repetition has
the advantage first of all of checking any mistakes. When a long piece of
measuring or numerical work of any kind is undertaken there are invariably
moments when the attention seems to wander, and some small error is the
result. But there are also certain errors of a systematic character
similar to those denoted by the term "personal equation," which has found
its way into other walks of life. In the operation of placing a cross
exactly over the image of a star, different observers would show slight
differences of habit; one might place it a little more to the right than
another. But when the plate is turned round the effect of this habit on
the measure is exactly reversed, and hence if we take the mean of the two
measures any personal habit of this kind is eliminated. It has been found
by experience that such personal habits are much smaller for measures of
this kind than for those to which we have long been accustomed in
observations made by eye on the stars themselves. The troubles from
"personal equation" have been much diminished by the photographic method,
and certain peculiarities of the former method have been clearly exhibited
by the comparison. For instance, it has gradually become clear that with
eye observations personal equation is not a constant quantity, but is
different for stars of different brightness. When observing the transit of
a bright star the observer apparently records an instant definitely
earlier than in recording the transit of a faint one; and this peculiarity
seems to be common to the large majority of observers, which is perhaps
the reason why it was not noticed earlier. But when positions of the stars
determined in this way are compared with their positions measured on the
photographic plates, the peculiarity is made clearly manifest. For
example, at Oxford, our first business after making measurements is to
compare them with visual observations on a limited number of the brighter
stars made at Cambridge about twenty years ago. (About 14,000 stars were
observed at Cambridge, and we are dealing with ten times that number.) The
comparison shows that the Cambridge observations are affected with the
following systematic errors:--

If stars of magnitude 10 are observed correctly,
then " " 9 " 0.10 secs. too early
" " 8 " 0.16 "
" " 7 " 0.19 "
" "