was a systematic personal bias in his measurements. Fortunately, in
most cases, the resulting value of the longitude is rather insensitive to
the choice of latitude used for the calculation, as can be seen from the
fairly consistent agreement between the longitudes calculated with and
without use of latitudes obtained from noon measurements (third
and fourth columns). Similarly, there is a pronounced tendency for
the calculated longitudes to be too far east. It is especially conspicu-
ous that all but one of the moon-star longitudes are too far east by
more than a degree. Of course the reason for this cannot be deter-
mined with certainty, but two possible explanations are use of an
incorrect value of the index error of the sextant, and a personal bias
in making the measurements.
The observer does not measure distances to the center of the moon,
but to the nearest or farthest point (the nearer or farther “limb”) of the
moon. The distance of a star to the center of the moon is then found by
adding or subtracting the known radius of the moon, as appropriate.
While looking through the sextant, the observer sees a direct image of
the star and, superimposed on it, a view of the moon that originates as
a reflection from a tiltable mirror. As the tilt of the mirror is adjusted,
the reading on the sextant scale changes. When the tilt of the mirror is
adjusted to bring the image of the star just into contact with the limb
of the moon’s image, the reading on the scale (after correction for
index error) is the angular distance from the star to the limb of the moon.
To this the moon’s radius must be added or subtracted, and the result
corrected for parallax and refraction.
First, consider the effects of improperly correcting for index error.
If a star is west of the moon and the sextant reading after correction
for index error is too small because of a wrong value of the index error,
the Greenwich time read from the Nautical Almanac will be too early
and the calculated longitude will be too far east. Conversely, if the star
is east of the moon and the corrected sextant reading is again too
small, the calculated longitude will be too far west. For the longitudes I
have calculated from moon-star distances, the star was west of the
moon in six cases for which the average error in the longitude is about
110 east, and east of the moon in three cases for which the average
error in longitude is again about 110 east. Thus, improper correction
for index error is not the main problem.
Next, consider a personal bias such that the observer always thinks
that, as seen in the sextant, a star is exactly touching the limb of the
moon when, in fact, there is a small gap between the two. If the mea-
surement is to the west side of the moon, which will be the case in the
early evening, the calculated Greenwich time will be too early and
the longitude too far east. If the measurement is to the east side of the