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in the spurs rowel deep, and at one bound came crashing through the rhododendrons to within some three or four feet of the place where the child stood. The alligator wheeled angrily round, to confront the intruder who dared to come between him and his toothsome supper; and my horse, driven wild with terror at the sight and smell of the monstrous reptile, reared, swerved, and threw me, galloping off like a mad creature. I was on my feet in a moment, and had just time to throw myself between the alligator and the boy, before the bloodthirsty jaws could close in the first fatal The brute recoiled a little, for alligators are cowardly as well as fierce, and they have been known to watch for hours in their reedy ambush, allowing men to pass them uninjured, until they could pounce securely on a woman or a child. But the reptile's slow blood had been too much stirred, by the expectation of an easy triumph, to permit him to decline the fight, and he crawled in upon me, uttering the hoarse cry, half-roar, half-whimpering moan, that a cayman gives under the sting of pain or fury.

snap.

I had my sheath-knife out, a strong doubleedged blade of Barcelona steel, with a cross-handle and buckthorn haft; but this seemed a poor weapon against such a foe. By a hasty impulse one of those life-saving thoughts that come upon us at moments of extreme peril, as if they were the whisperings of inspiration-I tore the blue woollen poncho from my shoulders-happily, I had adopted the New Spain style of dress-and, wrapping the mantle around the tough handle of my whalebone riding-whip, I forced it between the alligator's jaws as he closed with me, while at the same time, bending forward, I struck hard with my twoedged knife at his white throat, which was comparatively unprotected. The first stab told, for the white streak was soon crimsoned with blood; but the second stroke failed, for the knife slipped, and rattled uselessly on the armour-plates of the creature's mailed back; and then began a struggle for death or life between my terrible antagonist and myself. My strength was nothing to that of the huge reptile, and I felt myself dragged to right and left as if I had been a rat in the gripe of a terrier, yet I held on fast to the whalebone handle of the whip, while the sharp teeth vainly gnashed and tore at the spongy wool that clogged them, and I retained my hold in sheer desperation, striking in with my knife whenever I got a chance, but usually baffled by the tenacious armour of my invulnerable adversary.

Charlie, a few feet distant, was sobbing piteously, at times crying aloud in appeal to Guachos whom he knew Sancho !' 'Diego!' 'El Negro!'-to help 'Mirry Warburton;' for the dear little fellow, delivered from his first agony of alarm, seemed now to think only of my peril. The idea was a good one, although the child's weak voice could not of course reach far. Exerting the full strength of my lungs, I twice shouted forth the well-known desert cry when a jaguar is sighted: Mozos, a mi! -El Tigre!-Mo-zos!'—and I fancied, as I uttered the second call, that I heard a distant answer, like a faint echo. But now I had need of all my breath and all my muscles, for the infuriated animal with which I fought, tearing the cloth of the soft mantle

day-and the horrible odour of the creature, and the remorseless glare of its small bloodshot eye, impressed me with the fantastic notion that my enemy was something evil beyond the mere furious greed of a wild beast. Yet I grasped the whalebone whip-handle, and drove in the knife with all the force of an arm that was fast growing exhausted. Spent, breathless, giddy, I was dragged down, and in a kneeling attitude, exerted the remains of my waning strength in a stab at the alligator's throat. The blade broke short off by the handle as it lodged among the stout scales of the neck!

Just then I heard a shout, and the tramp of a horse coming up at full and furious speed. On they came, the steed foam-flecked and gored by the spur, the rider brandishing high above his head the spiral coils of the lasso. I recognised the horseman in an instant. It was Juan, the boldest and most dexterous of all that Centaur brotherhood; and he knew me, and comprehended at a glance the state of affairs.

'Stand back, Englishman-stand back!' he cried aloud, and I'll do the rest; Mozos !-El Tigre!— Mo-zos!' And he whirled the lasso high, spurring his frightened horse near and nearer to the spot.

LOVE MEMORIES.

Ay, lad, it was here that we lingered
In the still of that sweet June night,
Till the larks were up, and the cloudless east
Was flushed with rosy light;

And a red-breast was out on the hawthorn there,
A-trilling a low sweet lay

To his mate and the wee brown birds that slept
In the nest on the bending spray.

