Plane trigonometry, by S.L. Loney.

PROPORTIONAL PARTS.

161

Find the number whose logarithm is 2'6283924.
On reference to the tables we find that the logarithm 6283924 is not
tabulated, but that the nearest logarithms are 6283889 and 6283991,
between which our logarithm lies.
We have then log 425-00= 26283889...................(1),
and log 425-01 = 2-6283991........................(2).
Let log (425-00 +.) = 2-6283924........................(3).
From (1) and (2) we see that corresponding to a difference -01 in the
number there is a difference '0000102 in the logarithm.
From (1) and (3) we see that corresponding to a difference x in the
number there is a difference '0000035 in the logarithm.
Hence we have x: -01:: -0000035: -0000102.
35.35
x= 2 x '01= 1=0 00343 nearly.
102 102
Hence the required number = 425-00 + '00343 = 425-00343.
151. Where logarithms are taken out of the tables
the labour of subtracting successive logarithms may be
avoided. On reference to page 153 there is found at the
extreme right a column headed Diff. The number 82 at
the head of the figures in this column gives the difference
corresponding to a difference unity in the numbers on
that page.
This number 82 means '0000082.
The rows below the 82 give the differences corresponding to '1, '2,.... Thus the fifth of these rows means that
the difference for '5 is '0000041.
As an example let us find the logarithm of 52746-74.
From page 153 we have
log 52746 = 4-7221895
diff. for -7 = -0000057
diff. for 04
= x diff. for 4 = 0000003
log 52746-74 = 4-7221955.

L. T.

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