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.