COMPUTATION SCALE.

Fig. 1, Plate 41. This scale is in fact two plotting scales, but divided different to the ordinary plotting scales, the chains counting right and left from the centre, and one side being double that of the other, purposely for calculating quantities, according to the rules given at page 57 for finding the area of a triangle.

Before the introduction of the improved calculating scale, this was considered the most perfect system in obtaining a true quantity; as, for example:

Suppose the plan to be plotted to 4 chains to the inch, the irregular fences equalised, and the whole field brought into straight lines, and then into triangles and trapeziums.

That part of the scale divided into 40 parts is applied to all the bases; then, by applying the two zeros exactly on the base, and brought to the vertex of the triangle, the side that is divided into 20 parts gives half the perpendicular at once, instead of having to divide the whole perpendicular.

When calculating a trapezoid, take the sum of the perpendiculars and multiply by the base.

DESCRIPTION AND USE OF THE IMPROVED COMPUTATION SCALE.

Fig. 2, Plate 41. This scale is usually made to 3 chains to the inch. The drawing shows only a portion of the scale. The large figures from 0 to 6, on the upper side, denote 6 acres; and from 6 to 12, on the lower side, 12 acres; each division is subdivided into 4 parts or 4 roods, and are numbered accordingly 1, 2, 3. The perches are engraved on the ivory scale attached to the movable metal frame, divided into 4 parts, each part equal in value to 10 poles; each part is subdivided into 5, equal to 2 poles each. Those on the right hand read with the acres and roods on the upper part of the scale; those on the left hand read with the acres and roods on the lower side of the scale.

The transparent horn is fixed to the metal frame; the horizontal lines engraved on it, parallel to the edge of the scale, are one chain apart; the vertical line is directly over the zero on the ivory scale, which divides the fence line between the two horizontal lines; and in like manner the two oblique lines are used to divide the fence lines that more immediately run in that direction.

When using the scale, first prepare a piece of tracing paper by drawing parallel lines one chain apart; lay the tracing paper so that any two lines touch two opposite corners of the field, as at A and B, Fig. 82, Plate 6. Keep the tracing paper firmly fixed to prevent its shifting; bring the vertical line to zero on the scale, and place that line on the fence at a, dividing it equally, taking care the two horizontal lines on the horn are over the first two lines on the tracing paper; hold the scale firm, and move the metal frame to the left until the vertical line equally divides the fence at b; then move the whole, being careful not to move the metal frame; then place the vertical line on the next parallel line at c, dividing the fence as before; hold the scale firm, and move the frame to d, dividing that fence equally; so proceed on with every parallel until the metal frame stops at 6 acres, which may be in a part of the parallel line, as shown at C; at this point make a mark on the tracing directly over the vertical line; without moving the metal frame, bring the vertical line to the fence at e, on the same parallel, and move the frame to the right hand to the mark made at C; without touching the metal frame, bring the whole back to ƒ and slide it to g, and so on to the last fence at h; at this point read the quantity from the scale.

Should the quantity exceed 12 acres, make a mark as before at C, and keep a memorandum, and then proceed as at the commencement, which must be added to the last quantity.

The quantity as shown on the scale is the content of a field calculated on the upper side of the scale, 3A. 3R. 16P.; but if it returned the reading on the lower side would be 6a. Or. 24p.;

if the scale had been expended once before, then it would be 16A. OR. 24P., and so on.

H. S. MERRETT'S PATENT IMPROVED COMPUTATION SCALE.*

Fig. 3, Plate 41. The difference between this and the last described scale is in making the same metal frame applicable to other scales, as 3, 4, 5 chains to the inch.

For which purpose three scales, 3, 4, and 5, to the inch are divided in like manner, and made to fit the same metal frame, which is made to hold horns divided in like manner to their respective scales.

Instead of the poles being divided on the ivory scale, as in the former example, they are divided on the scale with the acres, roods, and perches.

The screw in the metal frame acts as a clamp.

It is more desirable to divide the whole value of the scale

to a decimal number, as 10 acres.

In using these scales, remember always to keep the side C D of the metal frame for reading the quantities, that being a continuation of the vertical line on the horn.

It is used precisely in the same manner as before described. In all cases where accuracy is required the method described at page 68 and Fig. 83 is recommended as the best.

Where very irregular boundaries occur the computation scales are then most desirable.

THE DIAGONAL SCALE.

Fig. 4, Plate 41. This scale is seldom used, excepting for large works requiring great accuracy.

If the larger divisions be accounted as units, the first subdivision will be a tenth part of a unit, and the second, marked by the diagonal line upon the parallel lines, a hundredth part

of a unit.

* To be obtained only of the author.

But if we suppose the larger divisions to be tens, the first subdivisions will be units, and the second tenths; if the larger are hundreds, then will the first be tens and the second units.

The numbers, therefore, 576, 57.6, and 5.76, are all expressible by the same extent of the compasses; thus, setting one foot in the number 5 of the larger divisions, extend the other along the sixth parallel to the seventh diagonal.

For if the five larger divisions be taken for 500, seven of the first subdivisions will be 70, which, upon the sixth parallel taking in six of the second subdivisions for units, make the whole number equal 576.

Or if the five larger divisions be taken for five tens, or 50, seven of the first subdivisions will be seven units, and the six second subdivisions upon the sixth parallel will be six-tenths of a unit.

If the five larger divisions be only esteemed as five units, then will the seven first subdivisions be seven-tenths, and the six second subdivisions the six-hundredth part of a unit.

Example 1. To take off the number 4.79.

Set one foot of the compasses on the point where the fourth vertical line cuts the seventh parallel line, and extend the other foot to the point where the ninth diagonal cuts the seventh horizontal line.

Example 2. To take off the number 76.4.

Observe the points where the sixth horizontal cuts the seventh vertical and fourth diagonal line; the extent between these points will represent the number.

In the first example, each primary division is taken for one; in the second, it is taken for ten.

Example 3. To lay down a line of 7.85 chains.

Set one point of the compasses where the eighth parallel (counting upwards) cuts the seventh vertical line, and extend the other point to the intersection of the same eighth parallel with the fifth diagonal.

Set off the extent of 7.85 thus found on the line.

Example 4. To measure by the diagonal scale a line that is already drawn.

Take the extent of the line in the compasses, place one foot on the first vertical line, that will bring the other foot among the diagonals; move both feet upwards until one of them falls into the point where the diagonal from the nearest tenth cuts the same parallel as is cut by the other on the vertical line; then one foot shares the chain, and the other the hundredth part, or odd links. Then if one foot is on the eighth diagonal of the fourth parallel, while the other is on the same parallel, but coincides with the twelfth vertical, we have 12 chains 48 links, or 12.48 links.

PLOTTING SCALES.

Plotting scales are made either of ivory or boxwood: the ivory is preferable, the divisions being clearer; they are generally 12 inches long, and are distinguished by the number of chains to the inch; they are numbered numerically, and subdivided into 10 parts, each part equal to 10 links.

There should never be two scales on the same ivory, and the zeros always at the same end; the scale can then be used right or left.

It is required frequently to have a scale of feet; those scales should be separate from the general plotting scales. It will be found convenient to have a set of 6-inch scales, similar to Fig. 1, Plate 41, also a set of off-set scales, with zero in the middle.

STRAIGHT EDGE,

However simple it may appear, it is very difficult to obtain a straight edge, or long rule, of great length. It is one of the most important parts on laying down the principal lines of an extensive survey; equal to that in chaining a straight line in the field.

To prove the accuracy of a straight edge before using it, lay it on the paper prepared for the survey, fix two needles, place the edge against them and draw a very fine pencil line,