Find the angle for which log cot=1.67604.

Find the angle for which log tan=1.55407.

31. This table (p. 51), containing the circumferences and areas of circles, does not require explanation.

TABLE VI.

32. Table VI. (pp. 52-69) contains the natural sines, cosines, tangents, and cotangents of angles from 0° to 90°, at intervals of 1'. If greater accuracy is desired it may be obtained by interpolation.

NOTE. In preparing the preceding explanations, we have made free use of the Logarithmic Tables by F. G. Gauss. For Table VI. we are indebted to D. Carhart.

TABLE VII.

33. This table (pp. 70-75) gives the latitude and departure to three places of decimals for distances from 1 to 10, corresponding to bearings from 0° to 90° at intervals of 15',

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If the bearing does not exceed 45° it is found in the left-hand column, and the designations of the columns under "Distance are taken from the top of the page; but if the bearing exceeds 45°, it is found in the right-hand column, and the designations of the columns under "Distance" are taken from the bottom of

the page.

The method of using the table will be made plain by the following examples:

(1) Let it be required to find the latitude and departure of the course N. 35° 15' E. 6 chains.

On p. 75, left-hand column, look for 35° 15'; opposite this bearing, in the vertical column headed "Distance 6," are found 4.900 and 3.463 under the headings "Latitude" and "Departure" respectively. Hence, latitude or northing = 4.900 chains, and departure or easting 3.463 chains.

(2) Let it be required to find the latitude and departure of the course S. 87° W. 2 chains.

As the bearing exceeds 45°, we look in the right-hand column of p. 70, and opposite 87° in the column marked "Distance 2" we find (taking the designations of the columns from the bottom of the page) latitude = 0.105 chains, and departure 1.997 chains. Hence, latitude or southing 0.105 chains, and departure or westing 1.997 chains.

(3) Let it be required to find the latitude and departure of the course N. 15° 45' W. 27.36 chains.

In this case we find the required numbers for each figure of the distance separately, arranging the work as in the following table. In practice, only the last columns under "Latitude" and "Departure" are written.

Hence, latitude = 26.334 chains, and departure = 7.427 chains.