It will not, however, be necessary to take this into
account, as the displacement thus arising in the lapse of a single year
is far too minute to produce any inconvenient effect on the parallactic
ellipse.

[Illustration: Fig. 94.--61 Cygni and the Comparison Stars.]

The case of 61 Cygni is, however, exceptional. It is one of our nearest
neighbours in the heavens. We can never find its distance accurately to
one or two billions of miles; but still we have a consciousness that an
uncertainty amounting to twenty billions is too large a percentage of
the whole. We shall presently show that we believe Struve was right,
yet it does not necessarily follow that Bessel was wrong. The apparent
paradox can be easily explained. It would not be easily explained if
Struve had used the _same comparison star_ as Bessel had done; but
Struve's comparison star was different from either of Bessel's, and this
is probably the cause of the discrepancy. It will be recollected that
the essence of the process consists of the comparison of the small
ellipse made by the distant star with the larger ellipse made by the
nearer star. If the two stars were at the same distance, the process
would be wholly inapplicable. In such a case, no matter how near the
stars were to the earth, no parallax could be detected. For the method
to be completely successful, the comparison star should be at least
eight times as far as the principal star. Bearing this in mind, it is
quite possible to reconcile the measures of Bessel with those of Struve.
We need only assume that Bessel's comparison stars are about three times
as far as 61 Cygni, while Struve's comparison star is at least eight or
ten times as far. We may add that, as the comparison stars used by
Bessel are brighter than that of Struve, there really is a presumption
that the latter is the most distant of the three.

We have here a characteristic feature of this method of determining
parallax. Even if all the observations and the reductions of a parallax
series were mathematically correct, we could not with strict propriety
describe the final result as the parallax of one star. It is only the
_difference_ between the parallax of the star and that of the comparison
star. We can therefore only assert that the parallax sought cannot be
less than the quantity determined. Viewed in this manner, the
discrepancy between Struve and Bessel vanishes. Bessel asserted that the
distance of 61 Cygni could not be _mo