Curved Lines

W ILLIE and his parents loved the summer mornings, so they were always up very early. When Willie was dressed, he used to have a piece of bread to take out and eat with the warm new milk which the dairymaid gave him.

This morning, because it was his birthday, his father and mother said they would both come out with him; and they went to the paddock where the favourite cow, "Lily," was kept, to wait for the milkmaid.

The air was perfectly still, and the long cool shadows, and sparkling lights, the scent of lime-blossoms and fresh green grass, were quite fit for a birthday.

"Is it not lovely?" said Willie's mother.

"Yes! I wish I could paint; I would make a picture of the paddock this morning!" replied he.

"I hope you may be able to do so some day," said his father. "Talking of this, how do you get on with your drawing-master?"

"I have only been learning different lines and practising drawing them."

"Don't say 'only,' my boy, for when you are tolerably correct and quick in drawing these, you will have conquered one of the most troublesome things in your new study, and each succeeding step will be more pleasant than the last. What did Mr. Graphic teach you after straight lines?"

"He taught me curved lines, and he showed me about—"

"But let me hear about curved lines first, Willie. What is a curved line?"

"It is a line which does not go the shortest way between two points, but sweeps evenly out on one side or the other. I can show you some curved lines, father. Let me see,—Oh Lily's horns are two curved lines, and that tall grass-flower by the post, bending down with the dew, is a curved line."

"There is the weeping-willow tree beside the pond, nothing but curves all over, and the edge of the pond is another," added his father.

Just then the milkmaid came with her pail and stool, and sat down to milk Lily.

"Look, Patty," said Willie, running to her, "what a pretty new white mug my mother has given me to‑day! Please will you fill it with milk, and froth it well up?"

"Yes, I will," said Patty. "Dear me it is  pretty! all white,—Lily, milk, and mug!"

Patty took particular pains to froth the milk well, and the effect was splendid! Willie said, "Thank you," and then plunged his nose in and never left off drinking till the mug was empty. When he had done, and was rather out of breath, they all laughed; but Willie only stared, for he did not know the joke.

"Such a face, all over froth!" said his father.

Willie now laughed, too; and, after his mother had wiped his face, he ran about gathering wild flowers, while his father and mother stood still enjoying things in their quieter way.

Suddenly there came a little puff of wind from the southwest, which made the flowers nod and the leaves rustle gently. Then it ceased, and then came a bolder puff, and again another, till there was quite a high wind. The clouds which they had seen in the distance came riding grandly up and crowding into huge silvery masses. The big lime-trees rolled about, and roared as though they were in the most violent fits of laughter; and the wood pigeons, who had been cooing so quietly, blustered out with a great noise. The dead twigs from the old elms flew about in all directions, and the rooks cawed and screamed, half in terror, half in delight. It was merry and healthy, that warm south-west wind.

"See!" cried Willie's father, gaily, "nearly all our perpendicular lines are turned into curves! Look at the stems of the young larches and the poplar-trees as they stoop about!"

"Oh," exclaimed Willie, "that poor humble bee! he has been knocked off the great horse-daisy, and can't get back again for all his fuss!"

"How Sunbeam likes it," said his mother, as the chestnut colt galloped madly about, and then stopped short with eyes and nostrils wide open. "Look at his neck—there's a curve!"

The great clouds had now come overhead, and heavy raindrops began to fall, so they took shelter under a thick lime-tree. The wind lulled again, and in their snug nook they listened to the refreshing rain as it rattled among the leaves, making them a still brighter green. The thrushes called out joyously, and the wood-pigeons resettled themselves to their cooing. In about half-an-hour the sunlight broke suddenly through an opening in the clouds as they coursed rapidly away, and made the thousands of rain-drops look like little stars.

All at once Willie called out, "Oh, there's a rainbow! What a beautiful rainbow!"

"Yes, indeed," answered his mother; and the shower being nearly over, they all came out of their hiding-place to see better.

There was only a small part of the rainbow, and Willie's father asked him whether it were a straight line?

He replied, "No, it is a little curved. Ah! see, it grows longer! Now there's another bit of rainbow at the other side of the field!"

"Each grew and grew until presently the two met and made a whole glorious arch.

"That is part of a circle, you see, and a perfectly regular curve," said the father. "If the line could be continued exactly in the same manner down through the earth, it would make a great round like a hoop."

"Yes.—But do tell me what is  a rainbow? What makes it come there?"

"It is the effect of the sun's light on the raindrops as they fall from the clouds. But you cannot understand this yet. When you are a little older I will try to show you."

"Thank you, father!" and Willie sighed. He wished he were older! He was not wise enough to feel thankful that he had so many years before him, wherein to learn good and great things, nor to know he might one day wish himself younger, that he could have the same time over again.

They now walked towards the house, and, on arriving at the garden, Willie spied out his pretty little cousin Flora, who had come to wish him many happy returns of his birthday and bring him a present from her mother, in a funny, long-shaped parcel. She looked very slily at his curiosity, for she  knew quite well what was inside! Willie opened it eagerly, and found a nice bow with a quiver full of arrows.

"Oh, thank you, thank you! Tell my dear aunt I am very much obliged to her,—I did so want a bow!"

"Let me string it for you," said Flora, tugging with all her little strength till she had done it.

"Thank you, that's famous!" said he, and then shot off a few arrows; but so crookedly that Flora laughed at him, and he gave up, saying, "He would try by himself before she saw him shoot again." He was silent for a moment and then went on, pointing to his bow and expecting to astonish her this time, " Ah, Flora, if you  learnt drawing, you would know what is called a curved line!"

"Yes, but Mr. Graphic began to teach me a week ago, and so that's not any news at all."

"O-o-o-o!" gasped Willie, blushing. And his little rogue of a cousin giggled again.

"Look," she said, "there's my skipping rope which I brought with me; when I skip it makes a great curved line; and the chain-fence makes quantities  of curved lines. Oh! wouldn't it be nice to go and swing upon them?"

"Yes, come," cried Willie, bounding away with her.

"No, no, my dear children," said his mother; "they are all wet and would dirty your clothes; but you may go to the swing under the trees, for the shower will not have wetted that much."

"Ah, that's a curved line too," said Flora.

Here they had some fun, Willie's father swinging first one and then the other.

When they were tired of this, and were going in to breakfast, Flora found Willie's hoop lying on the ground close by, and said, "You careless boy! will you lend me this?"

"Oh, yes!"

So she ran with it towards the house.

"And that hoop is one curved line, is it not?" asked Willie's mother.

"It is; because it is the same all the way round, without any notches or joints. Mother, there's a great number  of different curved lines, Mr. Graphic says!"

"Yes, and we will talk about some of them again by and by; but let us come in now, dear."

When breakfast was over, little Flora said she must wish them good-bye, as she had to be home early to learn her lessons; and tying on her hat, she tripped away as lightly as a little bird.