The models would not of course be of the same size as the big carts, but they would have to keep what is called the same _proportion_ of sizes. The bigger must still be the bigger; and the smaller must still be the smaller. You could let one inch stand for one foot. Then the tiny model of the bigger cart--the cart which is four feet long and two feet broad--would only be four _inches_ long and two _inches_ broad. And the tiny model of the lesser cart--the cart which is three feet long and one foot and a half broad--would be only three _inches_ long and one _inch_ and a half broad. Anybody looking on those two tiny model carts could not possibly tell how big the real carts are. But he could tell one thing. He could know _how much bigger one cart is than the other_. This is what I hope to show you, by bringing down the sizes of worlds and moons--not how large they really are, but how much larger or how much smaller one is than another. Also, by this means we learn to understand distances better. If you are looking at a map of the world, or of a part of the world, the _miles_ in that map have to be brought down into a very tiny space. A map of a country, made as large as the country itself, would take up a great deal too much room. So half-an-inch is made to do duty for perhaps fifty real miles, or a hundred real miles, or even a thousand real miles. In quite a small map, a continent or an ocean which is really two thousand miles across might be only one inch across. And yet, looking at that map, small though it is, you are able to see how near one country is to your own, and how very much farther off another country is. This is the way in which we are going to think about different worlds--those which are nearer and those which are farther. We have to make a sort of little map or model of them in our minds; letting one inch always picture two thousand real miles. QUESTIONS. 1. What is meant by the diameter of a ball? Its “through measure” from one side to the other, straight through the centre. 2. What is the circumference of a ball? Its measure round the outside. 3. Which is larger, the through measure or the measure round outside? The outside measure is about three times as large as the through measure. 4. Give an example or two. A ball one inch through is about three inches round outside. A ball four inches through is about twelve inches round outside. 5. What is the Earth’s diameter? The Earth is nearly 8,000 miles through. 6. And the Earth’s circumference? The Earth is nearly 25,000 miles round at the equator. 7. What is the Moon’s diameter? The Moon is about 2,000 miles through. 8. And the Moon’s circumference? The Moon is about 6,000 miles round outside. 9. How far is the Moon from the Earth? About 240,000 miles. 10. How long should a rope be to lie round the Earth on the equator? About 25,000 miles. 11. How many such ropes would reach all the way from here to the Moon?