Every Man His Own Teacher

12 signs or 360 degrees, the whole great circle of the Zodiac.

This table is of but little use to boys in common schools; it belongs to the higher orders of men in science, who are studying astronomy. However, a table like the following might be useful to boys, especially to those who intend to learn the art of surveying; but, as instruments and delineations of triangles, circles, &c. are necessary when we are working in rules of this kind, I shall only insert a few useful problems for the practical surveyor, and pass on to Reduction of Money.

4 quadrants 1 full and complete circle.

1. How to find a true corner, or to run a direct line from one known object to another, when there is a variation of compass.

Suppose we begin at A, and run S. 82° W. 20 chains. and 10 links, wishing to hit a beech corner tree; but by variation of compass, come out 30 links northerly from the corner; how many minutes variation are there? Answer,

51 minutes.

Therefore the line must be retraced N. 81° 9' E. from the beech tree to the place of beginning.

As the distance run, is to 57° .3;

So is the 30 links,

RULE.

to the variation required.

Multiply 57.3 degrees by 30 links and divide that product by the distance run, viz. 20 ch. 10 L. or 2010 links, the quotinet will be the answer.

Here note: If the divisor cannot be contained in the product, multiply by 60 to reduce the product into minutes; then divide, and the quotient will be the answer in minutes.

Beech

2010 Links.

N. 81° 9' E.

OPERATION.

57.3 degrees, the second term or multiplicand.
30 links, the third term or multiplier.

.630

82° 00 course run.

51 variation deducted.

Here the remainder is omitted, because we cannot run

to a fractional part of a minute.

RULE FOR PROOF.

As the sum of the hypothenuse and half the longest leg, is to 86 degrees; so is the shortest leg, to its opposite angle.

But in this case, the lines run so near a parallel direction with each other, that there is no material difference in their length; therefore we add half the base to the whole base, and call it equal to the hypothenuse and half the longest leg; or we consider the hypothenuse and base of equal length. OPERATION.

86 degrees, the second term or multiplicand.
30 links, the third term or multiplier.

2580

60 minutes in a degree.

154800 minutes for a dividend.

Continued.

2010 links, distance run.
1005 half the same.

3015 for a divisor: the quotient will be the proof in minutes. 3015)154800(51 minutes variation, or proof.

15075

..4050
3015

1035

NATURAL RADIUS.

How to find Natural Radius.

RULE.

1. Take the opposite angle of the side sought, and divide 4 times the square of its complement to 90 degrees, by 300 added to 3 times the said complement.

2. Add the quotient to said angle, their sum will be natural radius.

EXAMPLE.

In the following figure or triangle, the hypothenuse A C, and the angle at A, are given to find the side B C.