sufficient shelter; but, at the sides, the irksome sensation is still felt through a coat of earth half an inch thick if the descent is made perpendicularly. To escape the disturbing impression, the grub therefore goes deeper and deeper, hoping to obtain lower down the rest which is denied it above. It only ceases to move when worn out with the effort or stopped by an obstacle.

Now, in a soft diffused light, what can be the radiations capable of acting upon this lover of darkness? They are certainly not the simple luminous rays, for a screen of fine, heaped up earth, nearly half an inch in thickness, is perfectly opaque. Then, to alarm the grub, to warn it of the over proximity of the exterior and send it to mad depths in search of isolation, other radiations, known or unknown, must be required, radiations capable of penetrating a screen against which ordinary radiations are powerless. Who knows what vistas the natural philosophy of the maggot might open out to us? For lack of apparatus, I confine myself to suspicions.

To go underground to a yard's depth—and farther if my tube had allowed it—is on the part of the Flesh fly's grub a vagary provoked by unkind experiment: never would it bury itself so low down, if left to its own wisdom. A hand's breadth thickness is quite enough, is even a great deal when, after completing the transformation, it has to climb back to the surface, a laborious operation absolutely resembling the task of an entombed well sinker. It will have to fight against the sand that slips and gradually fills up the small amount of empty space obtained; it will perhaps, without crowbar or pickaxe, have to cut itself a gallery through something tantamount to tufa, that is to say, through earth which a shower has rendered compact. For the descent, the grub has its fangs; for the assent, the fly has nothing. Only that moment come into existence, she is a weakling, with tissues still devoid of any firmness. How does she manage to get out? We shall know by watching a few pupae placed at the bottom of a test-tube filled with earth. The method of the Flesh flies will teach us that of the greenbottles and the other Flies, all of whom make use of the same means.

Enclosed in her pupa, the nascent fly begins by bursting the lid of her casket with a hernia which comes between her two eyes and doubles or trebles the size of her head. This cephalic blister throbs: it swells and subsides by turns, owing to the alternate flux and reflux of the blood. It is like the piston of an hydraulic press opening and forcing back the front part of the keg.

The head makes its appearance. The hydrocephalous monster continues the play of her forehead, while herself remaining stationary. Inside the pupa, a delicate work is being performed: the casting of the white nymphal tunic. All through this operation, the hernia is still projecting. The head is not the head of a fly, but a queer, enormous mitre, spreading at the base into two red skull caps, which are the eyes. To split her cranium in the middle, shunt the two halves to the right and left and send surging through the gap a tumor which staves the barrel with its pressure: this constitutes the Fly's eccentric method.

For what reason does the hernia, once the keg is staved, continue swollen and projecting? I take it to be a waste pocket into which the insect momentarily forces back its reserves of blood in order to diminish the bulk of the body to that extent and to extract it more easily from the nymphal slough and afterwards from the narrow channel of the shell. As long as the operation of the release lasts, it pushes outside all that it is able to inject of its accumulated humors; it makes itself small inside the pupa and swells into a bloated deformity without. Two hours and more are spent in this laborious stripping.

At last, the fly comes into view. The wings, mere scanty stumps, hardly reach the middle of the abdomen. On the outer edge, they have a deep notch similar to the waist of a violin. This diminishes by just so much the surface and the length, an excellent device for decreasing the friction along the earthy column which has next to be scaled. The hydrocephalous one resumes her performance more vigorously than ever; she inflates and deflates her frontal knob. The pounded sand rustles down the insect's sides. The legs play but a secondary part. Stretched behind, motionless, when the piston stroke is delivered, they furnish a support. As the sand descends, they pile it and nimbly push it back, after which they drag along lifelessly until the next avalanche. The head advances each time by a length equal to that of the sand displaced. Each stroke of the frontal swelling means a step forward. In a dry, loose soil, things go pretty fast. A column six inches high is traversed in less than a quarter of an hour.

As soon as it reaches the surface, the insect, covered with dust, proceeds to make its toilet. It thrusts out the blister of its forehead for the last time and brushes it carefully with its front tarsi. It is important that the little pounding engine should be carefully dusted before it is taken inside to form a forehead that will open no more: this lest any grit should lodge in the head. The wings are carefully brushed and polished; they lose their curved notches; they lengthen and spread. Then, motionless on the surface of the sand, the fly matures fully. Let us set her at liberty. She will go and join the others on the Snakes in my pans.



CHAPTER XI. THE BUMBLEBEE FLY

Underneath the wasp's brown paper manor house, the ground is channeled into a sort of drain for the refuse of the nest. Here are shot the dead or weakly larvae which a continual inspection roots out from the cells to make room for fresh occupants; here, at the time of the autumn massacre, are flung the backward grubs; here, lastly, lies a good part of the crowd killed by the first touch of winter. During the rack and ruin of November and December, this sewer becomes crammed with animal matter.

Such riches will not remain unemployed. The world's great law which says that nothing edible shall be wasted provides for the consumption of a mere ball of hair disgorged by the owl. How shall it be with the vast stores of a ruined wasps' nest! If they have not come yet, the consumers whose task it is to salve this abundant wreckage for nature's markets, they will not tarry in coming and waiting for the manna that will soon descend from above. That public granary, lavishly stocked by death, will become a busy factory of fresh life. Who are the guests summoned to the banquet?

If the wasps flew away, carrying the dead or sickly grubs with them, and dropped them on the ground round about their home, those banqueters would be, first and foremost, the insect-eating birds, the warblers, all of whom are lovers of small game. In this connection, we will allow ourselves a brief digression. We all know with what jealous intolerance the nightingales occupy each his own cantonment. Neighborly intercourse among them is tabooed. The males frequently exchange defiant couplets at a distance; but, should the challenged party draw near, the challenger makes him clear off. Now, not far from my house, in a scanty clump of holly oaks which would barely give the woodcutter the wherewithal for a dozen faggots, I used, all through the spring, to hear such full-throated warbling of nightingales that the songs of those virtuosi, all giving voice at once and with no attempt at order, degenerated into a deafening hubbub.

Why did those passionate devotees of solitude come and settle in such large numbers at a spot where custom decrees that there is just room enough for one household only? What reasons have made the recluse become a congregation? I asked the owner of the spinney about the matter.

'It's like that every year,' he said. 'The clump is overrun by Nightingales.'

'And the reason?'

'The reason is that there is a hive close by, behind that wall.'

I looked at the man in amazement, unable to understand what connection there could be between a hive and the thronging nightingales.

'Why, yes,' he added, 'there are a lot of nightingales because there are a lot of bees.

Another questioning look from my side. I did not yet understand. The explanation came: 'The bees,' he said, 'throw out their dead grubs. The front of the hive is strewn with them in the mornings; and the nightingales come and collect them for themselves and their families. They are very fond of them.'

