of disposing of
objections of the sort raised by Cornu, to insist that it is not
sufficient to show that the observed variations, attributed to the
unsteadiness of the Earth's Pole, are near the limit of precision
attainable in linear differential measures, and in the indication of
the direction of gravity by means of the air bubble of the level; or
to show that there are known variations in divided circles and in
levels, dependent on temperature and seasons. Nor need we require of
objectors the difficult, although essential, task--which they have
not distinctly attempted--of showing that these errors are not
eliminated, as they appear to be, by the modes in which astronomers
use their instruments. Neither need we even urge the fact that a
large portion of the data which have been utilised in the present
researches on the latitude were derived by methods which dispense
with levels, or with circles, a part of them indeed with both, and
yet that the results of all are harmonious. On the contrary, let us
admit, although merely for argument's sake, that all the known means
of determining the direction of gravity--including the plumb-line,
the level, and a fluid at rest, whether used for a reflecting surface
or as a support for a floating instrument--are subject to a common
law of periodical error which vitiates the result of astronomical
observation, obtained by whatever methods, and in precisely the same
manner. Now, the observed law of latitude variation includes two
terms, with periods of fourteen and twelve months respectively. Since
the phases of the first term are repeated at intervals of two months
in successive years, and hence in a series of years come into all
possible relations to conditions of temperature dependent on season,
the argument against the reality of this term, on this ground,
absolutely fails, and needs no further notice. As to the second, or
annual term, while the phases, as observed in any given longitude,
are indeed synchronical with the seasons, they are not so as regards
different longitudes. If, therefore, the times of any given phase, as
observed in the same latitude, but in successively increasing
longitudes, occurred at the same date in all of them, there would be
a fatal presumption against the existence of an annual period i