NOTE. When an angle is required, a side must be the first term. When a side is required, an angle must be the first term.

To find the course from C to A, Fig. 2, adopt the following rule.

Suppose yourself standing at the angle A; make the side AB radius, then state; as the log. of the side AB 220; is to radius; so is the log. of the side BC, 150 to the tangent of the angle at A. See the example worked.

As log. of AB, 220-2.342423

:

R.10.000000 :: log. BC, 150--2.179160 2.176091

12.176091

2.342423

: Tang. of A 34° 17′ 9.833668

In the column of tangents, under 34° against 17', you will find the last term or that which is nearest to it. The course from A to C is N. 34° 17′ E. or from C to A, S. 34°, 17', W. Next find the distance.

CASE III.

TO FIND THE DISTANCE.

Make the side AC radius. From the point at A describe the arch Cx. In this case, the side BC is a sine as it lies within the arch. Take the following rule.

As the sine of the angle at A, is to the side BC, so is radius to the side AC. See the example worked.

B

220

Fig. 3.

150

Suppose you begin at a pine and run north 125 rods to a hemlock, then east 216 rods to a spruce, what is the course and distance from the spruce to the pine? By CASE II. find the course, and by CASE III. the distance. Suppose yourself standing at the pine, and making the northing radius, the proportion will be,

The course from the spruce to the pine is S 60° W.

NOTE. As the easting is greater than the northing, the course is over 45°. therefore look at the bottom of the page to find it.

To find the distance from the spruce to the pine, make that side radius, and the proportion will be, as the sine of the angle at the pine; is to the easting; so is radius to the distance required; or as the sine of the angle at the spruce; is to the northing; so is radius to the distance from the spruce to the pine.

As sine at the pine 60° 9.937531 As sine at the spruce 30°,9.698970 : the easting 216.5,

: : radius,

2.335458: northing, 125, 10.000000:

12.335458

9.937531

radius,.

2.096910

10.000000

12.096910

9.698970

required dist. 250 rods, 2.397927: required dist. 250 rods, 2.397940

The following courses and distances of a survey are given, and the course and distance of the closing line are required.

Beginning at a maple tree, thence running as follows:S. 80° W. 90 rods, N. 15° W. 95 rods, N. 85° E. 45 rods, S. 10° E. 40 rods, N. 85° E. 42 rods to a beach tree. First, arrange the given courses and distances in a table, having a blank line for the course, distance, latitude and departure of the closing line. Find by the traverse table the latitude and departure of each course and distance, and insert them in

Subtract the sum of the southings from that of the northings, and 44.32 will remain to fill the blank in the column of southings. Also, subtract the sum of the eastings from that of the westings, and 19.60 will remain to fill the blank in the column of eastings.

These numbers or distances are the legs of a right angled triangle, the hypothenuse of which is the closing line. You are now standing at the beach tree.

Make the southing radius and to find the course, the proportion will be,

:: tangent of the course, 23° 51′ 9.645656

The course of the closing line is S. 23°, 51', E. which may fill the blank in the column of courses.

To find the distance make the line from the beach to the maple, or the closing line radius, and the easting will be a

As the sine of the course 23° 51' 9.606751

The distance is 48.48 rods, which may be entered in the blank space in the column of distances, and the survey will be complete.

In the table of logarithms, against 484, in the column under 8, the last term, or the logarithm which is nearest to it is found 8 must be annexed to 484, and as the index is a unit, or 1, the two left hand figures are integers, and the others are decimals.

:

Former editions of this work contained several cases in Rectangular Trigonometry, which depended on secants for solution, but as secants are not retained in the tables which accompany this edition, those cases are also excluded from it. In Practical Surveying, no case will occur, which cannot be solved by these tables, nor can one occur, which depends on a solution by Rectangular Trigonometry, and which cannot be solved by the cases here treated of; therefore, secants are of no use to the practical surveyor.

Young learners meet with much perplexity in giving decimals their proper places when calculating latitudes and departures by inspection from the traverse table. This sub

ject claims some attention.

What is the latitude and departure of N. 84o E. 70 rods and 2 links?

The distance is 70.08 rods. The decimal is 8.100 of a rod. Over 840 in the traverse table against 70, the lat. is 7.32, and the dep. is 69.62.

Against 8, over latitude is 0.84, so nigh a unit that one may be added to the second decimal in the lat. and over dep. is 7.98, so near 8 that that number may be added to the second decimal in the departure. Ans. lat. 7. 33, dep. 69.70.

When a course departs 10° from a meridian and it is required to add the lat. and dep. of 10 links or.40 of a rod to the lat. and dep. of the number of rods contained in the distance; under 10° against 40; the lat. is 39.39, and the dep. is 6.95. As the two right hand figures of the latitude are un

ures of the dep. are over 50, a unit or 1, may be added to the left hand figure and the two last rejected, and the answer will stand, lat. .39, dep. .07. If the decimal is called 4 tenths, the separating point in both lat. and dep. may be carried over one figure towards the right, adding a unit to the dep. and the right hand figure in each rejected, and the result will be the same. 75°, 5 links or 2 tenths; lat. 0.52 dep. 1.93; carry over the point, lat. .05; dep. .19; 65°, five links or two tenths, lat. 0.85, dep. 1.81, lat. .08, dep. .18; 81°, 15 links or 6 tenths, lat. 0.94, dep. 5.93; lat. .09, dep. .59; 28°, 2 links or 8-100, lat. .07, dep. .04; 7° 151. or 6 tenths lat. 60 dep. .07.

What is the latitude and departure on N. 100 E. 6.5 rods? This need not be taken by two inspections, one for the integer and another for the decimal, but under 10°, against 65, the latitude is 64.01, and the departure is 11.29.

The separating point may be placed between the two first figures in each, and as the fourth figure in the departure is 9, a unit may be added to the third, the fourth figure in each may be omitted, and the latitude is 6.40 rods and the departure is 1.13 rods.

PRACTICAL SURVEYING.

NO. I.

EXPLANATION OF THE COMPASS, WITH DIRECTIONS HOW TO USE IT, AND HOW TO PROVE THE ACCURACY OF IT.

In surveying, each angular point is considered the centre of a circle divided into 360 equal parts called degrees.

The circle is also divided into four equal parts, called quadrants, by north and south, and east and west lines crossing each other at right angles on the centre. Each quadrant is divided into nine equal divisions, and each division contains ten degrees.

The following figure represents the card, or the graduation