A TANGLED TALE.

KNOT VIII.

A SERPENT WITH CORNERS.

'Water, water, every where,
Nor any drop to drink.'

'IT'LL just take one more pebble.'

'What ever are you doing with those buckets?'

The speakers were Hugh and Lambert. Place, the beach of Little Mendip. Time, 1.30 P.M. Hugh was floating a bucket in another a size larger, and trying how many pebbles it would carry without sinking. Lambert was lying on his back, doing nothing.

For the next minute or two Hugh was silent, evidently deep in thought. Suddenly he started. 'I say, look here, Lambert!' he

cried.

'If it's alive, and slimy, and with legs, I don't care to,' said Lambert.

'Didn't Balbus say this morning that if a body is immersed in liquid it displaces as much liquid as is equal to its own bulk?' said Hugh.

'He said things of that sort,' Lambert vaguely replied.

'Well, just look here a minute. Here's the little bucket almost quite immersed so the water displaced ought to be just about the same bulk. And now just look at it!' He took out the little bucket as he spoke, and handed the big one to Lambert. 'Why, there's hardly a teacupful! Do you mean to say that water is the same bulk as the little bucket?'

'Course it is,' said Lambert.

'Well, look here again!' cried Hugh, triumphantly, as he poured the water from the big bucket into the little one. Why, it doesn't half fill it!'

'That's its business,' said Lambert. If Balbus says it's the same bulk, why, it is the same bulk, you know.'

'Well, I don't believe it,' said Hugh.

'You needn't,' said Lambert. 'Besides, it's dinner-time. Come along.'

They found Balbus waiting dinner for them, and to him Hugh at once propounded his difficulty.

'Let's get you helped first,' said Balbus, briskly cutting away at the joint. You know the old proverb, "Mutton first, mechanics afterwards"?'

The boys did not know the proverb, but they accepted it in perfect good faith, as they did every piece of information, however startling,

that came from so infallible an authority as their tutor. They ate on steadily in silence, and, when dinner was over, Hugh set out the usual array of pens, ink, and paper, while Balbus repeated to them the problem he had prepared for their afternoon's task.

A friend of mine has a flower-garden-a very pretty one, though no great size-'

'How big is it?' said Hugh.

"That's what you have to find out!' Balbus gaily replied.

All I

tell you is that it is oblong in shape-just half a yard longer than its width-and that a gravel-walk, one yard wide, begins at one corner and runs all round it.'

'Joining into itself?' said Hugh.

Not joining into itself, young man. Just before doing that, it turns a corner, and runs round the garden again, alongside of the first portion, and then inside that again, winding in and in, and each lap touching the last one, till it has used up the whole of the area.'

'Like a serpent with corners?' said Lambert.

'Exactly so. And if you walk the whole length of it, to the last inch, keeping in the centre of the path, it's exactly two miles and half a furlong. Now, while you find the dimensions of the garden, I'll go and think out that sea-water puzzle.'

'You said it was a flower garden?' Hugh inquired, as Balbus was leaving the room.

'I did,' said Balbus.

'Where do the flowers grow?' said Hugh. But Balbus thought it best not to hear the question. He left the boys to their problem, and, in the silence of his own room, set himself to unravel Hugh's mechanical paradox.

'To fix our thoughts,' he murmured to himself, as, with hands deep-buried in his pockets, he paced up and down the room, we will take a cylindrical glass jar, with a scale of inches marked up the side, and fill it with water up to the 10-inch mark: and we will assume that every inch depth of jar contains a pint of water. We will now take a solid cylinder, such that every inch of it is equal in bulk to half a pint of water, and plunge 4 inches of it into the water, so that the end of the cylinder comes down to the 6-inch mark. Well, that displaces 2 pints of water. What becomes of them? Why, if there were no more cylinder, they would lie comfortably on the top, and fill the jar up to the 12-inch mark. But unfortunately there is more cylinder, occupying half the space between the 10-inch and 12-inch marks, so that only one pint of water can be accommodated there. What becomes of the other pint? Why, if there were no more cylinder, it would lie on the top, and fill the jar up to the 13-inch mark. But unfortunately sudden accents of terror. A bright idea struck him.

-Shade of Newton!' he exclaimed, in 'When does the water stop rising?'

'I'll write a little essay on it,' he said.

Balbus's Essay.

'When a solid is immersed in a liquid, it is well known that it displaces a portion of the liquid equal to itself in bulk, and that the level of the liquid rises just so much as it would rise if a quantity of liquid had been added to it, equal in bulk to the solid. Lardner says, precisely the same process occurs when a solid is partially immersed : the quantity of liquid displaced, in this case, equalling the portion of the solid which is immersed, and the rise of the level being in proportion.

'Suppose a solid held above the surface of a liquid and partially immersed a portion of the liquid is displaced, and the level of the liquid rises. But, by this rise of level, a little bit more of the solid is of course immersed, and so there is a new displacement of a second portion of the liquid, and a consequent rise of level. Again, this second rise of level causes a yet further immersion, and by consequence another displacement of liquid and another rise. It is selfevident that this process must continue till the entire solid is immersed, and that the liquid will then begin to immerse whatever holds the solid, which, being connected with it, must for the time be considered a part of it. If you hold a stick, six feet long, with its end in a tumbler of water, and wait long enough, you must eventually be immersed. The question as to the source from which the water is supplied-which belongs to a high branch of mathematics, and is therefore beyond our present scope does not apply to the sea. Let us therefore take the familiar instance of a man standing at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses he remains steadfast and unmoved, and we all know that he must be drowned. The multitudes who daily perish in this manner to attest a philosophical truth, and whose bodies the unreasoning wave casts sullenly upon our thankless shores, have a truer claim to be called the martyrs of science than a Galileo or a Kepler. To use Kossuth's eloquent phrase, they are the unnamed demigods of the nineteenth century.'

