however, to outline briefly the theory of stadia surveying. In Fig. 4 we have:

i= distance between stadia wires.

s=space intercepted on the rod for any given reading. f=outer or inner focal length of objective.

d = distance to rod from outer focus.

f+c=the "constant" (given for each instrument usually on a card in the carrying case) = distance from axis of the instrument to outer focus.

Outer Focus

D

FIG. 4.-Diagram illustrating the theory of stadia surveying.

D= total distance from the axis of the instrument to the rod

The ratio of f to iis determined as follows:

Choose a convenient point from which to measure and set up the instrument so that its center is a distance equal to f+c behind the point. Carefully measure off 100 ft. from the point and establish another point on which to hold the rod. At this distance the wires should intercept 1 ft., upon the rod; if they do not they should be adjusted until they do. The formula given above then becomes d=100s which is convenient for calculation, since every foot of rod reading means 100 ft. of distance from the outer focus. The total distance, D, is obtained by adding f+c to the observed distance. Since f+c is small it may be neglected except in very close work.

Rod

The distance between the stadia wires should be checked for readings of 200 and 300 ft. when convenient. It is well to have permanent points established for this work of adjusting and the wires should be tested frequently.

The rod reading gives the slope distance when reading at an angle and this distance must be reduced to horizontal distance for plotting on the map, and vertical distance for determining difference of elevation. The solution is a trigonometrical problem upon which is based the construction of stadia tables giving horizontal distances and differences of elevation per 100 ft. for angles up to 30 degrees. The common devices for furnishing these figures are stadia tables, stadia diagrams, slide rule, and the Beaman Stadia Arc. Tables for use in the field should be of convenient size to fold and carry in the pocket, and should be mounted on waterproof cloth.

The Beaman Stadia Arc (Reference: “Stadia Surveying," published by W. & L. E. Gurley, Troy, New York) carries two scales; the one marked H gives the percentage reduction which must be applied to the observed slope distance to give the horizontal distance per 100 ft. For example, with a rod reading of 640 ft. and the H scale reading 3 the horizontal distance will be 640(640×.03)=620.8 ft. The scale marked V has the initial graduation 50, this is subtracted from the arc reading (when a whole number on the V scale is opposite the index) preserving the algebraic sign. The observed stadia distance is multiplied by the resulting number and the proper sign is retained with the product. The length of the rod between the middle stadia wire and the bottom is added to negative readings and subtracted from positive The result is the difference in elevation between the instrument and the bottom of the rod; this difference is added to or subtracted from the heighth of instrument according to its sign. Example: rod reads 640 ft., V scale reads 33, middle wire cuts the rod 7.4 ft. above the bottom, heighth of instrument is 2162.4 ft.

ones.

=

=

33-50-17; 17x6.4 108.8; 108.8-7.4 116.2 2162.4 116.2=2046.2= elevation of new point.

In general in stadia surveying the following points should be observed; the rod should be held plumb and should be in good focus; the instrument should be in good adjustment. It is well not to continue work when atmospheric disturbances are great, especially if accuracy is desirable. When the air is unsteady due to "shimmer or convection currents, read with the lower wire as far from the bottom of the rod as possible. Stadia wires should be adjusted as nearly under working conditions as possible. With large vertical angles the distance should be read with great accuracy; with small angles on long sights the angle should be read with care.

The stadia rod for use in this kind of mapping should be 10 or 12 ft. long, of light 3/4 in × 4 in. material; it should be painted black and white and need show no divisions less than 1/10 of a foot, Fig. 5 shows a suitable design for such a rod. This will permit readings to within 10 ft. which is about the limit for a self-reading rod at distances over 500 ft. At less distance the reading may be estimated more accurately. Stadia is not used in this work where exact locations are desired, these are obtained by triangulation or the method of resections. The rod should have some sort of device by means of which it may be plumbed accurately; a light iron pendu lum set in a case on the back of the rod will do as well as a rod level; the base of the rod should. be shod with a light strip of iron. Proper divisions may be painted on aluminium strips of convenient length for carrying; these are nailed to a suitable piece of board for use in the field.

FIG. 5.-Rod for use in ordinary stadia work where great accuracy is unnecessary; smallest divisions represent 1/10 ft.

CHAPTER II

TOPOGRAPHIC MAPPING

It is the writers intention in this and the following chapter to give a concise description of a quick and accurate method of making a mine surface map. The scheme here outlined has been used in mapping properties in the Western and Southwestern States and Mexico; but, while it is especially adapted to arid districts, it can be used with modifications anywhere but in heavily wooded country.

The theoretical discussions have been made as brief as possible, and no attempt has been made to go into the more elaborate methods of topographic surveying, which may be found in any one of several excellent texts.

A mine surface map should show:

1. The astronomic meridian with the magnetic variation line; also the locations of permanent points established by the survey, and the system of the coördinates by which points are located. 2. Property boundaries or claim lines.

3. Mine openings such as shafts, tunnels, and prospect pits. 4. Buildings, roads, railroads, etc.

5. A graphic representation of the natural features of the surface, such as hills, drainage, etc.

This last requirement may best be fulfilled by a topographic map, which shows lines on which all points have the same elevation. Such lines, called contours, are usually drawn at fixed intervals depending on the scale of the map and the nature of the surface of the ground. Any contour on a map of a small area represents the intersection of a horizontal surface with the surface of the ground; or the contour line may be regarded as the shore line of an imaginary body of water in which hills are islands (the contour line will close upon itself), and valleys are

straits or embayments. Fig. 6 shows a part of such a map; the hatched portion represents the plane of the 4175 ft. contour. Fig. 7 is a section constructed along the coördinate N 1000 of Fig. 6; the parallel horizontal lines represent the planes of the different contours.

A topographic map gives at a glance a general idea of the surface of the ground and its relations to artificial features; it

FIG. 6.-Portion of a topographic map. The hatched areas are those which would show above water if the country were submerged to the level of the 4175 ft. contour.

shows, for instance, in Fig. 6, that a claim covers most of a well-known hill and that its Northeast corner is in the "draw" on the other side of the main ridge.

From the map an approximate determination of elevation may be made by simply referring to the contour nearest the point in question, or more accurately by measuring the distance of the point from the nearest contour and comparing it to the distance between contours.