and after
those dates, the higher one. The minimum and maximum of this annual
component of the variation occur at the meridian of Greenwich, about
ten days before the vernal and autumnal equinoxes respectively, and
it becomes zero just before the solstices.

"2. As the resultant of these two motions, the effective variation of
the latitude is subject to a systematic alternation in a cycle of
seven years' duration, resulting from the commensurability of the two
terms. According as they conspire or interfere, the total range
varies between two-thirds of a second as a maximum, to but a few
hundredths of a second, generally speaking, as a minimum.

"3. In consequence of the variability of the coefficient of the
annual term above mentioned, the apparent average period between 1840
and 1855 approximated to 380 or 390 days; widely fluctuated from
1855 to 1865; from 1865 to about 1885 was very nearly 427 days, with
minor fluctuations; afterwards increased to near 440 days, and very
recently fell to somewhat below 400 days. The general course of these
fluctuations is quite faithfully represented by the law of eq. (3),
(No. 267), and accurately, even down to the minor oscillations of
individual periods, by the law of eq. (15), hereafter given, and
verbally interpreted above. This law also gives a similarly accurate
account of the corresponding oscillations in the amplitude. The
closeness of the accordance between observation and the numerical
theory, in both particulars, places the reality of the law beyond
reasonable doubt."

Those who cannot follow the details of the above statement will
nevertheless catch the general purport--that the difficulties felt by
Professor Newcomb have been surmounted; and this is made clearer by a
later extract:--

"A very important conclusion necessarily follows from the agreement
of the values of the 427-day term, deduced from the intervals between
the consecutive values of T in Table XII., namely, that there has
been no discontinuity in the revolution, such as Professor Newcomb
regarded as so probable that he doubted the possibility of drawing
any conclusions from the comparison of observations before and after
1860 (_A. J._, 271, p. 50).

[Sidenote: Theory must go, if it will not fit observation.]

"The present investigation dem