the analogy is
perfect. Travellers by some of the fast twin-screw steamers have had
unpleasant occasion to notice this phenomenon, when the engineer does not
run the two screws precisely at the same speed; there come times when the
ship vibrates violently, separated by periods of comparative stillness.
Instances from other walks of life may recur to the memory when once
attention is called to the general facts; but enough has been said to
explain the point numbered (2) in the subjoined statement. To understand
the rest, we must remember that if the two waves are not equal in
"amplitude," _i.e._ if the backward and forward motion is not the same in
both, they cannot annul one another, but the greater will always
predominate. Those interested in following the matter further should have
no difficulty in constructing simple examples to illustrate such points.
We will proceed to give Mr. Chandler's statements:--

[Sidenote: Chandler's final formulae.]

"We now come upon a new line of investigation. Heretofore, as has
been seen, the method has been to condense the results of each series
of observations into the interval comprised by a single period, then
to determine the mean epoch of minimum and the mean range for each
series, and, finally, by a discussion of these quantities, to
establish the general character of the law of the rotation of the
pole. It is now requisite to analyse the observations in a different
way, and discover whether the deviations from the general provisional
law, in the last column of Table II., are real, and also in what
manner the variation of the period is brought about. The outcome of
this discussion, which is to be presented in the present paper, is
extremely satisfactory. The real nature of the phenomenon is most
distinctly revealed, and may be described as follows:--

"1. The observed variation of the latitude is the resultant curve
arising from two periodic fluctuations superposed upon each other.
The first of these, and in general the more considerable, has a
period of about 427 days, and a semi-amplitude of about 0".12. The
second has an annual period with a range variable between 0".04 and
0".20 during the last half-century. During the middle portion of this
interval, roughly characterised as between 1860 and 1880, the value
represented by the lower limit has prevailed, but before