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the Tithe Commissioners : but how far such behaviour is to be commended, I leave the reader to judge.

Having given the student a great variety of examples, both in small and large surveys, it will now be proper to describe the drawing instruments, required in laying down extensive surveys, as well as the more perfect field instruments, required in railway and other engineering surveys; which are often of a complicated character, as are also private surveys of woodlands and mountainous districts. These subjects will be treated of in Chap. V., where the proper forms of the field books will

be given, for extensive surveys of every description.


The nature of this scale will be best understood
from its construction.—To construct a vernier scale,
which will enable us to take off a number to three
places of figures: divide all the primary divisions into
tenths, and number these subdivisions, 1, 2, 3, &c.,
from the left hand towards the right, throughout the
whole extent of the scale. Then take off, with the
compasses, eleven of these subdivisions, set the extent
off backwards, from the end of the first primary
division, and it will reach beyond the beginning of
this division, or zero point, a distance equal to one of
the subdivisions. Now divide the extent, thus set
off, into ten equal parts, marking the divisions on the
opposite side of the divided line to the strokes mark-
ing the primary divisions and the subdivisions; and
number them 1, 2, 3, &c., backwards from right to
left. Then, since the extent of eleven subdivisions
has been divided into ten equal parts, so that these
ten parts exceed by one subdivision the extent of ten
subdivisions, each one of these equal parts, or, as it
may be called, one division of the vernier scale, exceeds
one of the subdivisions by a tenth part of a subdivi.
sion, or a hundreth part of a primary division. In
our figure the distances between the primary divisions
are each one inch, consequently the distances between
the subdivisions are each one-tenth of an inch, and
the distances of the divisions on the vernier scale are
each one tenth and one-hundredth of an inch.

See also: “Mathematical Instruments,” by J. F. Heather, Woalo's Berios, 18. 68.


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Example 1. Let the given number be 253.

Increase the first figure 2 by 1, making it 3; because the vernier scale commences at the end of the first primary division, and the primary divisions are measured from this point, and not from the zero point.* The first figure, thus increased, represents 35 of the subdivisions from the zero point, from which the third figure 3 must be subtracted, leaving 32, since three divisions of the vernier scale will contain three of these subdivisions together with three-tenths of a subdivision. Now place one point of the compasses nipon the third division of the vernier scale, and extend the other point to the 32nd subdivision, or the second division beyond the third primary division, and, laying down the distance between the points of the compasses, it will represent 253, or 25-3, or 2.53, according as the primary divisions are taken for hundreds, tens, or units.

GENERAL RULE.—To take any number to three places of figures from this vernier scale.--Increase the first figure by one; snbtract the third figure from the second, borrowing one from the first increased figure, if necessary, and extend the compasses from the division ugon the vernier scale indicated by the third figure, to the subdivision indicated by the number remaining after performing the above subtraction.



During the time necessarily occupied in plotting an extensive survey, the paper on which the work is drawn, is affected by the different states of humidity of the air, and the parts laid down from the same scale, at different times, will not exactly correspond, unless the scale has been first laid down on the paper itself, and all the distances of the survey have been taken from the scale so laid down, which will always be in the same state of expansion or contraction as the work on the plan. Therefore, for plotting an extensive survey, and accurately filling in the minutiæ, a diagonal, or vernier scale may be advantageously laid upon the paper on which the plan is to be made. A vernier scale is preferable to a diagonal scale, because in the latter it is extremely difficult to draw the diagonals with accuracy, and we have no check upon its errors; while in the former, the uniform manner in which the strokes of one scale separate from those of the other, is strong evidence of the truth of both.

* If the vernier scale were placed to the left of the zero point, a distance less than one primary division could rot always be found upon the scale.

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The above engraving represents the instrument, which consists of a beam A A, of any length required, generally made of well-seasoned mahogany. Upon its face is inlaid throughout its whole length, a slip of holly or boxwood a a, on which are engraved the divisions or scale, either in feet and decimals or inches and decimals, or such parts of either as may be required. Those made for the use of the Ordnance survey of Ireland, were divided to a scale of chains, 80 of which occupied a length of six inches, which, therefore, represented one mile, six inches to the mile being the le on which that important survey is plotted; the present survey of the metropolis being plotted to a scale of 60 inches to a mile.* Two brass boxes B and C are adapted to the beam; of which the latter may be moved, by sliding to any part of its length, and its position fixed by tightening the clamp screw E. Connected with the brass boxes are the points of the instrument G and H, which may be made to have any extent of opening by sliding the box C along the beam, the other box B being firmly fixed at one extremity of the beam. The object to be attained by this instrument is the nice adjustment of the points G, H to any definite distance apart. This is accomplished by two verniers, or reading places b, c each fixed at the side of an opening in the brass boxes, to which they are attached, and affording the means of minutely subdividing the principal divisions aa on the beam, which appear through these openings. D is a clamp screw for a similar purpose to the screw E, that is, to fix the box B, and prevent motion in the point it carries after adjustment. F is a slow motion screw, by which the point G may be moved any minute quantity for perfecting the setting of the instrument.

