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latitude is determined, as explained in the Astronomical Problems. The latitudes and longitudes have lately been adapted to the Ordnance Maps publishing on the enormous scale of 6 inches to 1 mile, to seconds of latitude and longitude, with a very trifling maximum error, a triumph of practical science that a few years since would have been deemed impossible.



THE more minutely the triangulation has been carried on, the easier and the more correct will be the interior filling-up, whether entirely by measurement with the chain and theodolite, or only partially so, the remainder being completed by sketching; the former of these methods will be first explained.

Small triangles are formed by actual measurement with the chain between the nearest trigonometrical points (upon the accuracy of which they depend), the directions of the lines forming the sides of which are to be selected with reference to the ultimate objects of the delineation of the boundaries of woods, estates, parishes, &c.* Where it is practicable, these lines should connect conspicuous permanent objects, such as churches, mills, &c.; and in all cases the old vicious system of measuring field after field, and patching these separate little pieces together, should be most carefully avoided. The method of keeping the field-book in measuring the interior with the chain, and plotting from its contents, is of course similar to the usual mode of surveying estates, parishes, &c.; and, as stated in the preface, this preliminary knowledge is

* Great assistance is derived from a rough diagram representing the proposed method of proceeding, with references to the marks left on the measured sides of the triangles to be subsequently connected by check lines, either joining two sides, or extending from one side to the opposite angle; this may appear at first to be a waste of time, but it will soon be found to be the contrary, as the lines will be all run in directions advantageous to the fillingup of the interior. These marks should be made on the ground, so as to be easily recognised, and should be copied in the margin of the field-book.

+ Very excellent instructions for the guidance of surveyors employed in forming plans of estates and parishes are to be found in the report from Captain Dawson, Royal Engineers, to the Tithe Commissioners of England and Wales, November, 1836, from which report Mr. Bruff, in his "Engineering Field-book," has extracted a number of valuable directions.

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supposed to have been already acquired. But on an extensive survey one general system must of necessity be vigorously enforced, to insure uniformity in all the detached portions of detail.

Previous to commencing any measurement, the ground should be carefully walked over for the purpose of laying out the work, and marks set up at the average height of a theodolite, on the highest parts of the different hills, on the necks of the ridges jutting out from them, and at the level of lakes and rivers in various parts of their course, as well as on the site of permanent objects, such as churches, &c. These levelling marks should be all numbered and entered in a separate book, termed a field levelling book, intended to contain reciprocal angles of elevation and depression, afterwards taken between them, for the calculation of the horizontal values of the measured lines and of their comparative altitudes; which quantities are subsequently reduced to their actual heights above the level of the sea*. During the measurement of the principal lines, suitable points are selected at which to connect them by check lines, or on which to base minor triangles, and of course with a view to the determination of the natural and artificial boundaries, that, measured lines running near them, the whole of the interior content may be computed from the "Register," made out directly from the field-book, the calculation from the plot being afterwards made simply as a check upon the other. All trigonometrical points and levelling marks should, if practicable, be measured up to with the chain during the progress of the survey, and their distinctive letters or marks entered in the field-books. Allowance may be made for short distances, by holding up one end or portions of the chain till it appears horizontal, and dropping a pointed plummet on the ground, in measuring up or down a slope, or by deducting the number of links corresponding to the angle of elevation or depression, as marked on the reverse of the vertical arc of the theo

* nong the advantages of connecting

well-arranged series of levels with the plan of any portion of country, is that of rendering it at once available to the engineer in selecting the best trial lines for railroads or canals. The present system of tracing horizontal contour lines at short vertical intervals, instead of sketching the features of the ground, which used to be practised on the Ordnance Survey, affords not only the means of deciding upon the best trial lines, but actually furnishes data for constructing accurate sections across the country in any direction.

dolite; 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 :


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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 :


Elevation or


B 12 54 C 4° 15′ 0′′Ele. 9,9988041

Apparent Elevation
or Depression.

C 984 D 3° 20' 30"De. 9,9992609



3,0982975 1251,5 3,098297561,33 416,33|




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2,9929951 982,25 2,992995137,88 378,45



* 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 66 9.8195439 (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


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