This time I had solved the puzzle. Delicious food, abundant and fresh each day, had brought the songsters together. Contrary to their habit, numbers of nightingales are living on friendly terms in a cluster of bushes, in order to be near the hive and to have a larger share in the morning distribution of plump dainties.

In the same way, the nightingale and his gastronomical rivals would haunt the neighborhood of the wasps' nests, if the dead grubs were cast out on the surface of the soil; but these delicacies fall inside the burrow and no little bird would dare to enter the murky cave, even if the entrance were not too small to admit it. Other consumers are needed here, small in size and great in daring; the fly is called for and her maggot, the king of the departed. What the greenbottles, the bluebottles and the flesh flies do in the open air, at the expense of every kind of corpse, other flies, narrowing their province, do underground at the Wasps' expense.

Let us turn our attention, in September, to the wrapper of a wasps' nest. On the outer surface and there alone, this wrapper is strewn with a multitude of big, white, elliptical dots, firmly fixed to the brown paper and measuring about two millimeters and a half long by one and a half wide. Flat below, convex above and of a lustrous white, these dots resemble very neat drops fallen from a tallow candle. Lastly, their backs are streaked with faint transversal lines, an elegant detail perceptible only with the lens. These curious objects are scattered all over the surface of the wrapper, sometimes at a distance from one another, sometimes gathered into more or less dense groups. They are the eggs of the Volucella, or bumblebee fly (Volucella zonaria, LIN.)

Also stuck to the brown paper of the outer wrapper and mixed up with the Volucella's are a large number of other eggs, chalk white, spear-shaped and ridged lengthwise with seven or eight thin ribs, after the manner of the seeds of certain Umbelliferae. The finishing touch to their delicate beauty is the fine stippling all over the surface. They are smaller by half than the others. I have seen grubs come out of them which might easily be the earliest stage of some pointed maggots which I have already noticed in the burrows. My attempts to rear them failed; and I am not able to say which fly these eggs belong to. Enough for us to note the nameless one in passing. There are plenty of others, which we must make up our minds to leave unlabelled, in view of the jumbled crowd of feasters in the ruined wasps' nest. We will concern ourselves only with the most remarkable, in the front rank of which stands the bumblebee Fly.

She is a gorgeous and powerful fly; and her costume, with its brown and yellow bands, shows a vague resemblance to that of the wasps. Our fashionable theorists have availed themselves of this brown and yellow to cite the Volucella as a striking instance of protective mimicry. Obliged, if not on her own behalf, at least on that of her family, to introduce herself as a parasite into the wasp's home, she resorts, they tell us, to trickery and craftily dons her victim's livery. Once inside the wasps' nest, she is taken for one of the inhabitants and attends quietly to her business.

The simplicity of the wasp, duped by a very clumsy imitation of her garb, and the depravity of the fly, concealing her identity under a counterfeit presentment, exceed the limits of my credulity. The wasp is not so silly nor the Volucella so clever as we are assured. If the latter really meant to deceive the Wasp by her appearance, we must admit that her disguise is none too successful. Yellow sashes round the abdomen do not make a wasp. It would need more than that and, above all, a slender figure and a nimble carriage; and the Volucella is thickset and corpulent and sedate in her movements. Never will the wasp take that unwieldy insect for one of her own kind. The difference is too great.

Poor Volucella, mimesis has not taught you enough. You ought—this is the essential point—to have adopted a wasp's shape; and that you forgot to do: you remained a fat fly, easily recognizable. Nevertheless, you penetrate into the terrible cavern; you are able to stay there for a long time, without danger, as the eggs profusely strewn on the wrapper of the wasps' nest show. How do you set about it?

Let us, first of all, remember that the bumblebee fly does not enter the enclosure in which the combs are heaped: she keeps to the outer surface of the paper rampart and there lays her eggs. Let us, on the other hand, recall the Polistes [a tree nesting wasp] placed in the company of the wasps in my vivarium. Here of a surety is one who need not have recourse to mimicry to find acceptance. She belongs to the guild, she is a wasp herself. Any of us that had not the trained eye of the entomologist would confuse the two species. Well, this stranger, as long as she does not become too importunate, is quite readily tolerated by the caged wasps. None seeks to pick a quarrel with her. She is even admitted to the table, the strip of paper smeared with honey. But she is doomed if she inadvertently sets foot upon the combs. Her costume, her shape, her size, which tally almost exactly with the costume, shape and size of the wasp, do not save her from her fate. She is at once recognized as a stranger and attacked and slaughtered with the same vigor as the larvae of the Hylotoma sawfly and the Saperda beetle, neither of which bears any outward resemblance to the larva of the wasps.

Seeing that identity of shape and costume does not save the Polistes, how will the Volucella fare, with her clumsy imitation? The wasp's eye, which is able to discern the dissimilar in the like, will refuse to be caught. The moment she is recognized, the stranger is killed on the spot. As to that there is not the shadow of a doubt.

In the absence of bumblebee flies at the moment of experimenting, I employ another fly, Milesia fulminans, who, thanks to her slim figure and her handsome yellow bands, presents a much more striking likeness to the wasp than does the fat Volucella zonaria. Despite this resemblance, if she rashly venture on the combs, she is stabbed and slain. Her yellow sashes, her slender abdomen deceive nobody. The stranger is recognized behind the features of a double.

My experiments under glass, which varied according to the captures which I happened to make, all lead me to this conclusion: as long as there is more propinquity, even around the honey, the other occupants are tolerated fairly well; but, if they touch the cells, they are assaulted and often killed, without distinction of shape or costume. The grubs' dormitory is the sanctum sanctorum which no outsider must enter under pain of death.

With these caged captives I experiment by daylight, whereas the free wasps work in the absolute darkness of their underground retreat. Where light is absent, color goes for nothing. Once, therefore, that she has entered the cavern, the bumblebee fly derives no benefit from her yellow bands, which are supposed to be her safeguard. Whether garbed as she is or otherwise, it is easy for her to effect her purpose in the dark, on condition that she avoids the tumultuous interior of the wasps' nest. So long as she has the prudence not to hustle the passers by, she can dab her eggs, without danger, on the paper wall. No one will know of her presence. The dangerous thing is to cross the threshold of the burrow in broad daylight, before the eyes of those who go in and out. At that moment alone, protective mimicry would be convenient. Now does the entrance of the Volucella into the presence of a few wasps entail such very great risks? The wasps' nest in my enclosure, the one which was afterwards to perish in the sun under a bell glass, gave me the opportunity for prolonged observations, but without any result upon the subject of my immediate concern. The bumblebee fly did not appear. The period for her visits had doubtless passed; for I found plenty of her grubs when the nest was dug up.