It was at your grandfather's wedding, lad,
That Jenny and I had been,

And I was the bravest of all the lads,
And she of the girls was queen;

And homeward we walked through the dewy fields,
When the dancing and mirth were o'er;
And I stood with her dear little hand in mine,
Here, under the porch by the door.

There was never a soul astir in the house,
But all was as still as could be;
And even although they had all been awake,
They could never have seen her and me;
For the ivy was thick, and we whispered so low,
Oh, they ne'er could have heard us there,
As she gave me a wild red rose from the flowers
She had worn in her beautiful hair.

O the passionate love of life's spring tide!
Though now I am old and gray,

Each low murmured word I remember as well
As if it were yesterday:

How I thrilled at the touch of the soft brown locks

That over her shoulders curled,

And trembled for joy when I dared to kiss
The rosiest lips in the world!

Get me a bit of the blossom, lad,
That wreathes on the hawthorn tree,
And leave me here till I dream awhile
Of the life that was never to be.
For the shadowy phantoms of long ago
I see through a mist of tears:
Your hope lies hid in the coming, lad,
But mine in the bygone, years.

to pulp, was gradually getting its grim jaws free. Printed and Published by W. & R. CHAMBERS, 47 PaterTwice, already, had my wrist and arm been grazed by its keen teeth-I bear the white scars to this

noster Row, LONDON, and 339 High Street, EDINBURGH. Also sold by all Booksellers.

CHAMBERS'S JOURNAL

No. 447.

OF

POPULAR

LITERATURE, SCIENCE, AND ART.
Fourth Series

CONDUCTED BY WILLIAM AND ROBERT CHAMBERS.

SATURDAY, JULY 20, 1872.

THE ROMANCE OF ARITHMETIC. SURELY figures owe us whatever little of romance is to be got out of them. Have they not been associated from our earliest childhood with the taste of tears and slate-pencil? Have they not been the invariable cause of one's income being insufficient to meet one's expenditure? Have they not tyrannised over our tastes and enjoyments? And has not the sole reason of that gap which, at every year's end, prevents some of us, in spite of the most laudable intentions, from making both ends meet, been the obstinate persistence of two and two in their sullen refusal to make any more than four? I am rejoiced to learn that Pythagoras, who said something civil about all the other numbers, had a very poor opinion of figure two. I am delighted to know that he regarded this disreputable figure as the symbol of disorder, of division, of confusion, and inequality; as a hopelessly depraved number of evil augury, as an exceeding bad principle-nay, as the very Old Bad Principle himself. I've no patience with figure two, nor with the way in which it gets held up to public esteem in connection with what is supposed to be the very satisfactory proposition that two and two make four. I cannot regard it in that light. Whatever is good for anything ought to improve and increase; and if this boasted pair of twos had any genuine enterprise at all about them they would have made at least six by this time-in which case I might without difficulty have learned what a balance meant in my banker's book. As it is, they have not merely wasted their opportunities, but done me a personal injury. Besides, it is my opinion that three and one make four in a manner quite as successful, and very much less obtrusive.

PRICE 1d.

table the product of nine comes to nine. Multiply by what you like and it gives the same result. Begin with twice nine, 18; add the digits together, and 1 and 8 make 9. Three times nine are 27; and 2 and 7 make 9. So it goes on, up to eleven times nine, which gives 99. Very good; add the digits; 9 and 9 are 18, and 8 and 1 are 9. Going on to any extent, it is impossible to get rid of figure 9. Take a couple of instances at random. Three hundred and thirtynine times nine are 3051; add up the figures and they give 9. Five thousand and seventy-one times nine are 45639; the sum of these digits is 27; and 2 and 7 are 9.

M. de Maivan found out another queer thing about this number-namely, that if you take any row of figures, and reversing their order, make a subtraction sum of it, the total is sure to be 9. For example:

Take 5071

Reverse the figures 1705

=

3366 18, and 1 + 8 = 9. The same result is obtained if you raise the numbers so changed to their squares or cubes. Starting with 62, begin the sum over again. By reversing the digits we get 26, which, subtracted from 62, leaves 36, or 3+ 6 = 9. The squares of 26 and 62 are, respectively, 676 and 3844. Subtract one from the other and you get 3168 = 18, and 1+8=9. So with the cubes of 26 and 62, which are 17576 and 238328. Subtracted, they leave 220752 = 18, and 1 + 8 = 9.

