1851 Great Exhibition: Official Catalogue: Class X.: John Sang
338. SANG, JOHN, Kirkaldy, Scotland — Inventor and Manufacturer.
A planometer or self-acting calculator of surface.
This instrument is used for measuring the area of figures drawn on paper, which it does in an accurate and rapid manner, the operator merely requiring to guide the point of a pen round the outline of the figure, however irregular it may be. It measures any figure, but its great advantage consists in determining the area of those of irregular forms, the measuring and calculating of which by scales in the common manner is a laborious process, and one requiring to be repeatedly performed and revised, in order to ensure minute accuracy, and to do away with the chance of arithmetical errors. Adapted for the use of surveyors of land and engineers, and also calculated to assist students of physical geography, of geology, and of statistics; to the latter it affords the means of indicating from the best maps, with little trouble, the extents of states and other subdivisions, and of correcting the approximations given in published tables.
In order to use the platometer it is to be laid on the figure in such a manner that the tracer can be carried round its outline. The handle is to be held like a pen in writing, and the tracer is to be brought on the outline and pressed very slightly into the paper, so as to make a small mark. The index is to be read. The tracer is then to be carried along the outline until the mark be again reached. The index is to be read again, and the difference between the two readings is the area of the figure in square inches, tenths and hundredth parts, or the area may be got without subtraction, by setting the index at zero at the commencement, but the former is the preferable mode. When the boundary consists of straight lines the process is aided by using a straight-edged ruler to guide the tracer, as in drawing.
The numbers engraved on the silver index indicate square inches, which are divided by lines into tenths, and further by a vernier in the common manlier into hundredth parts. This index reads up to 20 inches; the brass index carries on the divisions as far as 100 square inches. The instrument will measure any figure not exceeding 4 inches in breadth and 22 in length. If the figure is of greater size it is to be divided by pencil lines into parts, which are to be treated separately. The only adjustment required is, when the instrument is lifted out of its case, to make the two indices read zero at the same time, which is readily done by lifting up the brass one and turning it a little forward or backward. If the tracer be carried round the figure in the direction that the hands of a watch move, the first reading is less than the last. If it be carried in the opposite direction the first reading is greater.
The mode of action is very simple. The rollers (A, A) are attached to the same axis, on which there is also a cone, which revolves with them; they are exactly of equal size, so that as they move up and down the paper; the axis of the cone is always parallel to the same line. The four friction rollers, of which three (B, B, B) are shown in the drawing, carry a frame and the tracing point to the right or left, parallel to that line which it is possible to trace on the surface of the cone parallel to the paper. Attached to this frame is the index wheel (I), the edge of which touches the cone in that line, and is made to revolve by it; consequently, the revolving motion of the index-wheel is in proportion to the motion of the tracer up or down the paper, multiplied by the right and left distance of the wheel from the apex of the cone; and therefore, when the tracer is made to describe any complete perimeter, the whole rotatory motion of the index-wheel represents the algebraic sum of the products of ordinates to every point in that perimeter, multiplied by the increment of their co-ordinates; or it is a measure of the included space.
It is obvious that while this arrangement of motions should in theory indicate the product of the ordinating lines by the increment of their co-ordinates, the result of mechanical imperfections in the motion is also a product, so that very great care and nicety must be used in the construction of the instrument. The specimen exhibited is the first model made by the inventor's own hands; it performs its work nevertheless very correctly. It is true that the area of a three or four-sided figure will be found a little more accurately by a scale and calculation than by the instrument. This may be tested by measuring the same figure a few times each way, and observing the difference of the results; but on the other hand, an irregular or curved figure will be measured more accurately by the instrument than by the scale, and with infinitely less labour, which may be tested in the same way. This is not because the instrument measures the irregular figure more accurately than it does the simple ones, but because the scale measures them less so. The accuracy meant is the absence of minute errors. In respect to great errors, caused by mistaken figures in calculation, the instrument is exceedingly preferable, even for simple boundaries, as it is not liable to faulty arithmetic.