Other flies rewarded me for my assiduity. I saw some—at a respectful distance, I need hardly say—entering the burrow. They were insignificant in size and of a dark gray color, not unlike that of the housefly. They had not a patch of yellow about them and certainly had no claim to protective mimicry. Nevertheless, they went in and out as they pleased, calmly, as though they were at home. As long as there was not too great a number at the door, the wasps left them alone. When there was anything of a crowd, the gray visitors waited near the threshold for a less busy moment. No harm came to them.

Inside the establishment, the same peaceful relations prevail. In this respect I have the evidence of my excavations. In the underground charnel house, so rich in Fly grubs, I find no corpses of adult flies. If the strangers had been slaughtered in passing through the entrance hall, or lower down, they would fall to the bottom of the burrow anyhow, with the other rubbish. Now in this charnel house, as I said, there are never any dead bumblebee flies, never a fly of any sort. The incomers are respected. Having done their business, they go out unscathed.

This tolerance on the part of the wasps is surprising. And a suspicion comes to one's mind: can it be that the Volucella and the rest are not what the accepted theories of natural history call them, namely, enemies, grub killers sacking the wasps' nest? We will look into this by examining them when they are hatched. Nothing is easier, in September and October, than to collect the Volucella's eggs in such numbers as we please. They abound on the outer surface of the wasps' nest. Moreover, as with the larvae of the wasp, it is some time before they are suffocated by the petroleum fumes; and so most of them are sure to hatch. I take my scissors, cut the most densely populated bits from the paper wall of the nest and fill a jar with them. This is the warehouse from which I shall daily, for the best part of the next two months, draw my supply of nascent grubs.

The Volucella's egg remains where it is, with its white color always strongly marked against the brown of the background. The shell wrinkles and collapses; and the fore end tears open. From it there issues a pretty little white grub, thin in front, swelling slightly in the rear and bristling all over with fleshy protuberances. The creature's papillae are set on its sides like the teeth of a comb; at the rear, they lengthen and spread into a fan; on the back, they are shorter and arranged in four longitudinal rows. The last section but one carries two short, bright red breathing tubes, standing aslant and joined to each other. The fore part, near the pointed mouth, is of a darker, brownish color. This is the biting and motor apparatus, seen through the skin and consisting of two fangs. Taken all round, the grub is a pretty little thing, with its bristling whiteness, which gives it the appearance of a tiny snowflake. But this elegance does not last long: grown big and strong, the bumblebee fly's grub becomes soiled with sanies, turns a russety brown and crawls about in the guise of a hulking porcupine.

What becomes of it when it leaves the egg? This my warehousing jar tells me, partly. Unable to keep its balance on sloping surfaces, it drops to the bottom of the receptacle, where I find it, daily, as hatched, wandering restlessly. Things must happen likewise at the wasps'. Incapable of standing on the slant of the paper wall, the newborn grubs slide to the bottom of the underground cavity, which contains, especially at the end of the summer, a heaped up provender of deceased wasps and dead larvae removed from the cells and flung outside the house, all nice and gamy, as proper maggot's food should be. The Volucella's offspring, themselves maggots, notwithstanding their snowy apparel, find in this charnel house victuals to their liking, incessantly renewed. Their fall from the high walls might well be not accidental, but rather a means of reaching, quickly and without searching, the good things down at the bottom of the cavern. Perhaps, also, some of the white grubs, thanks to the holes that make the wrapper resemble a spongy cover, manage to slip inside the Wasps' nest. Still, most of the Volucella's grubs, at whatever stage of their development, are in the basement of the burrow, among the carrion remains. The others, those settled in the wasps' home itself, are comparatively few.

These returns are enough to show us that the grubs of the bumblebee fly do not deserve the bad reputation that has been given them. Satisfied with the spoils of the dead, they do not touch the living; they do not ravage the wasps' nest: they disinfect it.

Experiment confirms what we have learnt in the actual nests. Over and over again, I bring wasp grubs and Volucella grubs together in small test tubes, which are easy to observe. The first are well and strong; I have just taken them from their cells. The others are in various stages, from that of the snowflake born the same day to that of the sturdy porcupine. There is nothing tragic about the encounter. The grubs of the bumblebee fly roam about the test-tube without touching the live tidbit. The most that they do is to put their mouths for a moment to the morsel; then they take it away again, not caring for the dish.

They want something different: a wounded, a dying grub; a corpse dissolving into sanies. Indeed, if I prick the wasp grub with a needle, the scornful ones at once come and sup at the bleeding wound. If I give them a dead grub, brown with putrefaction, the worms rip it open and feast on its humors. Better still: I can feed them quite satisfactorily with wasps that have turned putrid under their horny rings; I see them greedily suck the juices of decomposing Rosechafer grubs; I can keep them thriving with chopped up butcher's meat, which they know how to liquefy by the method of the common maggot. And these unprejudiced ones, who accept anything that comes their way, provided it be dead, refuse it when it is alive. Like the true flies that they are, frank body snatchers, they wait, before touching a morsel, for death to do its work.

Inside the wasps' nest, robust grubs are the rule and weaklings the rare exception, because of the assiduous supervision which eliminates anything that is diseased and like to die. Here, nevertheless, Volucella grubs are found, on the combs, among the busy wasps. They are not, it is true, so numerous as in the charnel house below, but still pretty frequent. Now what do they do in this abode where there are no corpses? Do they attack the healthy? Their continual visits from cell to cell would at first make one think so; but we shall soon be undeceived if we observe their movements closely; and this is possible with my glass roofed colonies.

I see them fussily crawling on the surface of the combs, curving their necks from side to side and taking stock of the cells. This one does not suit, nor that one either; the bristly creature passes on, still in search, thrusting its pointed fore part now here, now there. This time, the cell appears to fulfil the requisite conditions. A larva, glowing with health, opens wide its mouth, believing its nurse to be approaching. It fills the hexagonal chamber with its bulging sides.

The gluttonous visitor bends and slides its slender fore part, a blade of exquisite suppleness, between the wall and the inhabitant, whose slack rotundity yields to the pressure of this animated wedge. It plunges into the cell, leaving no part of itself outside but its wide hind quarters, with the red dots of the two breathing tubes.

It remains in this posture for some time, occupied with its work at the bottom of the cell. Meanwhile, the wasps present do not interfere, remain impassive, showing that the grub visited is in no peril. The stranger, in fact, withdraws with a soft, gliding motion. The chubby babe, a sort of India rubber bag, resumes its original volume without having suffered any harm, as its appetite proves. A nurse offers it a mouthful, which it accepts with every sign of unimpaired vigor. As for the Volucella grub, it licks its lips after its own fashion, pushing its two fangs in and out; then, without further loss of time, goes and repeats its probing elsewhere.

What it wants down there, at the bottom of the cells, behind the grubs, cannot be decided by direct observation; it must be guessed at. Since the visited larva remains intact, it is not prey that the Volucella grub is after. Besides, if murder formed part of its plans, why descend to the bottom of the cell, instead of attacking the defenseless recluse straight way? It would be much easier to suck the patient's juices through the actual orifice of the cell. Instead of that, we see a dip, always a dip and never any other tactics.