The powerfully be-nine influence of this figure is exemplified in another way. Write down any number, as, for example, 7549132, subtract therefrom the sum of its digits, and no matter what figures you start with, the digits of the product will always come to 9.

7549132 = sum of digits 31.
31
7549101

The most romantic of all numbers is figure nine, because it can't be multiplied away or got rid of anyhow. Whatever you do, it is as sure to turn up again as was the body of Eugene Aram's victim. One remarkable property of this figure (said to have been first discovered by W. Green, who died A very good puzzle has been based on this prinin 1794) is, that all through the multiplication ciple, as follows: Get another person to write down

= sum of digits 27, and 2 + 7 = 9.

a horizontal row of figures, as many as he likes, without letting you see what he is about from beginning to end of the whole performance. He is then to reckon up the sum of the digits, and subtract that from his row of figures. When he has done this, bid him cross out any figure he pleases from the product, and tell you how much the figures add up, without the crossed-out figure. From the numbers so given you will be able to tell what figure he has crossed out, by only bearing in mind the fact learned above-namely, that if no figure at all had been crossed out, the result would necessarily be 9 or a multiple of 9. Hence you will see that the crossed-out figure must needs be the one required to bring the sum given to the next multiple of 9. Supposing, for instance, he gives his result at 37, you may be sure that he has robbed the product of 8, that being the figure needed to restore the total to the next multiple of 9-namely, 45. His sum would stand as under:

405678237= sum of digits 42.

42

405678195=37.

There is only one case in which you can be at fault, and that is in the event of a multiple of 9 being returned to you as a product. Of course, then, you will know that either a 9 or a 0 must have been struck out. Had the 9 been struck out in the above instance, the result would have been 36 had it been the 0, the product would have been 45. Both being multiples of 9, it would be impossible to tell with certainty whether the missing figure were 9 or 0; but a good guess may generally be formed, because, if the figures appear suspiciously low in proportion to the time taken to tot up the sum, you may speculate that your product has most likely sustained the loss of the highest number.

many more, half as many more, and a third as many more as there are now in the basket, with five more added to that, the number would by so much exceed threescore as it now falls short of it.' The second knight, getting awfully bewildered, speculated wildly on forty-five.

'Not so,' said this royal ready reckoner. 'But if there were a third as many more, half as many more, and a sixth as many more as there are now, there would be in my basket as many more than forty-five as there now are under that number.'

Prince Wladomir then decided the number of plums to be thirty; and by so doing obtained this invaluable housekeeper for his wife. The Lady Libussa thereupon counted him out fifteen plums and one more, when there remained fourteen. To the second knight, she gave seven and one more, and six remained. To the first knight, she gave half of these and three more; and the basket was empty. The discarded lovers went off with their heads exceedingly giddy, and their mouths full of plums.

Double Position, or the Rule of False, by which problems of this sort are worked, ought to demolish the commonplace about two wrongs not making a right. Two wrongs do make a right, figure-atively speaking, at all events. Starting with two wilfully false numbers, you work each out to its natural conclusion. Then, taking the sum of your iniquities as compared with the falsehoods with which you started, you have only to multiply them crosswise to get terms which will bring you straight to the truth. To be more precise, after the cross-multiplication, if the errors are alikethat is, both greater or both less than the number you want-take their difference for a divisor, and the difference of their products for a dividend. If unlike, take their sum for a divisor, and the sum of their products for a dividend. The quotient will be the answer. This is good arithmetic, and, for those who can receive it, not bad philosophy. There is an enormous self-righting power about error, and if we could only manage the crossmultiplication properly, we might get some surprising results.

