08 MATHEMATICS. 
equal milled rollers, CC. These rollers pass through apertures made in the 
ruler, projecting on the other side sufficiently to rest upon the paper. The 
ruler, carried on this axle with its rollers, will admit of any number of 
parallel lines being drawn. The greatest possible care must be taken to 
have all parts of these two rulers perfectly accurate. If the two rulers of 
the first form be not constantly parallel, or the rollers of the second be not 
perfectly equal in diameter, the results will be erroneous. The common 
square, or T square, with movable head, supplies the place of the parallel 
ruler, and is more certain in practice. 
Here also must be introduced the protractor (pl. 2, fig. '74), used in 
measuring and describing angles. It consists of an arc of brass, generally 
a semicircle, although sometimes a full circle is employed. In the semicir- 
cular protractor, the diameter falls along a ruling edge, and a small notch is 
made in the middle of this, answering to the centre of the circle. The cir- 
cumference of the semicircle is divided into 180°, and, if of sufficient size 
(8—10 inches in diameter), into five minute subdivisions. A rule is sometimes 
attached to the protractor, turning about its centre, for the purpose of 
measuring or describing angles more accurately. By attaching a vernier to 
this rule, very small subdivisions, even to a minute, may be read off. 
Directing our attention now to the instruments used in geodetical opera- 
tions, the first one to be mentioned is the measuring staff. ‘This is nothing 
but a staff of dry, oiled wood, tipped at each end with brass or iron, and 
divided into feet and inches, for the purpose of measuring straight lines in 
the field. When in use, it is either laid flat on the ground, or upon posts 
whose tops lie in a horizontal plane. Two or three of these are always 
required, in order that when one is laid down, another may be placed in 
contact with it,—the two extremities touching, and both lying in the same 
straight line. The first one is then to be taken up and placed at the other 
extremity of the second, and the operation thus continued. The base line 
for determining the length of a degree of the meridian in France, was 
measured by this instrument. Glass rods are sometimes employed, as was 
the case in the great English trigonometrical survey. 
The measuring chain (pl. 5, fig. 27) affords results that are sufficiently 
accurate for ordinary purposes: it is therefore the one generally employed 
in common surveying. ‘This consists of links of strong brass or iron wire, 
connected together by rings, and so arranged that the interval from the 
centre of one ring to that of the next amounts to just one foot. Ten of 
such links, or in some cases 12, form one rod, and this amount, and 
sometimes half and quarter rods, is indicated by rings, D, of peculiar shape. 
In America Gunter’s Chain is universally used. Here the entire chain is 
66 feet in length (= to four rods or poles), and is divided into 100 links, 
every tenth link being indicated by a piece of brass of peculiar shape. 
Each link, then, including the connecting rings, is 7.92 of an inch. At 
the ringed extremities, A and B, of the chain when in use, chain staves are 
driven into the ground over which these extremities pass. [ach staff 
(fig. 28) has a pointed iron foot, c, and a cross piece, 6, upon which the ring 
rests, and which is of use to enable the staff to be driven into the ground, by the 
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