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use the scale, a sheet of tracing paper, having lines ruled on it at an equal distance apart, is spread over the area to be measured (see Fig. 49). The process of measuring the area simply consists in measuring the lengths of the successive horizontal strips abcd, efgh, &c., until the whole area has been gone over. To do this, place the scale so that the wire on the slide is in the position aẻ, and the scale itself is parallel to the horizontal lines on the tracing paper. The slide is then moved along to the position cd. The scale itself is then bodily moved until the wire of the slide is in the position ef, when the slide is moved along to għ, care being taken while moving the scale that the position of the slide is not changed. By this means the length of each strip is measured in succession, and the total length of the sum of all the strips is read off the scale at the conclusion of the operation in units of area.

The width of the strips is usually about in., and the scale is so constructed as to read so many acres per lineal inch, in. wide, according to the scale for which it is intended. It is thus obvious that the computing scale only applies to plans drawn to the scale for which it is made. It may, however, be used for other scales by multiplying the result as scaled by a constant which will vary for each scale and is easily calculated. The tracing paper has to be twisted about until the whole area is included between two of the parallel lines as shown in Fig. 49.




Fig. 49.-Areas by
Computing Scale.

Area of Survey executed with Incorrect Chain.—The true area of a survey which has been executed with an incorrect chain may be found as follows :—

True area of survey

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Copying Plans.--The most common method of copying plans is to trace them on tracing paper or tracing linen. When a tracing is very much crumpled or dirty, the use of a “copying glass" facilitates operations. This consists of a strong sheet of plate glass in a wooden frame with sometimes the addition of a mirror underneath to reflect light upwards. The plan to be

copied is placed on the glass, and the light underneath enables the tracing to be done more readily. Tracing even on ordinary drawing paper can be done with a copying glass. A plan may be copied by pricking through the salient points on to another sheet placed underneath it. These points are then joined, and the minor details plotted in. Pricking through is apt to spoil a plan, and is most useful when the plan consists of straight lines principally. For copying tracings various photographic processes are now employed. The ferro-prussiate process gives white lines on a blue ground. Specially prepared papers may also be had which give black lines on a white ground. The tracing to be copied is stretched in a glass frame over the prepared paper, and the face of the tracing exposed to the sun. The prepared paper is then simply washed in clean water immediately on being taken out of the frame, and the parts which were under the lines on the tracing and were unacted upon by the sun come out in white or black as the case may be. If the tracing is fairly clean and not crumpled, these processes give very good copies.

Another method of copying a plan is to trace it and transfer it to another sheet of paper by placing the tracing on it with a sheet of transfer paper between them. By going over the lines of the tracing with a hard pencil or style we get a copy on the sheet of paper underneath, which has then to be inked in.

Enlarging and Reducing Plans.-The only really accurate method of enlarging and reducing plans is to replot them from the field books to the required scale. For ordinary purposes, however, a fairly accurate copy, enlargement, or reduction may be made by ruling the whole plot into squares 1 or 2 in. in the side. The same number of squares is ruled on another sheet to the required scale, and the copy is made by transferring the part included in each square separately. Each point is fixed by scaling its rectangular co-ordinates, one of the corners of a square being taken as the origin. For this purpose the proportional compasses shown in Fig. 40 are useful.

To avoid spoiling the plotted survey, it is a good plan to cover it with a sheet of tracing paper, and draw the squares upon it.

The Pantagraph.-This is an instrument for copying, en

larging, or reducing plans by simply going over the lines with a tracing point. It is shown in Fig. 50.


Fig. 50.-Pantagraph.

The Eidograph.-This is a similar instrument, and was invented by Professor Wallace to remedy the unsteadiness of the pantagraph, which arises from its numerous joints and supports upon the paper.

As a rule, neither the pantagraph nor the eidograph is a satisfactory instrument. They require a great deal of room on the drawing table, and for copying, enlarging, or reducing plans, one of the methods already described is recommended. Full descriptions of both the pantagraph and the eidograph are to be found in Heather's "Mathematical Instruments."*

Lithographing Plans When a great many copies of plans are required, it is usual to have them lithographed. The process of lithographing consists of first making a tracing of the plan in specially prepared lithographic ink. This is laid face downwards on the stone, and the copy transferred to it. From the stone as many copies as are required are printed off. As the tracing is damped before it is laid on the stone, it expands, and sometimes gets stretched unequally. The impression is therefore usually larger than the original. The paper on which the copies are taken off the

*To get really satisfactory results with the pantagraph and eidograph, very well made and expensive instruments are necessary, and an extra large table to use them on.

stone being also damp during the process, shrinks after drying, which to some extent counteracts the expansion and stretching of the tracing. As a rule, however, lithographic copies are not to be depended on when much accuracy is required. All drawings to be lithographed should have a scale drawn on them so that it may be affected by the expansion and shrinkage along with the drawing. Even then the lithographs will often be found not to scale.

Reducing Plans by Photography.-The 6 in. Ordnance Sheets are reduced from the 25 in. sheets by photography. The details are then traced from the photograph, and the tracing is placed on a copper plate. The lines are then gone over with a sharp instrument which cuts through the tracing and indents the copper underneath it. When great accuracy is required, as in the case of the main stations, the points are plotted on the copper. Engravings from copper usually shrink, as they are taken off the copper when damp, and all measurements should therefore be taken with the scale drawn on the sheet. A process for photographing the details directly on to copper or zinc has also been introduced.



Instruments: Theodolite.-By far the most useful instrument to the surveyor is the theodolite. The chief use of the theodolite is for measuring and setting out horizontal and vertical angles and for ranging out lines. Fig. 51 shows the instrument, as made by W. F. Stanley, Great Turnstile, Holborn, London. Fig. 52 shows Cooke's transit theodolite, as made by Messrs T. Cooke & Sons, York, and 8 Victoria Street, Westminster. Very good instruments are also made by Messrs Troughton & Simms, 138 Fleet Street, London (see Fig. 53). Each maker's instrument varies in small details of construction, but the main features in all are the same.

ab is the telescope, which is simply an ordinary telescope with the addition of a diaphragm c. The diaphragm is either a glass with fine lines etched on it, or a brass ring having fine spider's hairs or wires stretched across it, as shown in Fig. 54. Stadia hairs (see Chapter VI.) should be added as shown at s, s. The diaphragm is held in place by the four capstan screws d, d,d, d, Figs. 52 and 54, and is adjusted either horizontally or vertically by means of these screws. When properly adjusted, the intersection of the hairs at the centre of the diaphragm is in the axis or "collimation line" of the telescope. The telescope is focussed by moving the object glass at a out or in by means of a milled headed screw at the side of the telescope near the eyepiece (not shown in Fig. 52). When properly focussed, the image of the object observed coincides with the diaphragm. The image is viewed through the eyepiece b, which magnifies it. The eyepiece is adjusted by pulling it out or in until a clear view of the cross hairs of the diaphragm is obtained. By the addition of extra glasses an erect image in place of the usual inverted image may be obtained, but at the expense of the power of the telescope. There is no special advantage in having

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