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with the first meridian, or the line upon which the theodolite was first set. This method, now in general use among surveyors, saves the trouble of shifting the protractor at every angle, and also insures greater accuracy in plotting, as a great number of bearings being laid down from one meridian*, a trifling error in the direction of one line does not affect the next. As the work progresses, of course other lines are selected as meridians; and it should be an invariable rule, on beginning and ending a day's work, always to take the angles between the back or forward stations and any two or three fixed points that may be visible.
This rigidly mechanical method of surveying the interior evidently leaves nothing to be filled up in the field, except the features of the ground, either by sketching or by tracing horizontal contour lines at fixed vertical intervals. The comparative heights, however, obtained by levelling with the theodolite during the survey, present so many certain points of reference as to the relative command of the ground, and are of course of the greatest assistance in the subsequent delineation of the features upon the outline plan. Where the boundaries of parishes, townlands, &c., are to be ascertained and shown on the plan, there must be persons procured whose local knowledge can be depended upon, and whose authority to point them out to the surveyors is acknowledged.
The most accurate method of calculating the contents contained between the various boundaries of parishes, estates, &c.†, has been
* The readiest way of plotting lines whose directions have all reference to one meridian is by the use of a circular pasteboard protractor, with the centre cut out. A parallel ruler or angle (if the angle and ruler be preferred) is stretched across its diameter to the opposite corresponding angle, the zero having been first laid on the meridian line and moved forward to the point from whence the bearing is to be drawn. For surveys on a very large scale, however, the semicircular brass protractor, with a vernier, is better adapted and is more
The contents even of the fields and other inclosures can be calculated from the fieldbook; but if the parishes and larger figures are so determined, the minute subdivisions of the interior may be taken from the plan. On the Ordnance Survey of Ireland, the number of acres in the different parishes, baronies, &c., were calculated, as also those covered by water, and given in a table accompanying the "Index Map" of each county; but the contents of the fields were not computed, though the hedges and other inclosures are shown on the plot. The contents of inclosures can be very quickly ascertained from the plan, by drawing lines in pencil about one or two chains distant, across the paper, both longitudinally and trans
already stated to be from the data furnished by the field-book, in which case every measured figure must be either a triangle or a trapezoid. The diagram and the content plot must be first drawn in outline, and used as references during the calculation to prevent errors and to assist in filling up the content register; and from this the acreage of the different portions is taken. The following example of the field-book, with the diagram content plot, and content register, all deduced from it, will better explain the details of this system.
In this specimen of a field-book, all offsets, except those having relation to the boundary lines (supposed to be of townlands, or any division of property, the contents of which are to be calculated from the field-book), are purposely omitted, to prevent confusion, the example being given solely to illustrate the method of calculating these larger divisions. The rough diagrams are drawn in the field-book not to any scale, but merely bearing some sort of resemblance to the lines measured on the ground, for the purpose of showing, at any period of the work, their directions and how they are to be connected; and also of eventually assisting in laying down the diagram and content plot. On these rough diagrams are written the distinctive letters by which each line is marked in the field-book, and also its length, and the distances between points marked upon it, from which other measurements branch off to connect the interior. The boundary lines are further distinguished from those run merely for the purpose of taking offsets to the minute subdivision of property, &c. (and which, as before observed, are omitted in the present instance, both in the field-book and the
versely, or by laying a piece of transparent paper so ruled over it; the number of squares in each field are then counted, and the broken portions either estimated by the eye or reduced to triangles for calculation.
The "computing scale,” upon a principal similar to the pediometer described at the end of this work, also affords the means of ascertaining mechanically the acreage of inclosures divided into triangles or trapeziums. It has been for many years in use at the Tithe Commission Office, for the purpose of calculating and checking the contents of plans surveyed under the Act of Parliament, and is productive of a great saving of time, as well as insuring considerable accuracy. The principle of the construction of the pediometer depends upon the following equation, combined of the sum and difference of a diagonal of the trapezium and the two perpendiculars. Let a represent the diagonal, and 6 the sum of the two pera b (≥ a + § 6) 2 — (} a — § 6)2 2
pendiculars; then the area
plot), by dotted lines; so that, in plotting the diagram to a scale, their difference is at once perceptible.
The form of keeping the field-book is similar to that practised on the Ordnance Survey, reference to the letters distinguishing former measurements being always made; and the letter of the beginning and ending of every line by which it is designated in the diagram, being also written at the top and bottom of its representative in the field-book.
The construction lines all forming triangles, and offsets having reference to the boundaries, are retained in the content plot, for the purpose of assisting, and preventing mistakes in the calculation.
In the content plot and diagrams the trigonometrical points A, B, C, D, are on an average rather more than half a mile apart, so that in reality the same number of divisions of townlands would not occur in the space comprised within them; and, instead of letters, they would be distinguished by the name of the townland or parish.
The large letter B 2 on the diagram of the triangle A B C refers to the distinctive mark of the field-book; and the small figures 3, 4, 5, &c., written along the construction lines, to the different pages of the same book, to which reference can thus be made at any moment.
The contents only of the large divisions are calculated from the field-book. Those of the minute inclosures are (if required) obtained from the plot, from which the contents of townlands and parishes are also computed, for the purpose of checking the previous calculations.
The method of calculating these contents by means of the measured triangles and offsets will be easily comprehended by comparing together the field-book, content plot, and content register, for the triangle CAD. That for A B C, being on exactly a similar principle, has been omitted, as it could add nothing to the explanation of the system.