LOGARITHMS. 368
Therefore while the number increases from 62500 to 62600, the logarithm increases .0007. Now our number is 43 100, of the way from 62500 to 62600; hence if to the logarithm of 62500 we add 43 100, of .007, a nearly correct logarithm of 62543 is obtained.
Thus log 62543 = 4.7959 .0003 correction. = 4.7962
(d) Suppose the logarithm of a decimal, as .0005245, is required. The number lies between .0005240 and .0005250. In the column headed N we find the first two significant figures, 52; on a line with these and in the columns headed 4, and 5, we find the mantissæ .7193 and .7202. Prefixing the characteristic [ Art. 437], we have
log .0005250 = 4.7208 log .0005240 = 4.7193 differences .0000010 0009
Now .0005243 is .0000003 greater than .0005240, hence log .0005243 equals log .0005240 plus {.0000003 .0000010} or {3 10} of .0009 (the difference of logarithms);
that is, log .0005248 = 4.7193 .0003 (nearly) = 4.7196
In practice negative characteristics are usually avoided by adding them to 10 and writing -10 after the logarithm. Thus in the above example 4.7196 = 6.7196 - 10.
445. The increase in the logarithms on the same line, as we pass from column to column, is called the tabular difference. In finding the logarithm of 62548, we assumed that the differences of logarithms are proportional to the differences of their corresponding numbers, which gives us results that are approximately correct. Tor greater accuracy we must use tables of more places.
