This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1864 Excerpt: ...the product l(b + ). l(c + 5) either by actual multiplication or by help of the columns log l(a + ) already used: then to find the product db. dc, which, as the numbers are small, can be done by inspection of Crelle's table; to add these products together for coe/(b, c), and then to take out the logarithm of the sum. ...
Read More
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1864 Excerpt: ...the product l(b + ). l(c + 5) either by actual multiplication or by help of the columns log l(a + ) already used: then to find the product db. dc, which, as the numbers are small, can be done by inspection of Crelle's table; to add these products together for coe/(b, c), and then to take out the logarithm of the sum. However, it may be observed that the quantity-fadb.dc bears a very small ratio to the product /(6 + ). l(c + ), excepting near to the end of the life table, and that therefore the logarithm of the sum may be found from the logarithms of the two parts by help of any of the appropriate auxiliary tables. 165. If we know the logarithms of two numbers P and Q, and wish to find the logarithm of their sum, the natural operation is to take out the numbers P and Q, add these together, and then seek out the logarithm of the sum; but this though a simple is a tedious process, and becomes the more irksome when, if Q be small in comparison with P, the logarithm of P + Q differs but little from that of P. Hence computers have sought for some expedient whereby the labour may be reduced. Since P + Q = P(l+-%-), or log (P+Q) = logP + log(1 +- -), the quantity by which the desired logarithm exceeds the logarithm of P is a function of- -, which again is a function of log P-log Q. Taking advantage of this circumstance, tables have been constructed in which the argument is log N, and which give the corresponding values of log (1 +-y-) and of log (1--jf). By help of these the logarithms of P + Q and of P-Q may be found from log P and log Q. The manner of using them is this. Having found logP-log Q = logN, we enter the table with this as an argument, and opposite to it find log(l +-) or log(l---#-), according as we have to do with the sum ...
Read Less
