The elements of logarithms; with an explanation of the three and four place tables of logarithmic and trigonometric functions - Softcover
Synopsis
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. 1874 edition. Excerpt: ...is, to one figure beyond the tabulated figures; tut in the early part of the table it may be computed to five figures. Thus, we have log 59.43 = 1.7740, log 0.008147 = 7.9110--10, log 284.8 =2.4545, log 572610. =5.7579, log 0.073748 = 8.8678--10, log 0.5017 = 9.7004--10, log 3.1607 =0.4998, log 99.968 =1.9999; log-1 1.9155 = 82.32, log-(5.8760--10) = 0.00007517, log-1 0.0547 = 1.1342, log-1 (8.1577--10) = 0.014377, log-1 3.8291 = 6747, log-1 (9.5757--10) = 0.3765. § 4:9. Interpolation in this table is facilitated by the use of the right-hand division of the table, headed "ProPortional Parts." If we follow out the line which contains the tabulated logarithm corresponding to the first three significant figures of the given number, we shall find, under the fourth significant figure, the correction which corresponds to that figure, pointed off as if the mantissas in the table were whole numbers, and, in like manner, under the fifth significant figure of the antilogarithm, we shall find the correction for that figure, provided we move the point in that correction one place to the left, and so on. Thus, suppose it is required to find log 1273.64. We find mant log 127 = 1038, correction for.3 = 10.4 „ „.06 = 2.09 „ „.004= 0.139 „ „.364 = 13.-.log 1273.64 = 3.1051. In like manner, we find log 0.073748 = 8.8678--10, log 0.287428 = 9.4586--10, log 3.1607 =0.4998, log 10.0086 =1.0004, log 908.4 =2.9583, log 0.09994 =8.9998--10. In using this table of Proportional Parts, we should work from the nearest tabulated value. For each line of corrections is computed from the average value of the tabular difference for that line, and the smaller the proportional part taken, the less is the probability of error....
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