made either to exceed 45°, or that they should all stand below, or at least not exceed that half quadrant. Our reason for being urgent on this matter is, that there may be a uniformity in placing the sides in the traverse table after the draft has been computed. And let it be particularly noticed that, if the bearings are not suffered to exceed 45°, that the last expression of the bearing will signify the longest of the two sides. That is, suppose a draft taken underground was 2874°, measuring 45 feet 8 inches; now looking at the "converting table" we see that if this draft was taken with a "left-hand dial," that the bearing is 17° north of west (or N. of W.) and the two sides will be found by computation to be 13 feet 7 inches, and 43 feet 7 inches. Query, into what columns respectively must these numbers be placed? As the bearing was north of west, and our system states that "the last expression of the bearing will signify the longest of the two sides," consequently the longest side (43 feet 7 inches) must be placed in the “west” column, and 13 feet 7 inches in the north column.

If this order is followed up, it will render the working of traverses (which is the most important operation in mine surveying) a plain, pleasing, and satisfactory exercise. In this edition we would needs bring forward every thing likely to promote the advancement of the young mining officer in this paramount branch of his profession, and therefore give him to understand that, in traversing, there must be a regular course from beginning to end.

We shall make ourselves understood in this matter, by taking a case where a person makes a survey for the purpose of ascertaining the length and bearing of a level driven on an east and west lode; and, for some convenient purpose, he begins his dialling at some point about the middle of the level, and dials from thence to the eastern end; he then returns to the station or start at the middle of the level, and dials on to the western end, and thus completes the survey.

Now if he was to proceed to work the traverse from his dialling book in this state, his results would appear as if his level was almost without length or bearing, as his eastings would be balanced by his westings, &c.

In order to go systematically to work in this case, his first operation must be to reverse the order of one or the other of the liallings; that is, if he pleases to let the first remain, which is the

eastern dialling, and would accommodate the western part to suit the other, he must alter or reverse all the drafts, by converting (say) 16° south of west into 16° north of east, and so of all the

rest.

In winding up this course of instruction, we will take a short survey, and go through with it at length, and the student may accompany us if he pleases; for we are of the opinion that practical teaching is the best.

EXAMPLE.

It is required to sink a vertical shaft on the end of a level, and the diallings from the bottom of an old downright shaft are as follows:

This is the underground work, and our first operation is to find out the underlay of the winze, in order that it may stand as a common draft in the survey.

OPERATION.

The underlay, or angle made by the dip of the winze and a vertical line, being 25 degrees, we find it standing in the first table against 2 feet 7 inches, showing that every fathom of the winze gives a base of 2 feet 7 inches, and the length of the winze being 11 fathom 2 feet, we multiply

ft. in.
}) 2 7
11-2

4 4 5
10

4 5 3

fath. ft. in.

Here we find the base of the winze to be 4 5 8

The next thing is to refer to the converting table to reduce the drafts into bearings; taking special notice that the work was done with a right-hand dial.

We therefore find that No. 1. 35610 is 34°E. of N.

N. of E.

8 S. of W.

Our work is now prepared for entry in the traverse table as data for trigonometrical computation.

The above is the table with the bearings and lengths of the drafts entered in order for receiving the trigonometrical results in their proper and respective columns, and that every thing may be clear to the learner we shall let this table remain as it is, and make a similar one, in which the computations are entered, and proceed to take out the tabular numbers from the first mathematical table, and multiply them by their respective lengths.

Now the sides of the triangle formed by the first draft are ready to be transferred to the east and north columns of the trayerse table.

When the bearing does not diverge much from the cardinal point, there is but little difference between the length of the hypothenuse and the longest of the legs, as in the right-hand sides of the above two drafts.

The length of the draft being 15 fathom 4 feet, we have multiplied by 16, and deducted as the shortest method.

In the above, it will be seen that we have thrown the tabular length into inches and parts, and the practitioner will find this, in general, the easiest way of calculating.

Now the computations are ready for entry in the following

Now we might proceed to lay down the position or place of our new vertical shaft at the surface without any further operation. For by measuring off from the centre of the old shaft at surface 149 feet 2 inches, due east, and from the end of that line measuring 83 feet due north, would bring us exactly over the end of the fifth or last draft, where the shaft is to come down, but we would work out the direct length and bearing also, as before described, and apply it.

PROBLEM.

A new vertical shaft was commenced which is intended to intersect the main lode at the depth of 100 fathoms below the adit level, which is about 40 fathoms from surface in the vicinity of the new shaft. From a point in this level, a drift or cross-cut has been begun, and designed to be driven in a direct line to the centre of the new shaft, and from thence to rise against it, if necessary; and the aim and object of the survey is to ascertain the exact length and bearing of the said cross-cut, as every proper means have been adopted to certify that it has been commenced at the nearest point of the shaft.

The following is the whole course of dialling in its most simplified form, with the irregular surface lines reduced to horizontal measure, the angle of every draft converted into bearing, and the whole given in complete order for working the traverse without any preliminary preparation. The draft standing on the top of 934 feet is from the centre of the new shaft at surface to a line hung in the old engine shaft, which is also vertical to the adit, and the next draft is taken from that line in the adit and continued to the end of the 34th draft, through the same level, where the cross-cut commences.

It is also required to furnish the bearing of the lode from the 3d to the 34th draft inclusive.

REMARKS.

As this course of dialling has been rendered so plain, there appears to be no occasion to introduce a double entry of it, as the field and underground work is sufficiently manifest in the first three columns of the following table, in combination with the trigonometrical operation. It may be satisfactory to the student to be informed that this work has been accomplished and proved