Then what is there behind the wasp grub? Let us try to put it as decently as possible. In spite of its exceeding cleanliness, this grub is not exempt from the physiological ills inseparable from the stomach. Like all that eats, it has intestinal waste matter with regard to which its confinement compels it to behave with extreme discretion. Like so many other close-cabined larvae of Wasps and Bees, it waits until the moment of the transformation to rid itself of its digestive refuse. Then, once and for all, it casts out the unclean accumulation whereof the pupa, that delicate, reborn organism, must not retain the least trace. This is found later, in any empty cell, in the form of a dark purple plug. But, without waiting for this final purge, this lump, there are, from time to time, slight excretions of fluid, clear as water. We have only to keep a Wasp grub in a little glass tube to recognize these occasional discharges. Well, I see nothing else to explain the action of the Volucella's grubs when they dip into the cells without wounding the larvae. They are looking for this liquid, they provoke its emission. It represents to them a dainty which they enjoy over and above the more substantial fare provided by the corpses.

The bumblebee fly, that sanitary inspector of the Vespine city, fulfils a double office: she wipes the wasp's children and she rids the nest of its dead. For this reason, she is peacefully received, as an auxiliary, when she enters the burrow to lay her eggs; for this reason, her grub is tolerated, nay more, respected, in the very heart of the dwelling, where none might stray with impunity. I remember the brutal reception given to the Saperda and Hylotoma grubs when I place them on a comb. Forthwith grabbed, bruised and riddled with stings, the poor wretches perish. It is quite a different matter with the offspring of the Volucella. They come and go as they please, poke about in the cells, elbow the inhabitants and remain unmolested. Let us give some instances of this clemency, which is very strange in the irascible Wasp.

For a couple of hours, I fix my attention on a Volucella grub established in a cell, side by side with the Wasp grub, the mistress of the house. The hind quarters emerge, displaying their papillae. Sometimes also the fore part, the head, shows, bending from side to side with sudden, snake-like motions. The wasps have just filled their crops at the honey pot; they are dispensing the rations, are very busily at work; and things are taking place in broad daylight, on the table by the window.

As they pass from cell to cell, the nurses repeatedly brush against and stride across the Volucella grub. There is no doubt that they see it. The intruder does not budge, or, if trodden on, curls up, only to reappear the next moment. Some of the wasps stop, bend their heads over the opening, seem to be making inquiries and then go off, without troubling further about the state of things. One of them does something even more remarkable: she tries to give a mouthful to the lawful occupant of the cell; but the larva, which is being squeezed by its visitor, has no appetite and refuses. Without the least sign of anxiety on behalf of the nursling which she sees in awkward company, the wasp retires and goes to distribute its ration elsewhere. In vain I prolong my examination: there is no fluster of any kind. The Volucella grub is treated as a friend, or at least as a visitor that does not matter. There is no attempt to dislodge it, to worry it, to put it to flight. Nor does the grub seem to trouble greatly about those who come and go. Its tranquillity, tells us that it feels at home.

Here is some further evidence: the grub has plunged, head downwards, into an empty cell, which is too small to contain the whole of it. Its hindquarters stick out, very visibly. For long hours, it remains motionless in this position. At every moment, wasps pass and repass close by. Three of them, at one time together, at another separately, come and nibble at the edges of the cell; they break off particles which they reduce to paste for a new piece of work. The passers by, intent upon their business, may not perceive the intruder; but these three certainly do. During their work of demolition, they touch the grub with their legs, their antennae, their palpi; and yet none of them minds it. The fat grub, so easily recognized by its queer figure, is left alone; and this in broad daylight, where everybody can see it. What must it be when the profound darkness of the burrows protects the visitor with its mysteries!

I have been experimenting all along with big Volucella grubs, colored with the dirty red which comes with age. What effect will pure white produce? I sprinkle on the surface of the combs some larvae that have lately left the egg. The tiny, snow-white grubs make for the nearest cells, go down into them, come out again and hunt elsewhere. The wasps peaceably let them go their way, as heedless of the little white invaders as of the big red ones. Sometimes, when it enters an occupied cell, the little creature is seized by the owner, the wasp grub, which nabs it and turns and returns it between its mandibles. Is this a defensive bite? No, the wasp grub has merely blundered, taking its visitor for a proffered mouthful. There is no great harm done. Thanks to its suppleness, the little grub emerges from the grip intact and continues its investigations.

It might occur to us to attribute this tolerance to some lack of penetration in the wasps' vision. What follows will undeceive us: I place separately, in empty cells, a grub of Saperda scalaria and a Volucella grub, both of them white and selected so as not to fill the cell entirely. Their presence is revealed only by the paleness of the hind part which serves as a plug to the opening. A superficial examination would leave the nature of the recluse undecided. The wasps make no mistake: they extirpate the Saperda grub, kill it, fling it on the dust heap; they leave the Volucella grub in peace.

The two strangers are quite well recognized in the secrecy of the cells: one is the intruder that must be turned out; the other is the regular visitor that must be respected. Sight helps, for things take place in the daylight, under glass; but the wasps have other means of information in the dimness of the burrow. When I produce darkness by covering the apparatus with a screen, the murder of the trespassers is accomplished just the same. For so say the police regulations of the wasps' nest: any stranger discovered must be slain and thrown on the midden.

To thwart this vigilance, the real enemies need to be masters of the art of deceptive immobility and cunning disguise. But there is no deception about the Volucella grub. It comes and goes, openly, wheresoever it will; it looks round amongst the wasps for cells to suit it. What has it to make itself thus respected? Strength? Certainly not. It is a harmless creature, which the wasp could rip open with a blow of her shears, while a touch of the sting would mean lightning death. It is a familiar guest, to whom no denizen of a wasps' nest bears any ill will. Why? Because it renders good service: so far from working mischief, it does the scavenging for its hosts. Were it an enemy or merely an intruder, it would be exterminated; as a deserving assistant, it is respected.

Then what need is there for the Volucella to disguise herself as a wasp? Any fly, whether clad in drab or motley, is admitted to the burrow directly she makes herself useful to the community. The mimicry of the bumblebee fly, which was said to be one of the most conclusive cases, is, after all, a mere childish notion. Patient observation, continually face to face with facts, will have none of it and leaves it to the armchair naturalists, who are too prone to look at the animal world through the illusive mists of theory.



CHAPTER XII. MATHEMATICAL MEMORIES: NEWTON'S BINOMIAL THEOREM

The spider's web is a glorious mathematical problem. I should enjoy working it out in all its details, were I not afraid of wearying the reader's attention. Perhaps I have even gone too far in the little that I have said, in which case I owe him some compensation: 'Would you like me,' I will ask him, 'would you like me to tell you how I acquired sufficient algebra to master the logarithmic systems and how I became a surveyor of Spiders' webs? Would you? It will give us a rest from natural history.'

