latitude and increases the departure, so as to favour the balancing, there is evidence that the course contains some

error: If bying the distance on such a course, both

the latitude and departure are so diminished as to favour the balancing, it is good evidence of an excess of measure.

Cases may

In correcting surveys, there is less danger from diminishing distances than there is from increasing them. occur in which distances may be increased, but the surveyor should be very cautious about it.

As it is of importance that surveys should be correctly balanced before they are calculated, and as the work is commonly attended with some difficulty, a few examples are given for the assistance of the student. In each survey, the courses and distances are entered in the tables as they were taken in the field.

The difference between the sum of the northings and that of the southings is one rod and 8 links, and the difference between the sum of the eastings and that of the westings is 2 links. The taking of the course on the third line was attended with difficulty, and probably it contains some error, therefore, more than a proportion of the correction is made on the southing of it. There is also evidence that the first course contains some error, as the diminishing of the northing and the increasing of the westing favours the balancing. Twenty links are added to the different southings, and thirteen links are substracted from the different northings

Where corrections are made, the upper numbers are of no further use. If the corrections are made with red ink, they will all be seen at one view, and the work will appear handThis was Mr. Flint's practice.

somer.

In the correction of the two last surveys, the differences between the two columns of latitude, and between those of departure, in each example, are equally divided between their respective columns. A northing is added to the second course in the second example; also, a northing to the ninth, and a westing to the tenth, in the third example. When courses are entered in the field book, north, south, east, or west, they are as liable to contain errors, and they are as

In the last example, the difference between the northings and the southings is equally divided.

As it was judged that sufficient distances were made on the two westerly courses, the correction was made on the east

No. IV.

ON RECTANGULAR SURVEYING.

Rectangular surveying* is a name given to the method here treated of by the late Governor Treadwell.

In the operation of it the whole survey is reduced to squares and parallelograms, and each of these figures is divided into two right angled triangles of equal shape, or into two trapezoids of equal size and shape, by a boundary line of the field running obliquely through it, except when the boundary line is directly north and south, then the figure is divided into two squares or parallelograms.

The calculations are made from a meridian drawn either at the eastern or at the western extremity of the map; and the areas are produced by multiplying the latitudes by the longitudes made from this meridian.

All the spaces lying between the field and the meridian, and between the parallels of latitude of the northern and southern extremities of it, also large spaces lying without the figure on the opposite side of it, and between those parallels, are included in the calculation; but that which lies without, is eventually excluded.

Parallels of latitude are drawn from each angle to the meridian, which are called meridian distances.

In forming the column of meridian distances, when the meridian is drawn at the eastern extremity, the westings are added, and the eastings substracted; but when the meridian is laid on the west side, the eastings are added and the westings substracted.

The meridian distances proceeding from each end of a line are added together, to form the column of double mean distances, which the compiler of the foregoing work called second departure.

Meridian distances and double mean distances,† are more proper terms or names for these columns, than first departure and second departure.

The meaning of the term meridian distance, is the distance made from any meridian.

The following survey is calculated from the meridian of

* Rectangular calculation is as proper.

+ The compiler of the foregoing work would have made use of these names, but he was afraid of infringing on a certain copy-right