From Spons’ Workshop Receipts For Manufacturers Mechanics And Scientific Amateurs, Vol. III - Jointing Pipes to Pumps. London: E.& F.N. Spon, Ltd., Revised Edition, 1909.
A simple means of measuring angles is shown in Fig. 40. The board a usually of deal, which should be about 15 in. square, underneath it has screwed onto it in the centre a brass boss, which fits into a similarly shaped recess in the wooden head of a folding tripod stand. A brass clamping screw passes from below through a hole in the centre of the tripod head, and screws into the brass boss on the board. By this means the board, or plane table, as it is here termed, can be smoothly turned round horizontally into any position and securely clamped there.
On the top of the board is pasted or glued a cardboard protractor b. These protractors are about 12 in. diameter, and are graduated to ¼ degree, and can be bought for a small sum. Care should be taken to attach this flatly to the board.
The next essential is a sight-rule c. This consists of a flat piece of some hard wood about 15" in. long by 2-1/4" in. wide, and 1/2" in. thick, having one edge bevelled. On each end is fitted centrally a brass sight-vane - one d having a wide slot through its upstanding part, down the centre of which is fitted a fine wire or hair; the other e has a fine slit down its centre.
To measure an angle between two objects, the plane table is set up as level as possible by eye, the sight rule is placed across its centre of the protractor, and pointed in the direction of the left-hand object, the eye being applied to the slit in e, and the wire in d being brought into coincidence with the object. Care must be taken that the bevelled edge of the rule lies nearly over the centre of the protractor. This is easily ensured by placing the finger or the uncut end of as pencil touching the centre point, and using this as a pivot round which to turn the rule. The graduations of the protractor cut by the beveled edge of the rule are then read at each end, and their mean is taken as the true direction of the object. A similar observation is then taken to the right-hand object, care being always taken to use the mean of the readings at each end of the rule. The difference between the readings to the two objects give the angle required.
A most surprising degree of accuracy can be obtained by the use of this simple instrument by repeating the observations on a different part of the graduation. It is, in fact, a very fair theodolite without a telescope.
If a magnetic compass is used in conjunction with the plane table, and by its means the table and protractor be turned round and set magnetic north and south, accurate magnetic bearings of objects can be obtained with equal facility.