I seem to catch a sign of acquiescence. The story of my village school, visited by the chicks and the porkers, has been received with some indulgence; why should not my harsh school of solitude possess its interest as well? Let us try to describe it. And who knows? Perhaps, in doing so, I shall revive the courage of some other poor derelict hungering after knowledge.

I was denied the privilege of learning with a master. I should be wrong to complain. Solitary study has its advantages: it does not cast you in the official mould; it leaves you all your originality. Wild fruit, when it ripens, has a different taste from hothouse produce: it leaves on a discriminating palate a bittersweet flavor whose virtue is all the greater for the contrast. Yes, if it were in my power, I would start afresh, face to face with my only counselor, the book itself, not always a very lucid one; I would gladly resume my lonely watches, my struggles with the darkness whence, at last, a glimmer appears as I continue to explore it; I should retraverse the irksome stages of yore, stimulated by the one desire that has never failed me, the desire of learning and of afterwards bestowing my mite of knowledge on others.

When I left the normal school, my stock of mathematics was of the scantiest. How to extract a square root, how to calculate and prove the surface of a sphere: these represented to me the culminating points of the subject. Those terrible logarithms, when I happened to open a table of them, made my head swim, with their columns of figures; actual fright, not unmixed with respect, overwhelmed me on the very threshold of that arithmetical cave. Of algebra I had no knowledge whatever. I had heard the name; and the syllables represented to my poor brain the whole whirling legion of the abstruse.

Besides, I felt no inclination to decipher the alarming hieroglyphics. They made one of those indigestible dishes which we confidently extol without touching them. I greatly preferred a fine line of Virgil, whom I was now beginning to understand; and I should have been surprised indeed had any one told me that, for long years to come, I should be an enthusiastic student of the formidable science. Good fortune procured me my first lesson in algebra, a lesson given and not received, of course.

A young man of about my own age came to me and asked me to teach him algebra. He was preparing for his examination as a civil engineer; and he came to me because, ingenuous youth that he was, he took me for a well of learning. The guileless applicant was very far out in his reckoning.

His request gave me a shock of surprise, which was forthwith repressed on reflection: 'I give algebra lessons?' said I to myself. 'It would be madness: I don't know anything about the subject!'

And I left it at that for a moment or two, thinking hard, drawn now this way, now that with indecision: 'Shall I accept? Shall I refuse?' continued the inner voice.

Pooh, let's accept! An heroic method of learning to swim is to leap boldly into the sea. Let us hurl ourselves head first into the algebraical gulf; and perhaps the imminent danger of drowning will call forth efforts capable of bringing me to land. I know nothing of what he wants. It makes no difference: let's go ahead and plunge into the mystery. I shall learn by teaching.

It was a fine courage that drove me full tilt into a province which I had not yet thought of entering. My twenty-year-old confidence was an incomparable lever.

'Very well,' I replied. 'Come the day after tomorrow, at five, and we'll begin.'

This twenty-four hours' delay concealed a plan. It secured me the respite of a day, the blessed Thursday, which would give me time to collect my forces.

Thursday comes. The sky is gray and cold. In this horrid weather, a grate well filled with coke has its charms. Let's warm ourselves and think.

Well, my boy, you've landed yourself in a nice predicament! How will you manage tomorrow? With a book, plodding all through the night, if necessary, you might scrape up something resembling a lesson, just enough to fill the dread hour more or less. Then you could see about the next: sufficient for the day is the evil thereof. But you haven't the book. And it's no use running out to the bookshop. Algebraical treatises are not current wares. You'll have to send for one, which will take a fortnight at least. And I've promised for tomorrow, for tomorrow certain! Another argument and one that admits of no reply: funds are low; my last pecuniary resources lie in the corner of a drawer. I count the money: it amounts to twelve sous, which is not enough.

Must I cry off? Rather not! One resource suggests itself: a highly improper one, I admit, not far removed indeed from larceny. O quiet paths of algebra, you are my excuse for this venial sin! Let me confess the temporary embezzlement.

Life at my college is more or less cloistered. In return for a modest payment, most of us masters are lodged in the building; and we take our meals at the principal's table. The science master, who is the big gun of the staff and lives in the town, has nevertheless, like ourselves, his own two cells, in addition to a balcony, or leads, where the chemical preparations give forth their suffocating gases in the open air. For this reason, he finds it more convenient to hold his class here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of coke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with glass receivers, panoplies of bent tubes on the walls, and, lastly, a certain cupboard in which I remember seeing a row of books, the oracles consulted by the master in the course of his lessons.

'Among those books,' said I to myself, 'there is sure to be one on algebra. To ask the owner for the loan of it does not appeal to me. My amiable colleague would receive me superciliously and laugh at my ambitious aims. I am sure he would refuse my request.'

The future was to show that my distrust was justified. Narrow mindedness and petty jealousy prevail everywhere alike.

I decide to help myself to this book, which I should never get by asking. This is the half-holiday. The science master will not put in an appearance today; and the key of my room is practically the same as his. I go, with eyes and ears on the alert. My key does not quite fit; it sticks a little, then goes in; and an extra effort makes it turn in the lock. The door opens. I inspect the cupboard and find that it does contain an algebra book, one of the big, fat books which men used to write in those days, a book nearly half a foot thick. My legs give way beneath me. You poor specimen of a housebreaker, suppose you were caught at it! However, all goes well. Quick, let's lock the door again and go back to our own quarters with the pilfered volume.

And now we are together, O mysterious tome, whose Arab name breathes a strange mustiness of occult lore and claims kindred with the sciences of almagest and alchemy. What will you show me? Let us turn the leaves at random. Before fixing one's eyes on a definite point in the landscape, it is well to take a summary view of the whole. Page follows swiftly upon page, telling me nothing. A chapter catches my attention in the middle of the volume; it is headed, Newton's Binomial Theorem.

The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds? What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.

I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there and elsewhere by turns; there are, as the text tells me, arrangements, permutations and combinations. Pen in hand, I arrange, permute and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one's thinking apparatus.

'It will be plain sailing,' said I to myself, 'if algebra is no more difficult than this.'

I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfall in which one becomes more and more entangled, the longer one persists in struggling. What a delightful afternoon that was, before my grate, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal's table, I went downstairs puffed up with the joys of the newly initiated neophyte. I was escorted on my way by a, b and c, intertwined in cunning garlands.

Next day, my pupil is there. Blackboard and chalk, everything is ready. Not quite so ready is the master. I bravely broach my binomial theorem. My hearer becomes interested in the combinations of letters. Not for a moment does he suspect that I am putting the cart before the horse and beginning where we ought to have finished. I relieve the dryness of my explanations with a few little problems, so many halts at which the mind takes breath awhile and gathers strength for fresh flights.

