tion; the correction, thus determined, must be placed, collaterally, with the distance to which it refers, without distinguishing as to North, South, East or West.

Having found the several corrections for each of the latitudes and departures, add them together severally, and see whether their total agrees with the whole error, and if so, proceed to allot the corrections. If the error be an excess of Northings, subtract each correction from its collateral Northing or add it to the collateral Southing; if an excess of Easting, add to the Westing and subtract from the Easting; the corrected sums of the corrected latitudes and departures will then be found exactly to agree. We here subjoin an example:

In the above, the error is + .14 in the South and + .28 in the West, we will now divide this error proportionately among the several distances, by the rule previously given, viz., As the sum of the distances: the whole error:: each distance: its particular correction, or

62.27.14 :: 17.68: .040:: 6.37: .014:: 3.86: .008:: 14.63: .033 :: 19.73: .045, for the Northings and Southings.

And 62.27 .28 :: 17.68: .080 :: 6.37: .028 :: 3.86 : .016: 14.63 .066 :: 19.73: .090 for the Eastings and

Westings.

=

It will be observed that the sum of the several corrections as above apportioned amounts to .14 in the Northings and Southings or .095 + .045.14 and to .28 in the Eastings and Westings or .124 + .156 .28. This is the method of subdividing an error in theory, but in practice an approximation is sufficient, the proportion of error to each line being made without reference to calculation, the error when it is below the maximum allowed, of 1 Link in 10 Chains being equally divided between the two columns of Northings and Southings and of Eastings and Westings, and generally thrown into the longest lines. The example given however must not be understood as a specimen of the real extent of correction on such small distances, we have taken ample figures merely to serve the purpose of illustration.

We have omitted mentioning here the several methods given in other works on "Surveying by the Traverse system" of finding unknown distances, by adding up the Northings and Southings, and the Eastings and Westings of a Polygon, and applying the difference of the two severally, as the latitude and departure of the unknown line and thence finding the Chain distance. Polygonometry as given in Hutton's mathematics Vol. 3, and other books, treat of these methods, and to which we refer the reader for further information.

CHAPTER VIII.

ON THE METHOD OF PLOTTING BY TRAVERSE.

THESE differences of latitude and departure, or distances on the meridian and perpendicular of each station from the preceding one are not only applicable to the proof of the fieldwork, but are subservient also to the plotting and computation of the area of the Survey, which will now be explained.

All the distances on the meridian of each station from the preceding one, North or South, and all the departures of each station from the preceding one, East or West, can be referred to the meridian of the first station or starting point of the Survey, viz., station A. For instance, on the meridian of A, for the line AB the distance North is Ab and the departure East is ¿B; on the meridian of B, for the line BC, the distance South is Bk, and the departure East is kC; deduct the distance that B is North of A, from the distance that C is South of B, and we obtain the distance that C is South of A, or Bk Ab Ac; in like manner add the distance that C is East of B, to the distance that B is East of A, and we obtain the distance that C is East of the meridian of A, or kC+bB

=

=

CC.

Again, on the meridian of C for the line CD, the distance North is Cl, and the departure East is ID, deduct the distance that C is South of A, from the distance that D is North of C, and we obtain the distance that D is North of A, or CI Ac = Ad; in like manner add the distance that D is East of C, to the distance that C is East of A, and we obtain the distance that D is East of the meridian of A, or ID + cC=dD.

=

On the meridian of D, for the line DE, the distance North is Dm and the departure West is mE, add the distance that E is North of D to the distance that D is North of A, and we obtain the distance that E is North of A, or Dm + Ad Ae; also, deduct the distance that E is West of D from the distance that D is East of A, and we obtain the distance that E is East of A or dD eE, and so on all round the figure until arrived back at A, when the distance that A is North of J, the preceding station, deducted from the distance that J is South of A, or Aj — Js, and the distance that A is East of J, deducted from the distance that J is West of A, or jJ - SA will leave no remainder, proving that the calculation has been correctly made.

mE,

=

The line FG it will be perceived crosses the meridian of A, in this case, it is only necessary to deduct the distance that F is East of A from the distance that G is West of F, to obtain the distance that G is West of A or yG — fx = gG.

To plot therefore all these station points, draw a meridian line, and another perpendicular to it, representing the East and West direction. Fix on any point on this meridian line for the station A, lay off with a pair of common compasses and a scale of equal parts the distance Ab North of A, draw a line parallel to the East and West line through the point b, lay off the distance bB, East, and join the points A and B, we thus obtain the bearing and distance of the line AB.

Next lay off the distance Ac South of A, draw a line parallel to the East and West line, through the point c, lay off the distance cC East, and join the points B and C, thus obtaining the bearing and distance of the line BC.

Then lay off the distance Ad North of A, and with a parallel to the East and West line through the point d, lay off the distance dD East, join C and D, and we obtain the bearing and distance of the line CD, and so on all round the figure, observing that when the distances on the perpendicular are West of the meridian of A or starting point, they are laid

off West on the plot. The reduction of the distances on the meridian and perpendicular of each station to the first station or starting point is therefore easily effected by a simple addition or subtraction, and may be comprised in the following rule.

Rule. When the distances run North of the first station, add them one to another, until they change to South, then deduct them one by one until the Southing exceeds the Northing, when deduct the latter from the former, changing the denomination to South; all distances then going South, are added and those going North deducted, and so on, until arrived back at the original starting point.

Likewise in the distances on the perpendicular, when the distances run East of the meridian of the first station, add them one by one until they change to West, then deduct them until the Westing exceeds the Easting, when deduct the latter from the former changing the denomination to West; all distances then going West are added, and those going East deducted, and so on, until arrived back at the original starting point.

This method of plotting is by far the most perfect, and the least liable to error of any that has been contrived; it may appear to require more labour, than the common method by angular protraction or protraction by Bearings, on account of the computations required, but these are made with so much ease and expedition by the help of Traverse Tables,* that this objection would vanish, even if they were of no other use than for plotting, but as we have already said, they are subservient also to finding the Area, and which cannot be ascertained with

* A set of Traverse Tables has been published by Major J. T. Boileau, Bengal Engineers, to every minute and degree of the quadrant, and these Tables are now in general use in the Revenue Surveys; we therefore refer the Surveyor to this work, in which he will find the method of using them fully explained and much valuable information regarding the application of the system to general purposes.