That is a clever Persian story about Mohammed Ali and the camels, and though it will be familiar to many of my readers, they will scarcely be sorry to be reminded of it. A Persian died, leaving seventeen camels to be divided among his three sons in the following proportions: the eldest to have half, the second a third, and the youngest a The number 37 has this strange peculiarity: ninth. Of course, camels can't be divided into frac- multiplied by 3 or any multiple of 3 up to 27, it tions, so, in despair, the brothers submitted their gives three figures all alike. Thus, three times difficulty to Mohammed Ali. Nothing easier!' 37 will be 111. Twice three times (6 times) 37 said the wise Ali: 'I'll lend you another camel to will be 222; three times three times (9 times) 37 make eighteen, and now divide them yourselves.' gives three threes; four times three times (19 The consequence was, each brother got from one-times) 37, three fours; and so on. eighth to one-half of a camel more than he was entitled to, and Ali received his camel back again; the eldest brother getting nine camels, the second six, and the third two.

Johann August Musæus, one of the most popular German story-writers of the last century, in his story of Libussa, makes the Lady of Bohemia put forth the following problem to her three lovers, offering her hand and throne as the prize for a correct solution. I have here in my basket,' said the Lady Libussa, 'a gift of plums for each of you, picked from my garden. One of you shall have half and one more, the second shall again have half and one more, and the third shall again have half and three more. This will empty my basket. Now tell me how many plums are in it ?" The first knight made a random guess at three

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I will wind up for the present with a rather barefaced story of how a Dublin chambermaid is said to have got twelve commercial travellers into eleven bedrooms, and yet to have given each a separate room. Here we have the eleven bedrooms:

1 2 3 4 5 67 8 9 10 11

'Now,' said she, if two of you gentlemen will go into No. 1 bedroom, and wait there a few minutes, I'll find a spare room for one of you as soon as I've shewn the others to their rooms.'

Well, now, having thus bestowed two gentle men in No. 1, she put the third in No. 2, the fourth in No. 3, the fifth in No. 4, the sixth in No. 5, the seventh in No. 6, the eighth in No. 7, the ninth in No. 8, the tenth in No. 9, and the eleventh in No.

10. She then came back to No. 1, where you will remember she had left the twelfth gentleman along with the first, and said: 'I've now accommodated all the rest, and have still a room to spare, so, if one of you will please step into No. 11, you will find it empty.' Thus the twelfth man got his bedroom. Of course, there is a hole in the saucepan somewhere; but I leave the reader to determine exactly where the fallacy is, with just a warning to think twice before deciding as to which, if any, of the travellers was the odd man out.'

A WOMAN'S VENGEANCE.

CHAPTER XIII.-ON THE BRIDGE.

'SORROW may endure for a night, but joy cometh in the morning,' is a saw of great authority and acceptance, and yet we suspect that human experience, if appealed to generally, would reverse that saying. Surely it is at night, after some sort of meal, or drink, or even a pipe of tobacco, that our spirits fight against despondency, and we make the best of a bad job,' or, at all events, look forward to forgetting our troubles in sleep; whereas, on the other hand, when the blank day breaks, the full sense of our calamity is borne in upon us, and, like Miss Bella Wilfer, we wish that we were dead. At all events, on the morrow of his return to his old home, Arthur Tyndall awoke far more dispirited and displeased with himself than he had yet been, and early as it was, arose and dressed himself. For to lie in one's bed in the broad daylight, to think and think of the ruin that we have brought upon ourselves, or on the wrong we have done to others, is of all things the most intolerable.

Within doors, no one was stirring, but without, the ancient gardener was already sweeping one of the gravel-walks, and bade his young master 'goodmorning' heartily.

Foreign parts have not altered your ways of life, I see, Master Arthur,' said he approvingly; for you was always an early riser, like your poor father before ye.'

Yes; he had been an early riser, and at Swansdale especially, for a certain reason, which the sight of Old Giles recalled to his mind with a sharp pain. Often and often had he come upon the old man when, with rod and basket, he had gone forth from the Hall at that very hour-not to fish, but to pretend to fish from the river-side path that led to the Welcome. It was not unlikely even that Giles knew that he had done so, for, though no one in the village was aware of how far matters once had gone between Master Arthur' and 'Jenny,' there was a shrewd suspicion abroad that they were not indifferent to one another. How unchanged seemed every object that met his gaze since those palmy days of adolescence and first love; unsettled and doubtful days, indeed, but days of promise! How gloriously the tall trees sparkled with dew! How freshly rose the incense from the flower-beds! In the winding shrubbery-wilderness,' it used to be called, but, to his travelled eyes, accustomed to the wild luxuriance of nature, it seemed garden like the rest-how joyously sang the birds! There was the little wicket-gate to which she had once been 50 rash as to accompany him on his way back, and where they had parted with a whispered farewell: he had leaned upon it, and watched her trip homeward along the dewy fields, and when she turned and

