No. 3. Calculation Book.--This should be of the same size and shape as
the Log Book, and should contain outline forms for calculations. The
labour and confusion saved by using these, and the accuracy of work that
they ensure, are truly remarkable. The instruments used, the observations
made, and especially the tables employed, are so exceedingly diverse,
that I fear it would be to little purpose if I were to give special
examples: each traveller must suit himself. I will, therefore, simply
make a few general remarks on this subject, in the following paragraph.

Number of Observations requiring record.--A traveller does excellently,
who takes latitudes by meridian altitudes, once in the twenty-four hours;
a careful series of lunars once a fortnight, on an average; compass
variations as often; and an occulation now and then. He will want,
occasionally, a time observation by which to set his watch (I am
supposing he uses no chronometer). He ought therefore to provide himself
with outline forms for calculating these observations, even if he finds
himself obliged to have them printed or lithographed on purpose; and in
preparing them, he should bear the following well-known maxims in mind:--

Let all careful observations be in doubles. If they be for latitudes,
observe a star N. and a star S.; the errors of your instruments will then
affect the results in opposite directions, and the mean of the results
will destroy the error. So, if for time, observe in doubles, viz., a star
E. and a star W. Also, if for lunars, let your sets be in doubles--one
set of distances to a star E. of moon, and one to a star W. of moon.
Whenever you begin on lunars, give three hours at least to them, and
bring away a reliable series; you will be thus possessed of a certainty
to work upon, instead of the miserably unsatisfactory results obtained
from a single set of lunars taken here and another set there, scattered