ner in which such
a rule was first discovered. Let us suppose that a sailor at Calais, for
example, is making for harbour. He has a beautiful night--the moon is
full; it guides him on his way; he gets safely into harbour; and the
next morning he finds the tide high between 11 and 12.[45] He often
repeats the same voyage, but he finds sometimes a low and inconvenient
tide in the morning. At length, however, it occurs to him that _when he
has a moonlight night_ he has a high tide at 11. This occurs once or
twice: he thinks it but a chance coincidence. It occurs again and again.
At length he finds it always occurs. He tells the rule to other sailors;
they try it too. It is invariably found that when the moon is full, the
high tide always recurs at the same hour at the same place. The
connection between the moon and the tide is thus established, and the
intelligent sailor will naturally compare other phases of the moon with
the times of high water. He finds, for example, that the moon at the
first quarter always gives high water at the same hour of the day; and
finally, he obtains a practical rule, by which, from the state of the
moon, he can at once tell the time when the tide will be high at the
port where his occupation lies. A diligent observer will trace a still
further connection between the moon and the tides; he will observe that
some high tides rise higher than others, that some low tides fall lower
than others. This is a matter of much practical importance. When a
dangerous bar has to be crossed, the sailor will feel much additional
security in knowing that he is carried over it on the top of a spring
tide; or if he has to contend against tidal currents, which in some
places have enormous force, he will naturally prefer for his voyage the
neap tides, in which the strength of these currents is less than usual.
The spring tides and the neap tides will become familiar to him, and he
will perceive that the spring tides occur when the moon is full or
new--or, at all events, that the spring tides are within a certain
constant number of days of the full or new moon. It was, no doubt, by
reasoning such as this, that in primitive times the connection between
the moon and the tides came to be perceived.

It was not, however, until the great discovery of Newton had disclosed
the law of universal gravitation that it became possible to give a
physical explanation of the tides. It was then seen how the moon
attracts the whole e