e 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 ski