If the bearing be less than 45°, the angle will be found at the top of the page, if greater, at the bottom; then, if the distance be less than 50, it will be found in the columns (“ distances") of the left-hand page; if greater than 50, in the columns of the right-hand page. The table is calculated only to quarter degrees, for the bearings cannot be accurately ascertained to smaller fractions of a degree. 29. For the same bearing, and lines of different lengths, it is evident, that the latitudes and departures will be proportional to the distances. Therefore, when the distance is greater than 100, it may be divided by any number which will give a quotient less than 100; then, the latitude and departure of the quotient being multiplied by the divisor, the products are the latitude and departure of the whole course. It is also plain, that, for the same bearing, the latitude and departure of the sum of two or more distances, is equal to the sum of the latitudes and departures of those distances respectively. Hence, if we have any number greater than 100, as 614, we have only to regard the last figure as a cipher, and recollect, that 610+4=614, and that the latitude and departure of 610 are ten times as great, respectively, as the latitude and departure of 61, that is, equal to the latitude and departure of 61, multiplied by 10, or, with the decimal point removed one place to the right. Example 1. To find the latitude and departure, the bearing being 2940, and the distance 582. In this example, the latitude and departure answering to the course 29, and to the distance 58, were first taken from the table, and the decimal point moved one place to the right; then the latitude and departure answering to the same course, and the distance 5, were taken from the table and added. Example 2. To find the latitude and departure, the bearing If the distances were expressed in whole numbers and decimals, the manner of finding the latitudes and departures would still be the same, except in pointing off the decimal places; which, however, is not difficult, when it is remembered, that the column of distances in the table may be regarded as decimals by removing the decimal point to the left in the other columns. A TABLE OF LOGARITHMS. OF NUMBERS FROM 1 TO 10,000. N. 2 6 8 10 li 1.556303 61 12 1.079181 37 1.568202 62 Log. N. Log. N. Log. 0.000000 26 1.414973 51 1.707570 0.301030 27 1.431364 52 1.716003 0.477121 28 1.447158 53 1.724276 0.602060 29 1.462398 54 1.732394 0.698970 30 1.477121 55 0.778151 31 1.491362 56 1.748188 81 1.908495 0.845098 32 1.505150 57 1.755875 82 1.913814 0.903090 33 1.518514 58 1.763428 83 1.919078 0.954243 34 1.531479 59 1.770852 1.924279 1.000000 35 1.544068 60 1.778151 85 1.929419 1.041393 36 1.785330 86 1.792392 87 N. Log. 13 1.113943 38 1.579784 63 1.799341 88 1.944483 1.361728 48 24 1.380211 49 1.690196 74 1.869232 25 1.397940 50 1.698970 75 1.875061 1.653213 70 14 1.146128 39 1.591065 64 1.176091 40 1.602060 65 1.204120 41 1.612784 66 1.819544 91 17 1.230449 42 1.623249 67 1.826075 18 1.255273 43 1.633468 68 1.832509 93 -1.278754 44 1.643453 69 1.838849 94 1.973128 1.845098 95 1.977724 1.851258 96 1.982271 1.857333 97 1.986772 1.863323 98 1.991226 99 1.995635 100 2.000000 N.B. In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to 0's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second |