TABLE OF INCLINE MEASURE

The following table shows the comparative lengths of the three sides of a right-angled triangle, and the inclination per yard in inches for every degree of the quadrant:—

Column I. expresses the inclination in terms of the generally adopted angular measure, viz. degrees. The inclination is given in degrees from the horizontal.

Column II. gives the rise in inches for every yard of horizontal measure; the numbers corresponding with the number of degrees in the preceding column.

EXAMPLE. A road is 50 yards long (this length represents the horizontal measurement, and not the measurement on the slope), and has an inclination of 6 degrees, how much will one end of the road be higher than the other?

By referring to Column II. of the table, it is found that the figures which correspond with the 6 degrees in the preceding column is 3.78. This is the amount in inches which the road will rise in 1 yard, therefore in 50 yards it will rise fifty times this amount, and 3.78 x 50 189 inches 15 feet 9 inches.

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Column III. gives the horizontal length per unit rise for each degree. Expressing the inclination in terms of the horizontal per unit rise is a very common method in mining. A more correct heading for this column would be: "Horizontal measure, vertical being 1."

EXAMPLE 1.-A road has an inclination of 14 degrees: express this in terms of the vertical and horizontal.

In a line with 14 in the first column we find 401 in the third. Therefore the inclination of the road is 1 in 4.01.

EXAMPLE 2.-A road having an inclination of 12 degrees is 50 yards long (horizontal measurement), what is the perpendicular height?

The table gives 1 in 47 for 12 degrees. pendicular height is 50÷47 10-638 yards.

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Then the per

Column IV. gives relative lengths of the base and hypothenuse of a right-angle triangle for each degree, the length of the base being given per unit of the hypothenuse. On an inclined road the length of the hypothenuse would be represented by the actual measurement of the road.

EXAMPLE.-A brow dipping 16 degrees measures along the dip 106 yards, what is the horizontal length of the road?

The table gives the horizontal length per unit of the hypothenuse for 16 degrees as 96126. Therefore the horizontal measurement of the road is 106 × ·96126 = 101·89356 yards.

Column V. gives the relative lengths of the perpendicular and the hypothenuse of a right-angle triangle for each degree, the length of the perpendicular being given per unit of the hypothenuse.

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EXAMPLE.-A brow dipping 16 degrees measures along the dip 106 yards, how much is one end of the brow below the other (ie. the perpendicular height)?

The table gives the vertical rise per unit of the hypothenuse for 16 degrees as 27564, therefore the perpendicular height of the road is 106 × 27564 29.21784 yards.

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Column VI. gives the amount in links per chain which is to be deducted to convert inclined measurements to horizontal lengths. That is, the amount to be deducted from the hypothenuse to make it equal to the base. This column of figures fulfils the same purpose as Column IV., but not to the same degree of accuracy. As there are 100 links in a chain, the figures given in the column represent what may be termed the percentage of deduction, so that the figures may be employed to find the deduction for yards or feet, as well as link measure

ments.

EXAMPLE 1.-A road rising 16 degrees measures incline 106 yards, what is the horizontal length ?

on the The table gives 3.87 as the amount to be deducted per 100 for 16 degrees, therefore the deduction for 106 will be

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1064.1022 101.8978 yards the horizontal length of the road. The same example, calculated by the figures in Column IV., gave 101.89356 yards.

EXAMPLE 2.-An inclined road dipping 20 degrees measures 5 chains, how many links must be deducted to give the horizontal measurement?

The table gives 603 as the deduction per chain for 20 degrees, therefore the deduction for 5 chains = 6·03 × 5 = 30.15 links.