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 acc.u.mulation 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 gla.s.s 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 b.u.mblebee 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 pa.s.s 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 appet.i.te 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 fl.u.s.ter 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 pa.s.s and repa.s.s 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 pa.s.sers 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 gla.s.s; 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 trespa.s.sers 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 a.s.sistant, 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 b.u.mblebee 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 p.r.o.ne 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 c.o.ke 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 sc.r.a.pe 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 princ.i.p.al'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 cla.s.s here during the greater part of the year. The boys come to these rooms in winter, in front of a grate stuffed full of c.o.ke, like mine, and there find a blackboard, a pneumatic trough, a mantelpiece covered with gla.s.s 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 t.i.tle 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 antic.i.p.ations 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 princ.i.p.al'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 pa.s.sed 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.