smiled (for he knew that she was smiling, since she had her face towards him), he had smiled too and kissed his hand. He leaned upon it now, and gazed upon the vacant fields with an aching heart. But why had it not ached before, when absent from her? And why had it not yearned, on his return to England, to clasp her in his arms—as it did now? Why had his love smouldered so low that he had thought it cold and burnt out? And now, when it was too late, why, merely at the sight of her, had it flamed up anew, so fiercely that it threatened to consume him? Had he deceived himself, and loving her all along, persuaded himself -being tempted so to do by material advantage— that he no longer loved her? No! If he had come back yesterday, and found her, exactly as he had left her, 'a simple maiden in her flower,' he could have borne to look upon her with remorseful eyes, perhaps, but with steadfast ones. He had made up his mind to do so. He had been bound by no promise to do otherwise; she herself had told him that what had happened was likely to happen ; necessity (induced by his own act, but still necessity) had compelled him to the course he had taken. Of course, he had been inconsistent: woman is weak, illogical, and (very) contradictory, but there is no bound to the inconsistency of man. The most faithful forget their allegiance; the bravest become cowards. Picton himself was convicted of participation in an act which men of ordinary courage would die rather than have committed. Arthur, to do him justice, had given Jenny credit for the same readiness to forget and to forgive to forget him, that is, and to forgive herself as he had manifested towards her; or if that should not have been the case-if even she should still entertain some tenderness for himshe was such a very sensible girl (this was how the poor wretch had argued), that so soon as she heard of his engagement to another, she would at once dismiss him from her heart as a traitor, perhaps; yet if so, so much the better for her. But what if she thought him a traitor, and still had

not dismissed him from her heart!

Her air had been grave and cold; she had refused to hear what he had to say for himself: she had treated the idea of their meeting at the old trysting-place-though only to hear his excuses -with indignation and disdain; but he could not forget, how, stung with the studied carelessness of his first salutation: Why, Jenny, how you are grown!' she had answered, as it seemed in spite of herself: Yes; grown out of all knowledge.' Throughout the rest of their brief interview, she had been cold as snow; but that one sentence of reproach, forced from her, doubtless, by the sense of insult which his words had occasioned, still rang in his ears. And how beautiful, and like a gentlewoman, she had grown, and how, in comparison with her, had all other gentlewomen, such as his aunt, or Blanche (he would not even to himself say or 'Helen'), dwindled into insignificance. She had been always far cleverer than himself, he knew; but what a divine wisdom seemed now to dwell in those glorious eyes, yet not unmixed with pity either, when she denied his prayer such pity as the angel might have felt whose duty it had been to expel our first parents from the Gates of Paradise! And yet she was a woman too, for had she not trembled and changed colour when he had denounced her refusal to let him write to her as

having been the cause of their estrangement, and did not those signs betoken that she still loved him! He did not so much still love her (though all the old passion was revived within him), as love her anew, more fondly, more fiercely, than he had ever loved before; and in a few weeks he was pledged to wed, not her, but another!