We try together. Discreetly, so as to leave him the merit of the discovery, I shed a little light on the path. The solution is found. My pupil triumphs; so do I, but silently, in my inner consciousness, which says:

'You understand, because you succeed in making another understand.'

The hour passed quickly and very pleasantly for both of us. My young man was contented when he left me; and I no less so, for I perceived a new and original way of learning things.

The ingenious and easy arrangement of the binomial gave me time to tackle my algebra book from the proper commencement. In three or four days, I had rubbed up my weapons. There was nothing to be said about addition and subtraction: they were so simple as to force themselves upon one at first sight. Multiplication spoilt things. There was a certain rule of signs which declared that minus multiplied by minus made plus. How I toiled over that wretched paradox! It would seem that the book did not explain this subject clearly, or rather employed too abstract a method. I read, reread and meditated in vain: the obscure text retained all its obscurity. That is the drawback of books in general: they tell you what is printed in them and nothing more. If you fail to understand, they never advise you, never suggest an attempt along another road which might lead you to the light. The merest word would sometimes be enough to put you on the right track; and that word the books, hidebound in a regulation phraseology, never give you.

How greatly preferable is the oral lesson! It goes forward, goes back, starts afresh, walks around the obstacle and varies the methods of attack until, at long last, light is shed upon the darkness. This incomparable beacon of the master's word was what I lacked; and I went under, without hope of succor, in that treacherous pool of the rule of signs.

My pupil was bound to suffer the effects. After an attempt at an explanation in which I made the most of the few gleams that reached me I asked him:

'Do you understand?'

It was a futile question, but useful for gaining time. Myself not understanding, I was convinced beforehand that he did not understand either.

'No,' he replied, accusing himself, perhaps, in his simple mind, of possessing a brain incapable of taking in those transcendental verities.

'Let us try another method.'

And I start again this way and that way and yet another way. My pupil's eyes serve as my thermometer and tell me of the progress of my efforts. A blink of satisfaction announces my success. I have struck home, I have found the joint in the armor. The product of minus multiplied by minus delivers its mysteries to us.

And thus we continued our studies: he, the passive receiver, taking in the ideas acquired without effort; I, the fierce pioneer, blasting my rock, the book, with the aid of much sitting up at night, to extract the diamond, truth. Another and no less arduous task fell to my share: I had to cut and polish the recondite gem, to strip it of its ruggedness and present it to my companion's intelligence under a less forbidding aspect. This diamond cutter's work, which admitted a little light into the precious stone, was the favorite occupation of my leisure; and I owe a great deal to it.

The ultimate result was that my pupil passed his examination. As for the book borrowed by stealth, I restored it to the shelves and replaced it by another, which, this time, belonged to me.

At my normal school, I had learnt a little elementary geometry under a master. From the first few lessons onwards, I rather enjoyed the subject. I divined in it a guide for one's reasoning faculties through the thickets of the imagination; I caught a glimpse of a search after truth that did not involve too much stumbling on the way, because each step forward rests solidly upon the step already taken; I suspected geometry to be what it preeminently is: a school of intellectual fencing.

The truth demonstrated and its application matter little to me; what rouses my enthusiasm is the process that sets the truth before us. We start from a brilliantly lighted spot and gradually get deeper and deeper in the darkness, which, in its turn, becomes self-illuminated by kindling new lights for a higher ascent. This progressive march of the known toward the unknown, this conscientious lantern lighting what follows by the rays of what comes before: that was my real business.

Geometry was to teach me the logical progression of thought; it was to tell me how the difficulties are broken up into sections which, elucidated consecutively, together form a lever capable of moving the block that resists any direct efforts; lastly, it showed me how order is engendered, order, the base of clarity. If it has ever fallen to my lot to write a page or two which the reader has run over without excessive fatigue, I owe it, in great part, to geometry, that wonderful teacher of the art of directing one's thought. True, it does not bestow imagination, a delicate flower blossoming none knows how and unable to thrive on every soil; but it arranges what is confused, thins out the dense, calms the tumultuous, filters the muddy and gives lucidity, a superior product to all the tropes of rhetoric.

Yes, as a toiler with the pen, I owe much to it. Wherefore my thoughts readily turn back to those bright hours of my novitiate, when, retiring to a corner of the garden in recreation time, with a bit of paper on my knees and a stump of pencil in my fingers, I used to practice deducing this or that property correctly from an assemblage of straight lines. The others amused themselves all around me; I found my delight in the frustum of a pyramid. Perhaps I should have done better to strengthen the muscles of my thighs by jumping and leaping, to increase the suppleness of my loins with gymnastic contortions. I have known some contortionists who have prospered beyond the thinker.

See me then entering the lists as an instructor of youth, fairly well acquainted with the elements of geometry. In case of need, I could handle the land surveyor's stake and chain. There my views ended. To cube the trunk of a tree, to gauge a cask, to measure the distance of an inaccessible point appeared to me the highest pitch to which geometrical knowledge could hope to soar. Were there loftier flights? I did not even suspect it, when an unexpected glimpse showed me the puny dimensions of the little corner which I had cleared in the measureless domain.

At that time, the college in which, two years before, I had made my first appearance as a teacher, had just halved the size of its classes and largely increased its staff. The newcomers all lived in the building, like myself, and we had our meals in common at the principal's table. We formed a hive where, in our leisure time, some of us, in our respective cells, worked up the honey of algebra and geometry, history and physics, Greek and Latin most of all, sometimes with a view to the class above, sometimes and oftener with a view to acquiring a degree. The university titles lacked variety. All my colleagues were bachelors of letters, but nothing more. They must, if possible, arm themselves a little better to make their way in the world. We all worked hard and steadily. I was the youngest of the industrious community and no less eager than the rest to increase my modest equipment.

Visits between the different rooms were frequent. We would come to consult one another about a difficulty, or simply to pass the time of day. I had as a neighbor, in the next cell to mine, a retired quartermaster who, weary of barrack life, had taken refuge in education. When in charge of the books of his company he had become more or less familiar with figures; and it became his ambition to take a mathematical degree. His cerebrum appears to have hardened while he was with his regiment. According to my dear colleagues, those amiable retailers of the misfortunes of others, he had already twice been plucked. Stubbornly, he returned to his books and exercises, refusing to be daunted by two reverses.

It was not that he was allured by the beauties of mathematics, far from it; but the step to which he aspired favored his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose. The lover of study for its own sake and the persistent trapper hunting a diploma as he would something to put in his mouth were not made to understand or to see much of each other. Chance, however, brought us together.

I had often surprised our friend sitting in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The letters x and y often recurred, intermingled with figures. Every row ended with the sign of equality and a nought. Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a nought. Page after page was filled in this queer fashion, each line winding up with 0.

'What are you doing with all those rows of figures amounting to zero?' I asked him one day.

