60 MATHEMATICS. 
As part of the apparatus of the plane table, we will mention, first, the 
fork (fig. 22), which consists of two strips, A and C, fastened by the head, 
B, in such a manner that they may be slid upon the drawing board. The 
upper strip, A, runs out to a point which lies exactly above the spot, C, of 
the lower strip, to which the line for the plummet D is attached. A second 
plummet is often attached above B. These forks serve to bring a given 
point on the table directly above a certain point on the ground. ‘The point 
A is laid upon the point in question, and the table moved until the plummet 
hangs directly over the spot of earth. 
The erecting compass is another piece of supplementary apparatus, 
serving to set up the table in a direction parallel to the original one. This 
is nothing more than a small magnetic compass with a well divided dial, 
which can be screwed on the edge of the table. 
The devel serves to render the drawing board perfectly horiaeanal this 
being indispensably necessary to an accurate measurement. It is of two 
forms—the tub-shaped and the tubular. The twb-shaped level consists of a 
flat cylindrical vessel with an accurately ground bottom, and covered above 
by a plate of glass. The vessel is filled with alcohol so as to leave only a 
minute bubble of air, and the top cemented on air-tight. The instrument is 
inconveniently sensitive when the upper plate is perfectly plane; this is, 
therefore, generally very slightly convex, so that there may be a tendency 
in the bubble to seek the centre of the surface. 
The tubular level (pl. 5, figs. 28, 24) consists of a frame perfectly plane 
below, and inclosing a tube of glass closed at both ends. This tube is filled 
with alcohol, in which is a small bubble of air, which, when the tube is per- 
fectly horizontal, rests in its middle. As the glass tube by itself would be 
liable to breakage, it is inclosed in a tube of brass, which has a piece cut out 
of the middle portion above from E to F, to render the bubble visible. This 
exposed portion of the glass is protected by the bands aa. To be certain of 
the central situation of the bubble, several concentric circles are cut on the 
cover of the tub level, and on the tube of the tubular level, between which 
the bubble must rest. Several are necessary, owing to the varying size of 
the bubble, produced by its expansion or contraction. A small screw is 
placed beneath the tube level in the socket at B, to correct any deviation 
from a perfect parallelism of the surfaces. 
The diopter ruler, or sight ruler, is used to determine sight lines upon the 
plate of the tables. Its simplest construction is exhibited in fig. 25. A 
strong brass ruler, A, with bevelled edges, carries at its extremities two cross 
pieces, B and C, supporting hinged sight vanes, Dand E. The eye diopter, 
or sight vane, D, contains a narrow vertical slit, or several small holes one 
above the other. The object vane, E, consists of a frame, in the centre of 
which a fine hair or wire is stretched vertically. By bringing the slit, the wire, 
and the axis of the point sighted at, in one line, the projection of the vertical 
plane determined by this line of sight, may be drawn on the table along the 
edge of the ruler. 
In the preceding construction of the ruler, the sight line itself is not 
pbtained, but one parallel to it. To describe this line itself, the axes of the 
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