Straight Lines

"A RE you ready for your walk, my boy?" said Willie's father to him, one sweet afternoon in summer.

"Not quite, father, for I have still some of my books to put away; but I shall not be two minutes. Now I have done, and am ready for my nice walk."

"Come then, we will go by the lane to the sea-side. So you have had your first drawing-lesson with Mr. Graphic; how did you like it?"

"I enjoyed it very much, because he was so kind, and because I am glad I have begun drawing; but I haven't learned a great deal yet."

His father said, "When you had your first reading-lesson, you only learnt the letters A and B, but now you can read very nicely; so be satisfied with having learnt only so much of drawing. You will have something new to do almost every day, and you will find it always more and more amusing. I should like to know what you learnt."

"Mr. Graphic told me first all about straight lines, and then made me try to draw them."

"Well, what is a straight line, Willie?"

"The trunk of that fir-tree is almost a straight line."

"Why?" said his father.

"Because it hardly bends at all to the right or the left."

"Yes, but cannot you explain to me what is quite a straight line?"

"Mr. Graphic said it is the nearest way between one point and another. Stop, father,—the trunk of that tree is one point, and where I am is another; the quickest way I could get to it would be to run to it in a straight line. If I were to run out in a bend to one side or the other, or zigzag, of course I should be longer doing it. And Mr. Graphic told me that the crows fly in a straight line to and from the places where they feed and where they roost, because they always go the shortest way."

"Very well, Willie; these are good descriptions of straight lines which you only imagine; but we can also see plenty of real ones. Think of some to tell me of."

"I remember one, father. This morning I wanted to make a row in my garden of the little China-aster plants my aunt gave me yesterday, so I began to make holes for them all along one side with the gardener's dibble; but I found they were quite crooked, and I tried to do them right till I was tired; so I went to the gardener, and begged him to do them for me. He said he had not time to do them all, but he would show me the way, and then I should never have to beg any one to do it for me again. He stuck a piece of wood in at one end of the border, and another piece at the other end, and tied a string from one to the other. 'Now' he said, 'you can make your holes exactly under the string, and they will be in a neat straight line, and be done quickly, too.' "

"Yes," said his father; "and look at those men ploughing. What pains they take to make the furrows in straight lines, so as to waste no more room than they can help! And did Mr. Graphic tell you anything about straight lines in a perpendicular, and horizontal, and oblique position?"

"Oh, yes! I was just trying to think of all those names. They are rather hard. I think I can tell you what they mean, though. Please lend me your walking-stick, father. When I hold it upright, so (1), like a fir-tree, it is perpendicular; when I hold it out, so (2), it is horizontal; when I hold it slanting, like this (3), or this (4), I don't know what it's like—it is oblique."

"Very well, my boy! If you lean against the wall with your feet a good deal out, that will be an oblique line; if you lie on the ground, you will make a horizontal line; and now that you are standing, you make a perpendicular line."

After more pleasant talk they arrived at the beach, when Willie's father said, "There is a fine horizontal line; it is called the 'line of the horizon.' You know the earth is round. Where the water joins the sky is the edge of what you can see of it. In very large plains, such as they have in some parts of the world, the effect is the same. When people are in a vessel at sea they have that line all round them. Every way they look there is a horizontal line. And see those pretty little fishing-boats: as the waves rock them from side to side, their masts are sometimes in a perpendicular, sometimes in an oblique position.—I have to speak to the men who are building those new houses a little farther up on the beach; will you stop here and play, or come with me?"

"I will come with you, please, father, for I should like to watch the men doing their work."

"Come, then."

While his father gave orders to the people, Willie went to where some bricklayers were making a wall. They had a long string, with a piece of lead tied to the end, dangling from the top of their work.

He could not think at first what it was for, but he soon observed that the string hung with the weight in a perpendicular line, and that they used this as a guide by which to build their wall quite upright. "Then," thought he, "they must want a guide to help them to put the bricks horizontally, too." He found he was right, for the men used strings fastened along the top course of bricks to keep their work level, very much in the way the gardener did it for his planting; but still he did not know how they got this exactly horizontal. He saw that these houses were all made up of straight lines. The window-sills and tops of the windows were all horizontal, as also the door-steps and tops of the walls; and the sides of all these things were perpendicular. Also the roofs and tops of the porches were all of oblique lines meeting in a point at the top.

As they were returning home Willie felt tired, for the day was very hot, and when they got to the gate of the grounds he climbed up the bars and sat on the top, while his father leaned against it to rest himself. Soon they heard something fall pop on the ground near them, and, looking, they saw an apple which had just dropped off a tree close by. Willie thought if it were ripe this would be very nice to eat, so he jumped down to get it.

"Oh, it is quite ripe," he said, "and there are several more on the tree! If I had known there were good apples here, I should have come for them before! Will you have this one, father,—and give me a little bit?"

Just then another beauty, which had been jogged and loosened by the fall of the first one, came down almost on his nose.

"Thank you, my boy, but you see there is a whole one for each of us now," said his father. "Tell me what line they took in falling to the ground."

"A perpendicular line," said Willie: "for I suppose they went by the shortest road!"

"Yes; and look, there is a pretty instance of a perpendicular line. Do you see the little spider dropping himself from that bough to the one below, by means of his thread? He will fasten it on to the branch when he gets to it. There, he is doing it now; and it makes the first line of his web.

He will afterwards patiently add a great many other lines, oblique, horizontal, and perpendicular, till his clever flytrap is finished. Do you know that those tiny threads of silk, which seem to you as fine as it is possible for lines, to be, are each made of many threads stuck together?"

"No, I did not know that, father. It is very curious indeed!"

"Come, Willie, let us sit down on that bank to eat our apples."

"Yes, father; it will be better in the shade there."

While munching his apple, Willie observed, "Now that gate is all made up of perpendicular and horizontal lines, and one oblique one. Do you know, I think that learning to draw will make me look at everything a great deal more.—Mr. Graphic says, too, one cannot learn drawing rightly without learning a good many other things at the same time."

"It is quite true, Willie," answered his father; "you will, for one thing, learn a little science."

"What is science, father?"

"It is science to know why an apple falls to the ground it is science to make steam turn the wheels of a carriage; it is science to measure the distance of the sun and stars from our earth; and it is science to draw a view on paper correctly. You say yourself that learning to draw will make you look at everything much more, and this alone will teach you a great deal, if you also think upon what you see."

"But, father, people must be very clever to learn all those things."

"Not so! they want only steady attention and industry! But we must go now, for your dear mother is by this time expecting us home to tea."