using, he has always
before his mind's eye an ideal instrument of absolute perfection, to
which the actual meridian circle only makes an approximation.

Contrasted with the ideal instrument, the finest meridian circle is
little more than a mass of imperfections. The ideal tube is perfectly
rigid, the actual tube is flexible; the ideal divisions of the circle
are perfectly uniform, the actual divisions are not uniform. The ideal
instrument is a geometrical embodiment of perfect circles, perfect
straight lines, and perfect right angles; the actual instrument can only
show approximate circles, approximate straight lines, and approximate
right angles. Perhaps the spider's part of the work is on the whole the
best; the stretched web gives us the nearest mechanical approach to a
perfectly straight line; but we mar the spider's work by not being able
to insert those beautiful threads with perfect uniformity, while our
attempts to adjust two of them across the field of view at right angles
do not succeed in producing an angle of exactly ninety degrees.

Nor are the difficulties encountered by the meridian observer due solely
to his instrument. He has to contend against his own imperfections; he
has often to allow for personal peculiarities of an unexpected nature;
the troubles that the atmosphere can give are notorious; while the
levelling of his instrument warns him that he cannot even rely on the
solid earth itself. We learn that the earthquakes, by which the solid
ground is sometimes disturbed, are merely the more conspicuous
instances of incessant small movements in the earth which every night in
the year derange the delicate adjustment of the instrument.

When the existence of these errors has been recognised, the first great
step has been taken. By an alliance between the astronomer and the
mathematician it is possible to measure the discrepancies between the
actual meridian circle and the instrument that is ideally perfect. Once
this has been done, we can estimate the effect which the irregularities
produce on the observations, and finally, we succeed in purging the
observations from the grosser errors by which they are contaminated. We
thus obtain results which are not indeed mathematically accurate, but
are nevertheless close approximations to those which would be obtained
by a perfect observer using an ideal instrument of geometrical accuracy,
standing on an earth of absolute rigidity, and viewing the heavens
witho