The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many noughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry.

The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in which x and y played a prominent part. When my next-door neighbor reflected so long, clutching his forehead between his hands, he was trying to discover the hidden meaning of his own hieroglyphics; he saw the ghostly translation of his sums dancing in space. What did he perceive? How would the alphabetical signs, arranged first in one and then in another manner, give an image of the actual things, an image visible to the eyes of the mind alone? It beat me.

'I shall have to learn analytical geometry some day,' I said. 'Will you help me?'

'I'm quite willing,' he replied, with a smile in which I read his lack of confidence in my determination.

No matter; we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common stock: he would bring long hours of calculation, I my youthful ardor. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.

In those far off days it was the rule to make a little serious literary study take precedence of science. You were expected to be familiar with the great minds of antiquity, to converse with Horace and Virgil, Theocritus and Plato, before touching the poisons of chemistry or the levers of mechanics. The niceties of thought could only be the gainers by these preparations. Life's exigencies, ever harsher as progress afflicts us with its increasing needs, have changed all that. A fig for correct language! Business before all!

This modern hurry would have suited my impatience. I confess that I fumed against the regulation which forced Latin and Greek upon me before allowing me to open up relations with the sine and cosine. Today, wiser, ripened by age and experience, I am of a different opinion. I very much regret that my modest literary studies were not more carefully conducted and further prolonged. To fill up this enormous blank a little, I respectfully returned, somewhat late in life, to those good old books which are usually sold second-hand with their leaves hardly cut. Venerable pages, annotated in pencil during the long evenings of my youth, I have found you again and you are more than ever my friends. You have taught me that an obligation rests upon whoever wields the pen: he must have something to say that is capable of interesting us. When the subject comes within the scope of natural science, the interest is nearly always assured; the difficulty, the great difficulty, is to prune it of its thorns and to present it under a prepossessing aspect. Truth, they say, rises naked from a well. Agreed; but admit that she is all the better for being decently clothed. She craves, if not the gaudy furbelows borrowed from rhetoric's wardrobe, at least a vine leaf. The geometers alone have the right to refuse her that modest garment; in theorems, plainness suffices. The others, especially the naturalist, are in duty bound to drape a gauze tunic more or less elegantly around her waist.

Suppose I say: 'Baptiste, give me my slippers.'

I am expressing myself in plain language, a little poor in variants. I know exactly what I am saying and my speech is understood.

Others—and they are numerous—contend that this rudimentary method is the best in all things. They talk science to their readers as they might talk slippers to Baptiste. Kaffir syntax does not shock them. Do not speak to them of the value of a well selected term, set down in its right place, still less of a lilting construction, sounding rather well. Childish nonsense they call all that; the fiddling of a short sighted mind!

Perhaps they are right: the Baptiste idiom is a great economizer of time and trouble. This advantage does not tempt me; it seems to me that an idea stands out better if expressed in lucid language, with sober imagery. A suitable phrase, placed in its correct position and saying without fuss the things we want to say, necessitates a choice, an often laborious choice. There are drab words, the commonplaces of colloquial speech; and there are, so to speak, colored words, which may be compared with the brushstrokes strewing patches of light over the gray background of a painting. How are we to find those picturesque words, those striking features which arrest the attention? How are we to group them into a language heedful of syntax and not displeasing to the ear?

I was taught nothing of this art. For that matter, is it ever taught in the schools? I greatly doubt it. If the fire that runs through our veins, if inspiration do not come to our aid, we shall flutter the pages of the thesaurus in vain: the word for which we seek will refuse to come. Then to what masters shall we have recourse to quicken and develop the humble germ that is latent within us? To books.

As a boy, I was always an ardent reader; but the niceties of a well-balanced style hardly interested me: I did not understand them. A good deal later, when close upon fifteen, I began vaguely to see that words have a physiognomy of their own. Some pleased me better than others by the distinctness of their meaning and the resonance of their rhythm; they produced a clearer image in my mind; after their fashion, they gave me a picture of the object described. Colored by its adjective and vivified by its verb, the name became a living reality: what it said I saw. And thus, gradually, was the magic of words revealed to me, when the chances of, my undirected reading placed a few easy standard pages in my way.



CHAPTER XIII. MATHEMATICAL MEMORIES: MY LITTLE TABLE

It is time to start our analytical geometry. He can come now, my partner, the mathematician: I think I shall understand what he says. I have already run through my book and noticed that our subject, whose beautiful precision makes work a recreation, bristles with no very serious difficulties.

We begin in my room, in front of a blackboard. After a few evenings, prolonged into the peaceful watches of the night, I become aware, to my great surprise, that my teacher, the past master in those hieroglyphics, is really, more often than not, my pupil. He does not see the combinations of the abscissas and ordinates very clearly. I make bold to take the chalk in hand myself, to seize the rudder of our algebraical boat. I comment on the book, interpret it in my own fashion, expound the text, sound the reefs until daylight comes and leads us to the haven of the solution. Besides, the logic is so irresistible, it is all such easy going and so lucid that often one seems to be remembering rather than learning.

And so we proceed, with our positions reversed. I dig into the hard rock, crumble it, loosen it until I make room for thought to penetrate. My comrade—I can now allow myself to speak of him on equal terms—my comrade listens, suggests objections, raises difficulties which we try to solve in unison. The two combined levers, inserted in the fissure, end by shaking and overturning the rocky mass.

I no longer see in the corner of the quartermaster's eye the leery droop that greeted me at the start. Cordial frankness now reigns, the infectious high spirits imparted by success. Little by little, dawn breaks, very misty as yet, but laden with promises. We are both greatly amazed; and my share in the satisfaction is a double one, for he sees twice over who makes others see. Thus do we pass half the night, in delightful hours. We cease when sleep begins to weigh too heavily on our eyelids.

When my comrade returns to his room, does he sleep, careless for the moment of the shifting scene which we have conjured up? He confesses to me that he sleeps soundly. This advantage I do not possess. It is not in my power to pass the sponge over my poor brain even as I pass it over the blackboard. The network of ideas remains and forms as it were a moving cobweb in which repose wriggles and tosses, incapable of finding a stable equilibrium. When sleep does come at last, it is often but a state of somnolence which, far from suspending the activity of the mind, actually maintains and quickens it more than waking would. During this torpor, in which night has not yet closed upon the brain, I sometimes solve mathematical difficulties with which I struggled unsuccessfully the day before. A brilliant beacon, of which I am hardly conscious, flares in my brain. Then I jump out of bed, light my lamp again and hasten to jot down my solutions, the recollection of which I should have lost on awakening. Like lightning flashes, those gleams vanish as suddenly as they appear.