'There's a fallacy somewhere,' he murmured drowsily, as he stretched his long legs upon the sofa. I must think it over again.' He closed his eyes, in order to concentrate his attention more perfectly, and for the next hour or so his slow and regular breathing bore witness to the careful deliberation with which he was investigating this new and perplexing view of the subject.

LEWIS CARROLL.

Note by the writer.-For the above Essay I am indebted to a dear friend, now deceased.

ACCOUNT OF A VISIT TO SHOREDITCH.

HAVING often wished to see London life as it really is, at the east end, I gladly took advantage of an opportunity which occurred to carry out my desire. The following details, full of melancholy interest, are the results of my day's experience.

The Sisters of the Church,' Kilburn, whom I went to visit with a friend, gave me such accounts of their work in the east end of London, and of the misery and wretchedness in Shoreditch, that I was very pleased when they offered to take me with them on one of their visiting days.

Tuesday, and Whitsun Tuesday too, was the day fixed for my accompaying them on their errands of mercy. I accordingly reached the Home about half-past ten, and we very soon afterwards set off for the east end, which we reached by the underground railway, taking our tickets to Bishopsgate Station. Each sister carried a can, containing soup to be heated, and some sago pudding. The Mission House is quite a primitive little place, and is situated in Sclater Street, a narrow thoroughfare skirting the north of the old Eastern Counties Terminus, and introducing one to a labyrinth of wretched, ill-paved little streets, bordered by dirty, dilapidated houses, the abodes chiefly of a race of matchbox-makers and weavers. The Sisters occupy the ground floor and first story. The former consists of scullery and the front room, which is divided by a wooden partition, making a little kitchen, where they cook the dinners for the sick, and then carry them out into their own homes. Up stairs the room is also divided by a curtain, part being used as a sort of oratory. Here mothers' meetings, classes for girls preparing for baptism, confirmation, &c., are held; a woman living above, whose husband is a silk weaver, takes care of the house and keeps it clean. The lower room is ornamented with texts round the walls, and a table goes the length of the room, where the girls who come to the confirmation classes have a dinner on Tuesdays and Thursdays. Each week the Sisters have a list of sick sent them by the vicar of the parish, under whom they work, and then take the dinners to the persons mentioned.

The first thing to be done was of course to prepare the soup, and this one of the Sisters immediately proceeded to do, while another peeled some lemons, another cleaned the knives, &c.; altogether this part of the business seemed to me rather fun, and I tried to help where I could. The table was prepared for the children's dinner, and one sister went out to buy some meat pies, &c., for them. Each child pays a penny, but it being Whitsun Tuesday, none of them appeared; and so their food was divided among some other poor people. While

preparations were being made for our dinner, which we had before going on our round, I heard a most curious noise overhead. I was told this was silk-weaving, and as I had never seen any done before, I went up stairs to witness the performance. It was worked by the woman's husband who takes care of the Mission House, and lives on the second story. He was a very nice old man, but he looked weary and ill, and so indeed he was-he was suffering from a painful internal illness, and the pain in his back was sometimes so acute he could hardly bear it; but the woman was rather a whining old thing, full of troubles and worries. It seemed very hard work; he was making carriage blinds. I wonder how often grand ladies driving about in their carriages think of the pain and trouble it has taken many a poor creature to make the very blinds of their vehicles.

After dinner we set off. We divided into three parties; I went with Sister E and carried one of her cans. The people in the streets were most dreadful-looking-men, women, yes! and even boys, all drunk. Going down a passage a boy was pushed out of a door, nearly against me, by two women, one of whom was hitting him about the head, and the other quarrelling with the first, about it-the boy howling, and the women screaming and yelling. We now arrived at the first house, and I shall never forget it; I never saw anything so sad in my life before. We knocked, and a man, a toy-maker, the husband of the poor sick woman inside, opened the door. He was quite tipsy, and Sister E- whispered so to me, asking if I was frightened. Of course I said 'No, not with you,' and we entered. The room was small and very, very dirty. A little child was another inmate of the room, and her history is a most touching one. The first time Sister Ethe house she noticed the child had but one eye, and asked her how she had lost the other; if it was an accident? Oh! no,' was the answer, 'mother poked it out one day because I hadn't lighted the fire quick enough, so she took up a bit of wood from the grate and sent it into my eye.' Just fancy how the poor mite must have suffered! Can anything more horrible be imagined? I had heard so much about the little girl that I looked at her with great interest. She is very interesting looking, and her one poor brown eye has much intelligence in it. The Sisters are very fond of her, and she is very bright and quick.

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went to

The one object in the room, however, which attracted the eyes of all beholders was the poor sick woman. She was sitting on a chair, leaning forward, with her head resting on a most filthy pillow, moaning piteously, and rocking herself backwards and forwards, evidently in fearful suffering; and so indeed she was. She rarely ceases moaning, day or night, except when she sleeps. She has been in this state for three years, and for more than eighteen months no woman had crossed the threshold to do anything for her, and she had no one to feed her or wash her but this little child, her niece, who appeared to be about eight VOL. 5.

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PART 25.