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but in all considerable distances this deduction would be more correctly obtained by calculation from the data in the field levelling book, kept in the following form :




Apparent Elevation
or Depression.


The third column, headed "horizontal reading," is the reading of the vertical arc when the telescope is levelled, and is in fact the index error, which is however best determined by reciprocal angles of elevation and depression, as before explained; and under the head of remarks are kept horizontal angles to surrounding objects and other collateral details. From the angles thus observed, and the known distances between the places of observation, is made out the following table :—


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* The reduction marked on the reverse of the instrument can be made in the field by drawing the chain forward the stated number of links. It is, however, generally the practice at present upon the Ordnance Survey, to measure horizontal distances at once upon the ground, using in steep slopes only short portions of the chain, by which means all reductions and subsequent calculations are avoided. The forms given above and many of the directions are taken from the original instructions for the Interior Survey of Ireland.

This form almost explains itself: the first column refers to the plot or plan in which the points or lines are contained; the second shows the measured length of the line written between the letters marking its extremities; the third gives the mean elevation or depression of the second object, deduced from the reciprocal angles in the levelling field-book after applying the correction for the index error in the third column of the same book, and also those for curvature and refraction when very long distances render their effect sensible; the fourth column contains the log. cosine of the angle in the preceding one, and the logarithm of the distance, the natural number answering to the sum of which is entered in the fifth column. The sixth contains the logarithm of 669·8195439 (the proportion of one link to one foot), the log. sine of the angle, and the log. of the distance; and the number answering to the sum of these three logarithms gives the relative altitude in feet, which is entered in the seventh column. The eighth column shows absolute altitudes above low-water mark, those that have been previously determined by levelling being entered in red; the others are obtained by the addition or subtraction of the altitudes in the preceding column.

The survey of the roads (though, for the sake of saving unnecessary labour, it is as much connected with them as possible) is sometimes quite independent of the measured triangles connecting churches or other permanent objects and the minor trigonometrical points, which lines mutually constitute a check upon each other. The term traversing is generally applied to this, and indeed to all irregular surveying by the chain and theodolite. On starting from any point in road surveying, the instrument being adjusted and set to zero, the telescope is directed upon one of the most conspicuous stations; and after taking two or three angles to other fixed points, the forward angle is read off in the direction it is intended to pursue, and the upper plate firmly clamped. On arriving at the end of this line, the theodolite is set on the flag-staff or picket left at the back station, the plates remaining still clamped to the last angle; and the reading on the graduated limb when the telescope is pointed to the next forward station, is not the number of degrees contained between these two lines, but the angle that this second line forms


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 + b)2 − ( a − § b)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.

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