Plane trigonometry, by S.L. Loney.

PROPORTIONAL PARTS.

171

160. There is one point to be noticed in using the
columns headed Diff. It has been pointed out that 2021
(at the top of the second column) means '0002021. Now
the 790 (at the top of the eighth column) means not '000790,
but -0000790. The rule is this; the right-hand figure of
the Diff. must be placed in the seventh place of decimals
and the requisite number of cyphers prefixed. Thus
Diff. = 9 means that the difference is -0000009,
Diff.= 74,,,,,, 0000074,
Diff.= 735,,,,, 0000735,
Diff.= 2021,,,,,, -0002021,
whilst Diff. = 12348,,,,,, 0012348.
161. Page 170 also gives the tabular logs. of ratios
between 57~ and 58~. Suppose we wanted L tan 57~ 20'.
We now start with the line at the bottom of the page and
run our eye up the column which has Tang. at its foot. We
go up this column until we arrive at the number which is
on the same level as the number 20 in the extreme
right-hand column. This number we find to be 10-1930286,
which is therefore the value of
L tan 57~ 20'.
EXAMPLES. XXV.
1. Find 0 given that cos 0= -9725382,
cos 13~ 27'= 9725733, diff. for 1'= 677.
3
2. Find the angle whose sine is, given
sin 22~ 1' = 3748763, diff. for '= 2696.