They heave the log every two hours,-that is, twelve times for every twenty-four hours,-and from the reports which the captain receives of the results of those trials, it is easy for him to calculate how far the ship has come during the whole period. As he knows, too, exactly how far the pilot has been steering by the compass all this time, he has both the direction in which the ship has been sailing, and the distance to which she has come; and, of course, from these data he can calculate where she must now be. This mode of determining the ship's place is called by the reckoning. The other is called by observation.
The intelligent and reflecting boy who has carefully read and understood the preceding explanations will perceive that the two operations which we have been describing are in some sense the reverse of each other. By the former, the navigator ascertains by his measurements where the ship actually is to-day, and then calculates from that how far, and in what direction, she has come since yesterday. Whereas, by the latter method, his measurements determine directly how far, and in what direction, the ship has come; and then he calculates from these where she now is. Each method has its advantages. The former, that by observation, is the most sure and exact; but then it is not always practicable, for it may be cloudy. On the other hand, the latter-that is, by the reckoning-never fails, for the log can always be thrown, be the weather what it may; but it cannot be fully relied upon, on account of the currents in the water and the drifting of the vessel. Consequently, on board all ships they keep the reckoning regularly every day. Then, if they get a good observation, they rely upon that. If they do not, they go by the reckoning.
We now return to the story. And here, I suppose, is the place where those sagacious children, who, when they are reading a book in which entertainment and instruction are combined, always skip all the instruction, and read only the story, will begin to read again, after having turned over the leaves of this chapter thus far, seeing they contain only explanations of the mode of navigating a ship, and saying nothing about Hilbert and Rollo. Now, before going any farther, I wish to warn all such readers, that they will not be able to comprehend at all clearly the complicated difficulties which Hilbert and the others got into in respect to the lottery without understanding all that has been explained in the preceding pages of this chapter. I advise them, therefore, if they have skipped any of it, to go back and read it all, and to read it slowly too, and with the utmost attention. And I advise them, moreover, if they do not perfectly understand it all, to ask some older person to read it over with them and explain it to them. If they are not willing to do this, but insist on skipping the first part of the chapter, I advise them to make complete work of it, and skip the last half too; for they certainly will not understand it.
When Hilbert went back to the paddle box with his half sovereign, it was about eleven o'clock. The observation was to be made at twelve; and the results, both in respect to the observation and the reckoning, were to be calculated immediately afterward. The lottery which the men were making related to the number of miles which the ship would have made during the twenty-four hours. The men were just making up the list of subscribers to the tickets when Hilbert went up to them. He gave his half sovereign to the man who had the list. This man whom they called the Colonel, took the money, saying, "That's right, my lad," and put it in a little leather purse with the other half sovereigns.
"What's your name, Bob?" said he.
"Livingston," said Hilbert.
"Bobby Livingston," said the Colonel, writing down the name on his list.
"No," said Hilbert, contemptuously, "not Bobby Livingston. Hilbert Livingston."
"O, never mind," said the Colonel; "it's all the same thing. Bobby means boy."
The plan of the lottery was this: It was generally supposed that the ship's run would be about 270 miles; and it was considered quite certain, as has already been stated, that it would not be more than 280, nor less than 260. So they made twenty tickets, by cutting five of the Colonel's visiting cards into quarters, which tickets were to represent all the numbers from 261 to 280, inclusive. They wrote the numbers upon these cards, omitting, however, the first figure, namely, the 2, in order to save time; for as that figure came in all the numbers, it was considered unnecessary to write it. When the numbers were written thus upon the cards, the cards themselves were all put into a cap[B] and shaken up, and then every one who had paid a half sovereign drew out one, the colonel holding the hat up high all the time, so that no one could see which number he drew. This operation was performed in the midst of jokes and gibes and loud shouts of laughter, which made the whole scene a very merry one. When Hilbert came to draw, the merriment was redoubled. Some called on the Colonel to hold down the cap lower, so that Bob could reach it. Others said that he was sure to get the lucky number, and that there was no chance at all for the rest of them. Others, still, were asking him what he would take for his ticket, or for half of it, quarter of it, and so on. Hilbert was half pleased and half ashamed at being the object of so much coarse notoriety; while Rollo, who had drawn up toward the place, and was looking on from a safe distance as the proceedings that were going on, was very glad that he was not in Hilbert's place.
[Footnote B: Gentlemen always wear caps on board ship. Hats are in the way, and would, moreover, be in danger of being blown off by the wind; in which case, as they would go overboard at once, there would be no possibility of recovering them.]
The ticket that Hilbert drew was marked 67. It denoted, of course, the number 267; and that, being pretty near to the number of miles which it was thought the ship would probably make, was considered quite a valuable ticket. The owners of the several tickets, as soon as the drawing was completed, began to compare them and talk about them, and to propose bargains to one another for buying and selling them, or exchanging them. In these negotiations each man was endeavoring to outwit and circumvent his friend, in hopes of buying his ticket for a moderate sum, and drawing the whole prize with it. Others were engaged in betting on particular tickets. These bets, when they were made, they recorded in little memorandum books kept for the purpose. In fact, a very noisy and tumultuous scene of bargaining, and betting, and barter ensued.
Hilbert was very much pleased with his ticket. He went to show it to Rollo. He said he verily believed that he had got the exact ticket to draw the prize. He did not think the ship would go quite 270 miles.
"And if she does not," said he, "and should happen to go only 267 miles, then I shall have ten pounds; and that is almost fifty dollars."
So saying, Hilbert began to caper about the deck in the exuberance of his joy.
His antics were, however, suddenly interrupted by the Colonel, who just then came up to him and asked to see his ticket. Hilbert held it up so that the Colonel could see the number upon it.
"Sixty-seven," said the Colonel. "That is not worth much. Nobody thinks she'll go less than 270. However," he added, in a careless tone, "I'll give you twelve shillings for it. That is two shillings over what you paid for it-nearly half a dollar.[C] You'd better make sure of half a dollar than run the risk of losing every thing on such a poor ticket as that."
[Footnote C: The Colonel meant English shillings, which are twenty-four cents each in value.]
"Would you?" said Hilbert, turning to Rollo.
"I don't know," replied Rollo, shaking his head. "I don't know any thing about it."
"No," said Hilbert, turning to the Colonel again; "I believe I will keep my ticket, and take my chance."
The Colonel said, "Very well; just as you please;" and then went away. Hilbert had, after this, several other offers, all which he declined; and in about a quarter of an hour the Colonel met him again, as if accidentally, and began to talk about his ticket. He said that all the tickets under 270 were selling at a low price, as almost every body believed that the ship's run would be more than that; but still, he said, he would give a pound for Hilbert's ticket, if he wished to sell it. "Thus," said he, "you'll get back the half sovereign you paid, and another half sovereign besides, and make sure of it."