Whence do they come? Probably from a habit which I acquired very early in life: to have food always there for my mind, to pour the never failing oil constantly into the lamp of thought. Would you succeed in the things of the mind? The infallible method is to be always thinking of them. This method I practiced more sedulously than my comrade; and hence, no doubt, arose the interchange of positions, the disciple turned into the master. It was not, however, an overwhelming infatuation, a painful obsession; it was rather a recreation, almost a poetic feast. As our great lyric writer put it in the preface to his volume, Les Rayons et les ombres: 'Mathematics play their part in art as well as in science. There is algebra in astronomy: astronomy is akin to poetry; there is algebra in music: music is akin to poetry.'

Is this poetic exaggeration? Surely not: Victor Hugo spoke truly. Algebra, the poem of order, has magnificent flights. I look upon its formulae, its strophes as superb, without feeling at all astonished when others do not agree. My colleague's satirical look came back when I was imprudent enough to confide my extrageometrical raptures to his ears: 'Nonsense,' said he, 'pure stuff and nonsense! Let's get on with our tangents.'

The quartermaster was right: the strict severity of our approaching examination allowed of no such dreamer's outbursts. Was I, on my side, very wrong? To warm chill calculation by the fire of the ideal, to lift one's thought above mere formulae, to brighten the caverns of the abstract with a spark of life: was this not to ease the effort of penetrating the unknown? Where my comrade plodded on, scorning my viaticum, I performed a journey of pleasure. If I had to lean on the rude staff of algebra, I had for my guide that voice within me, urging me to lofty flights. Study became a joy.

It became still more interesting when, after the angularities of a combination of straight lines, I learnt to portray the graces of a curve. How many properties were there of which the compass knew nothing, how many cunning laws lay contained in embryo within an equation, the mysterious nut which must be artistically cracked to extract the rich kernel, the theorem! Take this or that term, place the + sign before it and forthwith you have the ellipse, the trajectory of the planets, with its two friendly foci, transmitting pairs of vectors whose sum is constant; substitute the—sign and you have the hyperbola with the antagonistic foci, the desperate curve that dives into space with infinite tentacles, approaching nearer and nearer to straight lines, the asymptotes, but never succeeding in meeting them. Suppress that term and you have the parabola, which vainly seeks in infinity its lost second focus; you have the trajectory of the bombshell; you have the path of certain comets which come one day to visit our sun and then flee to depths whence they never return. Is it not wonderful thus to formulate the orbit of the worlds? I thought so then and I think so still.

After fifteen months of this exercise, we went up together for our examination at Montpellier; and both of us received our degrees as bachelors of mathematical science. My companion was a wreck: I, on the other hand, had refreshed myself with analytical geometry.

Utterly worn out by his course of conic sections, my chum declares that he has had enough. In vain I hold out the glittering prospect of a new degree, that of licentiate of mathematical science, which would lead us to the splendors of the higher mathematics and initiate us into the mechanics of the heavens: I cannot prevail upon him, cannot make him share my audacity. He calls it a mad scheme, which will exhaust us and come to nothing. Without the advice of an experienced pilot, with no other compass than a book, which is not always very clear, because of its laconic adherence to set terms, our poor bark is bound to be wrecked on the first reef. One might as well put out to sea in a nutshell and defy the billows of the vasty deep. He does not use these actual words, but his gloomy estimate of the extreme difficulties to be encountered is enough to explain his refusal. I am quite free to go and break my neck in far countries; he is more prudent and will not follow me.

I suspect another reason, which the deserter does not confess. He has obtained the title needed for his plans. What does he care for the rest? Is it worth while to sit up late at night and wear one's self out in toil for the mere pleasure of learning? He must be a madman who, without the lure of profit, lends an ear to the blandishments of knowledge. Let us retreat into our shell, close our lid to the importunities of the light and lead the life of a mussel. There lies the secret of happiness. This philosophy is not mine. My curiosity sees in a stage accomplished no more than the preparation for a new stage towards the retreating unknown. My partner, therefore, leaves me. Henceforth, I am alone, alone and wretched. There is no one left with whom I can sit up and thresh the subject out in exhilarating discussion. There is no one near me to understand me, no one who can even passively oppose his ideas to mine and take part in the conflict whence the light will spring, even as a spark is born of the concussion of two flints. When a difficulty arises, steep as a cliff, there is no friendly shoulder to support me in my attempt to climb it. Alone, I have to cling to the roughness of the jagged rock, to fall, often, and pick myself up, covered with bruises, and renew the assault; alone, I must give my shout of triumph, without the least echo of encouragement, when, reaching the summit and broken in the effort, I am at last allowed to see a little way beyond.

My mathematical campaign will cost me much stubborn thought: I am aware of this after the first few lines of my book. I am entering upon the domain of the abstract, rough ground that can only be cleared by the insistent plow of reflection. The blackboard, excellent for the curves of analytical geometry studied in my friend's company, is now neglected. I prefer the exercise book, a quire of paper bound in a cover. With this confidant, which allows one to remain seated and rests the muscles of the legs, I can commune nightly under my lampshade, until a late hour, and keep going the forge of thought wherein the intractable problem is softened and hammered into shape.

My study table, the size of a pocket handkerchief, occupied on the right by the ink stand—a penny bottle—and on the left by the open exercise book, gives me just the room which I need to wield the pen. I love that little piece of furniture, one of the first acquisitions of my early married life. It is easily moved where you wish: in front of the window, when the sky is cloudy; into the discreet light of a corner, when the sun is troublesome. In winter, it allows you to come close to the hearth, where a log is blazing.

Poor little walnut board, I have been faithful to you for half a century and more. Ink-stained, cut and scarred with the penknife, you lend your support today to my prose as you once did to my equations. This variation in employment leaves you indifferent; your patient back extends the same welcome to the formulae of algebra and the formula of thought. I cannot boast this placidity; I find that the change has not increased my peace of mind; hunting for ideas troubles the brain even more than hunting for the roots of an equation.

You would never recognize me, little friend, if you could give a glance at my gray mane. Where is the cheerful face of former days, bright with enthusiasm and hope? I have aged, I have aged. And you, what a falling off, since you came to me from the dealer's, gleaming and polished and smelling so good with your beeswax! Like your master, you have wrinkles, often my work, I admit; for how many times, in my impatience, have I not dug my pen into you, when, after its dip in the muddy inkpot, the nib refused to write decently!

One of your corners is broken off; the boards are beginning to come loose. Inside you, I hear, from time to time, the plane of the death-watch, who despoils old furniture. From year to year, new galleries are excavated, endangering your solidity. The old ones show on the outside in the shape of tiny round holes. A stranger has seized upon the latter, excellent quarters, obtained without trouble. I see the impudent intruder run nimbly under my elbow and penetrate forthwith into the tunnel abandoned by the death-watch. She is after game, this slender huntress, clad in black, busy collecting wood lice for her grubs. A whole nation is devouring you, you old table; I am writing on a swarm of insects! No support could be more appropriate to my entomological notes.