The river-side path, that led to the lock as well as to the inn, lay before him, and he regarded it with wistful eyes. Should he take that, or the upper one, which led to the village churchyard, wherein stood his father's tomb, to visit which had been the object he had proposed to himself in going forth that morning? Something within him seemed to whisper that at whichever decision he should arrive it would be final. As he hesitated, there fell on his ear a splash of a pole in the water, and there glided by up-stream a punt, with a fisherman in it, bound, doubtless, for the osier-nets that hung in the back-water behind the lock. This trifling circumstance decided him. If he was to meet Jenny, it was certainly advisable that there should be no possible witness to their interview; and he struck at once into the path that conducted to the church. It was the nearest way to the village, likewise, for all the water-side parishioners, running straight up through the meadows, and dipping midway into a hazel coppice, in which was a rustic bridge that spanned a little tributary of the river, but little frequented save on Sundays. The last time he had trodden it, it had been by his father's side to church, on the eve of his own departure for abroad. They had not been so cordial as father and son should be; there were faults on both sides; but now that the old man was beyond the reach of all amends, they seemed to have been on Arthur's only. And yet a few minutes ago he had been debating in his mind as to whether this little pilgrimage of piety should not be postponed, forwell, for what? For a mad attempt to throw himself in the way of temptation; for an appeal to Jenny's feelings, that would be worse than hopeless, since, even if it should have succeeded, nothing could have come of it but shame and ruin. He could not shut her from his thoughts on the way, or even when upon the hill-top he stood beside his father's grave. Why had the old man been so stern, that confidence had never existed between them? How far nearer would he have now seemed to him had he been encouraged to disclose the secret wish of his young heart, even had it been denied him; but now death had divided them indeed. If Jack had died, and been laid here, who had been privy to that early hope, and to almost every thought and action of his life, how differently he would have felt; a portion of his very self would then seem to be lying yonder, whereas, though this was his own flesh and blood, and the author of his being, it did not seem so. Suppose his father had given him permission to marry Jenny, and instead of becoming an exile from home and country, he had done so, and, filled with love and gratitude, had been his son indeed, with little children to climb the old man's knee, and-since a lonesome life is hurtful to health as well as heart-to win him, perhaps, from the very grave itself. This thought of what might have been was too much to bear, and he turned away almost abruptly from the graveyard, and began to retrace his steps. Quick motion suited with his mood, and the way being down hill, he advanced very rapidly, with eyes fixed on

the ground; so rapidly, that, half-way through the copse, he came upon the narrow wooden bridge, and had his foot upon it before he perceived that it was already occupied by some one coming from the river-side. He looked up hastily, and lo, it was Jenny Renn!

She stood for an instant in the middle of the bridge, undecided whether to retreat or advance, and with her hand upon the side-rail-a picture and a poem in one-then came on slowly towards him.

Jenny, Jenny!' cried Arthur eagerly, holding out both his hands.

'My name is Alice Renn, Mr Tyndall,' was her cold reply.

'I thought that, seeing me from the river, you might have come to meet me,' said he imploringly.

No. I was going to the church to practise on the organ, for I am the organist now.'

The organist! Then he would hear her on Sunday, and every Sunday, from his pew, where he would be sitting with Helen. He would know she was behind the little curtain, looking down between its folds upon himself with scorn, upon his bride with pity.

'I have behaved very, very ill to you, Jenny' he began.

She stopped him with a quiet motion of her hand. 'I do not say so, Mr Tyndall; but if it is so, let me tell you this, that you behave worse in speaking of it.' She was very pale, but her voice was firm and resolute. As she stood erect upon the bridge, from which he had withdrawn, to let her pass, she was taller than he; and he felt she was his superior every way.

'I will not confess my baseness, since you forbid me to do so, Jenny,' said he dejectedly; but do not suppose that I am not punished for it. If you knew all, even though you could not love me any longer, you must needs pity me.'

If any misfortune has befallen you, I am indeed sorry,' returned she-' very sorry.'

'No misfortune, for I have brought it all upon myself-no misfortune, since, compared with that of which I may not speak, all ills that may happen to me are of small amount; but, for one thing, I am a ruined man.'

'I thought so!' gasped the girl; not, however, like one who hears the worst. There was a certain tone of relief, nay, almost of exultation, in her ejaculation. I thought so!' It seemed to say: 'I thought that nothing but dire necessity could have compelled him to such conduct.'-'Ruined, Mr Tyndall!' she continued ; ' that is bad news indeed. A few weeks, however, as I understand, will retrieve your fallen fortunes.' Her woman's heart could not refrain from giving him that stab; then perceiving she had wounded him to the quick, it melted within her. 'Forgive me, sir; I did not mean to pain you; far from it. Heaven knows I wish nought but good to you to you and yours But no more meetings such as this, I pray you.' Here she sobbed most pitifully; and he sprang forward, as he would have done five years ago, to comfort her.

She thrust him from her with some force, and pointed towards the Hall. 'Leave me, sir. As you are a gentleman, I entreat you to leave me.'

He obeyed her, but unwillingly; slowly, linger ingly, he went on his way, with many a look

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