* The first-class parish maps of the Tithe Commission survey are to a scale of three chains to one inch, or one mile to 263 inches. Plans of private estates are to various scales, but chiefly varying from 5 to 12 chains to an inch, the smaller scales being chiefly adopted where the estates are large, that the plans may be of a convenient size. The Ordnance survey of most of the towns in Ireland is also plotted on a scale of 120 inches to the mile, the others being plotted on a scale of 60 inches to the mile.




The method of setting the instrument may be understood from the above description of its parts, in conjunction with the following explanation of the method of examining and correcting the adjustment of the vernier b, which like all other mechanical adjustments, will occasionally become deranged. This verification must be performed by means of a detached scale. Suppose, for example, that the beam compass is divided into feet, inches, and tenths, and subdivided by the vernier into hundredths, &c. First set the zero division of the vernier to the zero of the principal divisions on the beam, by means of the slow motion screw F. This must be done with great care. Then slide the box C, with its point H, till the zero on the vernier C exactly coincides with any principal division on the beam, as 12 or 6 inches. To enable us to do this with extreme accuracy, some superior kinds of beam compasses have the box C also furnished with a tangent or slow motion screw, by which the setting of the points of division may be performed with the utmost precision. Lastly, apply the points to a similar detached scale, and, if the adjustment be perfect, the interval of the points G, H will measure on it the distance to which they were set on the beam. If they do not by ever so small a quantity, the adjustment should be corrected, by turning the screw F, till the points exactly measure that on the detached scale; then, by loosening the little screws which hold the vernier b in its place, the position of the vernier may be gradually changed, till its zero coincides with the zero on the beam; and, the screws being now tightened, the adjustment will be complete.

THE PANTAGRAPH. The pantagraph, used for reducing or enlarging maps, consists of four brass bars A B, AC, DF, and FE: the two longer bars A B, A C are connected by a moveable joint at A: the two shorter bars are connected in like manner with each other at F, and with the longer bars at D and E, and, being equal in length to the portions A D, A E of the longer bars, form with them an accurate parallelogram ADF E, in every position of the instrument. Several ivory castors support the machine parallel to the paper, and allow it to move freely over it in all directions. The arms A B and D F are graduated and marked }, ž, &c., and have each a sliding index which can be fixed to any of the divisions by a milled-headed clamping screw, seen in the engraving. The sliding indices have each of them a tube, adapted either to slide on a pin, rising from a heavy circular weight called the fulcrum, or to receive a sliding holder with a pencil or pen, or a blunt tracing point, as may be required.

When the instrument is correctly set, the tracing point, pencil, and fulcrum will be in one straight line, as shewn by the dotted line in the figure. The motions of the tracing point and pencil are then each compounded of two circular motions, one about the fulcrum, and the other about the joints at the ends of the bars, upon which they are respectively placed. The radii of these motions form sides about equal angles of two similar triangles, of which the dotted right line B C, passing through the tracing point, pencil, and fulcrum, forms one side: hence the distances passed over by the tracing point and pencil, in consequence of either of these motions, have the same ratio, and, therefore, the distances passed over in consequence of the combination of the two motions, have also the same ratio, which is that indicated by the setting of the instrument.

The engraving represents the pantagraph in the act of reducing a map to the scale of half the original. For this purpose the sliding indices are first clamped at the divisions on the arms, marked ]; the tracing point is then fixed in the socket at C, over the original map; the pencil is next placed in the tube of the sliding index, on the bar D F, over the paper to receive the copy;

and the fulcrum to that at B, on the bar A B. The machine being now ready for use, if the tracing point C be passed delicately and steadily over every line of the map, true copy, but of one half of the scale of the original, will be marked by the pencil on the paper beneath it.

The fine thread represented as passing from the pencil quite round the instrument to the tracing point C, enables the draughtsman at the tracing point to raise the pencil from the paper while he passes tho

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