Elements of Plane And Spherical Trigonometry With Logarithmic And Other ...

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Elements of Plane And Spherical Trigonometry With Logarithmic And Other ...
Newcomb Simon
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Entering column B with the same difference, we find B -- A =: .00395; whence log (a - S) = 1.265 32 - .003 95 = 1.261 37.
Exercises.
Find log {a + b) and log {a — b) from: 1. log a = 4.069 05; log b = 2.001 32.
2. log a = 3.926 93; log b = 1.201 59.
3. log a = 3.061 64; log b = 0.126 15.
4. log a = 1,22C 68; log b = 7.321 56.
5. log a = 0.693 17; log b = 6.010 23.
6. log a = 2.306 20; log b = 7.023 01.
Digitized by VjOOQ IC 48 LOGABITHMIO TABLES.
Case of nearly equal numbers. Near the beginning
... of the table the reverse is true: it is not possible to find A with accuracy to five places of decimals. But here the value of A taken from the tables^ though it be found to only two, three, or four places of decimals, will give as accurate a result as the computation of a and b to five places will admit of. Let us suppose, for example, that we have to find log (a — J) from log a = 9.883 15 log b = 9.882 96 JS=: 0.00019 We find A = 6.64-10; whence log (a — S) = 6.52 — 10.
We note that the value of A may be 6.63 or 6.65 as well as 6.64, $0 that the result cannot be carried beyond two decimals To show that these two are as accurate as the work admits of, we find the natural numbers a and b from Table I.


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