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. 1901 Excerpt: ...difference = 6, correction =.83 x 6 = 4.98, mantissa of log 781283 = 89276 + 5 = 89281. Therefore log 78.1283 = 1.89281 Observe that the correction added to the mantissa of log 7812 is 5, the nearest integer to 4.98 22. In the table of logarithms a column containing the required corrections (head Pp. Pts., i.e., ...
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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. 1901 Excerpt: ...difference = 6, correction =.83 x 6 = 4.98, mantissa of log 781283 = 89276 + 5 = 89281. Therefore log 78.1283 = 1.89281 Observe that the correction added to the mantissa of log 7812 is 5, the nearest integer to 4.98 22. In the table of logarithms a column containing the required corrections (head Pp. Pts., i.e., proportional parts) is given. In this column there are several small tables, each containing two columns of numbers. One of these columns consists of the consecutive numbers 1 to 9; the other, headed by a tabular difference, contains the correction corresponding to each one of the figures 1 to 9, when it is the fifth figure of the number whose logarithm is required. When it is the sixth figure, the corresponding tabular correction must evidently be divided by 10; when it is the seventh figure, by 100; and so on. Thus, in Ex. 1 of the preceding article, we take the correction opposite 5, under the tabular difference 16, and obtain 8, as before. In Ex. 2, we take the following corrections from the column headed by the tabular difference 6: for 8, correction = 4.8 for 3, correction = 0.18 final correction = 4.98, as before. Observe that the correction for the sixth figure of the given number does not affect the result. Ex. 3. Eind the log.0128546. We have mantissa of log 1286 = 10924, mantissa of log 1285 = 10890, tabular difference = 34. From the column of proportional parts headed by 34, we obtain: correction for fifth figure 4 = 13.6 correction for sixth figure 6 = 2.04 total correction = 15.64 Therefore, mantissa of log 128546 = 10890 + 16 = 10906, and log.0128546 = 8.10906-10. Observe that in this example the correction for the sixth figure does affect the result. EXERCISES III. Verify the following statements: 1. log 13 = 1.11394. 2. log 14.84 = ...
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