equal to the difference of a division of the limb, and of the vernier: then, in fig. 1, one revolution of the screw advances the vernier a distance equal to 20′; and, if the cylindrical head BB be divided into 60 equal parts, a revolution of the screw through one of these parts would advance the vernier a distance equal to 20".

Suppose, then, that in the illustration above given the screw has to be turned back, so that 14 of these graduations pass the index I, in order to bring the stroke at the end of the second division upon the vernier into coincidence with a stroke upon the limb; then the corresponding space moved through by the vernier would be equal to 20" x 14, or 4′ 40′′, and the reading of the instrument would be 22° 44′ 40′′.

Similarly, by means of a micrometer divided into ten equal parts, a distance to the thousandth part of an inch may be read off by the vernier in fig. 2. If the micrometer in this case were divided into one hundred equal parts, a distance might be read off to the ten-thousandth part of an inch; or the same effect may be produced by dividing the micrometer into ten equal parts, and making the screw of such fineness that ten complete revolutions move the vernier through a distance equal to the difference of a division of the limb and of the vernier, or the hundredth part of an inch.

The above engraving represents this instrument, which consists of a beam, AA, 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, aa, upon which are engraved the divisions or scale, either feet and decimals, or inches and decimals, or whatever particular scale may be required. Those made for the use of the persons engaged on the Ordnance survey of Ireland were divided to a scale of chains, 80 of which occupied a length equal to six inches, which, therefore, represented one mile, six inches to

A

the mile being the scale to which that important survey is plotted *. 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 fixed in position by tightening the clamp screw E. Connected with the brass boxes are the two 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. The object to be attained, in the use of this instrument, is the nice adjustment of the points G, H, to any definite distance apart. This is accomplished by two verniert or reading plates, 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 those openings. D is a clamp screw for a similar purpose to the screw E, namely, to fix the box B, and prevent motion in the point it carries after adjustment to position. F is a slow motion screw, by which the point & may be moved any very minute quantity for perfecting the setting of the instrument, after it has been otherwise set as nearly as possible by the hand alone.

The method of setting the instrument for use may be understood from the above description of its parts, and also by the following explanation of the method of examining and correcting the adjustment of the vernier, b, which, like all other mechanical adjustments, will occasionally get deranged. This verification must be performed by means of a detached scale. Thus, suppose, for example, that our beam compass is divided to feet, inches, and tenths, and subdivided by the vernier to 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 very nicely. Then slide the box c, with its point G, till the zero on the vernier c exactly coincides with any principal division on the beam, as twelve inches, or six inches, &c. 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 or divisions 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 GH will

The survey of the metropolis is plotted to a scale of 60 inches to the mile.

+ For a description of the vernier, see preceding article.

D

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 do exactly measure that quantity 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, then tightening the screws again, the adjustment will be complete.

PLOTTING SCALES.

Plotting scales, also called feather-edged scales, are straight rulers, usually about ten or twelve inches long. Each ruler has scales of equal parts, decimally divided, placed upon its edges, which are made sloping, so that the extremities of the strokes marking the divisions lie close to the paper. The primary divisions represent chains, and the subdivisions, consequently, ten links each, as there are 100 links on the surveying chain. Plotting scales may be procured in sets, each with a different number of chains to the inch.

The advantages of this arrangement are, that the distances required can be transferred with great expedition from the scale to the paper by the aid of the pricking-point alone, and the marks denoting the divisions are in no danger of becoming defaced, as upon the plain scale, by the frequent application of the compasses.

One of the best plotting scales consists of two feather-edged rulers, one sliding along the other in a dovetailed groove, so that the two are always at right angles to each other. We shall describe this instrument more particularly when we come to speak of plotting, after describing the instruments used in surveying.

THE PANTAGRAPH.

The pantagraph consists of four rulers, AB, AC, DF, and EF, made of stout brass. The two longer rulers, AB and A C, are connected together by, and have a motion round a center at A. The two shorter rulers are connected in like manner with each other at F, and with the longer rulers at D and E, and, being equal in length to the portions AD and AE of the longer rulers, form with them an accurate parallelogram, ADFE, 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, AB and

DF, are graduated and marked,, &c., and have each a sliding index, which can be fixed at 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 shown 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 rulers upon which they are respectively placed. The radii of these motions form sides about equal angles of two similar triangles, of which the straight line в C, passing through the tracing point, pencil, and fulcrum, forms the third sides. The distances passed over by the tracing point and pencil, in consequence of either of these motions, have then 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

Our engraving represents the pantagraph in the act of reducing a plan to a scale of half the original. For this purpose the sliding indices are first clamped at the divisions upon the arms marked; the tracing point is then fixed in a

socket at c, over the original drawing; the pencil is next placed in the tube of the sliding index upon the ruler D F, over the paper to receive the copy; and the fulcrum is fixed to that at B, upon the ruler a B. The machine being now ready for use, if the tracing point at c be passed delicately and steadily over every line of the plan, a true copy, but of one-half 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 at c, enables the draughtsman at the tracing point to raise the pencil from the paper, whilst he passes the tracer from one part of the original to another, and thus to prevent false lines from being made on the copy. The pencil holder is surmounted by a cup, into which sand or shot may be put, to press the pencil more heavily on the paper, when found necessary.

If the object were to enlarge the drawing to double its scale, then the tracer must be placed upon the arm D F, and the pencil at c; and, if a copy were required of the same scale as the original, then, the sliding indices still remaining at the same divisions upon DF and A B, the fulcrum must take the middle station, and the pencil and tracing point those on the exterior arms, A B and A C, of the instrument.

The successful use of the pantagraph in copying very minute and complicated drawings can only be attained by perseverance and experience, and we therefore proceed to mention some of the other means employed for the attainment of the same object. In fact, while the pantagraph affords the most rapid means of reducing a drawing, we cannot recommend its use for enlarging a copy, or even for copying upon the same scale.

To produce a Copy of the same Size as the Original. First Method.-Lay the original drawing upon the sheet of paper intended for the copy, and fix them together by means of weights or drawing pins *. 2. With a fine needle prick through all the angles and principal points, making corresponding punctures in the paper beneath. 3. Draw upon the сору such of the lines on the original as are straight, or nearly so, by joining the points thus marked upon the paper

The drawing pin consists of a brass head,

with a steel point at right angles to its plane. A represents it as seen edgewise, and в as seen from above.

+ See pricking point, page 8.