When a shaft has been sunk in error,* or not exactly at right angles with the lode.

Rule I.-Work for the base and perpendicular as before, by Case I., then find the deviation by the following.

Rule II.-Take out the base from the second table, standing

* Underlaying shafts are always intended to be sunk at right angles with the lode; that is, if the lode runs east and west, the horizontal bearing of the shaft will be either north or south, as the lode may happen to underlie. But it is sometimes the case, that through inattention of workmen or other causes, the shaft has declined from its true course and inclined toward the right or left, and as this is neither a trivial nor uncommon occurrence, and admits not of development by the ordinary mode of dialling, we have here introduced a rule which will hold good in all cases of the kind.

opposite the angle of error, and multiply it by the length of the shaft.

PROBLEM.

An oblique shaft A B was found to measure 89 feet 6 inches, on an angle of 53° 15', and it was also observed that the shaft had declined 3° 45′ west from the intended right angle of the east and west lode: required the base C D and perpendicular C A, and how far the shaft has departed from its true course A D.

Thus it is clear that if the above shaft was sunk on an east and west lode and the angle of error inclined westerly, that the foot of the shaft B would be 5 feet, 9 inches, in that direction beyond its designed course A D.

EXAMPLE 7.

To find the perpendicular depth of the junction of lodes.

When two lodes underlay in the same direction.

Rule.-Subtract the tabular number of the base of the lesser angle from the greater, then by direct proportion, say,

As this difference

Is to one fathom perpendicular,

So is the distance of the lodes at surface

To the junction of the lodes.

PROBLEM.

Two lodes were discovered at the surface, 12 fathoms apart from C to D, both underlaying north. The southernmost lode

D B made an angle of 38° 15': the other C B 23°. Required the perpendicular depth A B where these lodes will unite, supposing they both regularly continue their respective angles of declination.

DIAGONAL LODES.

If it is required to find the respective lengths of the lodes C B and D B, and the horizontal line D A, work by Case II., where the perpendicular is given.

Then CA + CD-DA, or C A added to CD gives the line D A, 25 fathoms, 5 feet, 9 inches, &c.

EXAMPLE 8.

To find the perpendicular depth of the junction of lodes.

CASE II.

When two lodes, by their underlay, incline indirectly towards each other.

Rule. Add the tabular bases together, then find the depth by direct proportion as in the last example.