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17. “ Perhaps it is not very far,” said Rollo. “ We may be pretty nigh the shore."
“ But we have sailed two or three miles, at least," replied his father, "since I first saw the light. Now, if we were so near the shore, as to be able to see the light of a lantern, we should have got by it entirely before this time, and have left it far behind us.
18. “But, though we have sailed two or threo miles, the light has only advanced along the horizon a little way; and so I judge that it must be five or six miles off. And if it is five or six miles off, it must be some large light; and I cannot think of any thing it is likely to be, except a lighthouse."
19. “I rather think it is a lighthouse myself," said Rollo.
66 If we watch it,” said his father, we shall see that it moves slowly along, as we advance on our way. Pretty soon it will be exactly opposite to us. Then presently it will begin to pass along behind us, and finally will get far astern.
20. “That changing of its direction, in conse. quence of our moving along, while it is really at rest itself, is its parallax. Now, the way we deter mine how far off any object is, when you cannot measure directly, is by observing its parallax; be. cause the nearer to us the object is, the greater will be its parallax."
“I don't understand that exactly,” said Rollo. 21. “ Why, the nearer it is,” replied his father, " the more rapidly it will appear to move along, when we are passing it. For instance, if there was a man out on the water here, with a lamp in his hand, only a quarter of a mile from where we are, as soon as the lamp came into view, we should see it appearing to glide along swiftly; and in a very few minutes, it would pass out of sight astern."
22. “ I wish there was one,” said Rollo. “ So do I,” replied his father • “but that cannot be. We cannot really witness that experiment; but you can see that it must be so, from the nature of the case.
So, if any object is at rest, at a distance from us, we can judge how far off it is, by observing how fast it seems to move while we are going by it.”
1. Just at the moment when Rollo's father had finished his explanation, a light suddenly came into view, a short distance before them, on the same side of the boat where they were sitting, and it came gliding swiftly along, so that it was almost opposite to them, before Rollo could recover from his surprise.
2. “ Why, father, what is that?" said he.
“I don't know," said his father. “It is some light very near, for it has a great parallax ; but I don't know what it can be. You may go forward, Rollo, and ask what it is."
3. Rollo came back in a few minutes, and said it was a light upon a vessel at anchor. A man told him that all the vessels had to carry lights, so that the steamboats might know where they were, and not run against them.
4. By this time, the lighthouse had got considerably astern, but it was distinctly in view ; while the light upon the vessel had almost disappeared, as the steamboat had got completely beyond it.
5. “ Now, you understand something about parallax," said Rollo's father. “ The lantern hung upon the vessel is nearest to us; next comes the light upon the lighthouse; and Sirius is the farthest off. They all appear to change their direction from us, inore or less rapidly, according to their distance.
6. “ The vessels lantern, a few minutes ago, was directly before us, and now it is almost directly behind. It has changed its direction nearly one hundred and eighty degrees in a few minutes. The lighthouse has been moving slowly along, and has not changed its direction more than forty or fifty degrees, perhaps, all the time that we have been looking at it. Sirius is farther off still, and even if we were to observe it with the nicest instruments, it would not seem to have moved in the least degree.
7. “ We can observe the parallax, very easily, in the case of these lights, and other things so near; but we cannot perceive the parallax of the heavenly bodies, without instruments and nice observations. The astronomers have such instruments, and they note how much the heavenly bodies change their direction from us, when they are observed from different places, and thus they can calculate the exact distance of their bodies from us."
8. “ I don't see how they can calculate the exact distance,” said Rollo. “ No,” said his father, “I do not suppose you
You can only understand a very little about such a subject. I only wanted to give you some general idea, how they measure the distances of heavenly bodies.
9. “ It will be of use to you sometimes, in enabling you to form some judgment of the distance of objects which you see, when you are riding or sailing. · Sailors can judge of the dëstance of a mountain, when they are sailing along the coast, by observing how fast it seems to move along the horizon."
10. Just at this moment, Rollo, who happened to be looking at the lighthouse, observed that it was beginning to move very swiftly around towards the stern of the boat.
“ Why, father," said he, “the lighthouse is mov. ing away very fast now.”
11. “ Yes," said his father; “I see that it is changing very fast; but that cannot be parallax. It must be, because the boat is turning out of its
I presume we are turning to go into the harbor."
12. So Rollo and his father walked forward, to see more distinctly what was going on. They advanced along the promenade deck, and took their stand by the wheelhouse, near the ladder which led down to the main deck below. There was a railing before them, to keep them from falling off.
13. They could see before them the dim form of the land, with the outlines of the buildings of a .town relieved against the sky; on the water, between them and the town, they saw a number of lights, which belonged to vessels lying in the harbor. One vessel was so near, that they could see the dark form of her hull floating on the water.
14. Other lights were at different distances. Rollo was very much interested, in observing the different degrees of rapidity with which they appeared to move, as the steamboat glided by them. He found that he could tell very easily which were near, and which were remote, by observing their apparent motion.
15. “Father,” said Rollo, after watching these lights a little while, “I can tell which lights are nearer than the others, by their moving quicker; but I cannot tell how far off any of them are.”
16. “ No,” replied his father, “I know you cannot. It requires some nice measurements and observations to do that."
“But I thought you said, father," rejoined Rollo, " that they could tell how far off the stars are, without measuring, by the parallax."
17. “ Yes," said his father; “that is, without measuring the distance to the stars; but they have to measure some other distances. For example, if we wanted to ascertain, how far off we were from that lighthouse, half an hour ago, it would have been necessary, to have taken an observation of its direction from us exactly, with an instrument.
18. “ Then, after we had sailed a certain dis. tance, we ought to observe the direction again very carefully, noting the exact distance we had sailed. Then we could make the calculation."
6. How should we do it?" asked Rollo.
19. “ O, you cannot understand that yet,” said his father. In order to know how to make such a calculation, it is necessary to understand trigonometry.”
“Is trigonometry hard?” asked Rollo..
“ No,” replied his father. “ not if the pupil is old enough to study it."
THE CRANBERRY PICKERS.
L. Far away among the hills,
Far from tower and town,
Desolate and brown,
2. The cranberry blossom dwelleth there
Amid the mountains cold,
Left on the dreary wold.
3. O, and 'tis very beautiful;
The flowers are pink and white,
Are evergreen and bright.