The formulæ in the tables on p. 73 and after can be deduced by two
methods,—one that of graphical construction, the other that of least
squares. The first method is the more simple and requires but little
calculation; though neatness and care are necessary in constructing
the diagrams. The second method will be described for the benefit of
those who possess the requisite mathematical knowledge. The formulæ
used in the preparation of the tables have been generally deduced
from the method of least squares, as the results are to a slight,
though insignificant, extent more accurate than those of the method
of graphical construction. This remark will explain why the figures
in some of the formulæ are carried to a greater number of places of
decimals than could be obtained by the other method.
We shall confine the numerical examples to Tables III. and IV., and
show how the formulæ of these tables have been deduced by the two
different methods.
Tables V., XIV., XVI., XXI., are to be found in the same manner as
Table III.; and Tables VI., IX., X., XI., XV., XVII., XVIII., XIX.,
XX., XXI., XXII., in the same manner as Table IV.
_THE METHOD OF GRAPHICAL CONSTRUCTION._