Getting Gold: A Gold-Mining Handbook for Practical Men

Nystrom gives this rule:—HP = ^{V × F}⁄₅₅₀. V = velocity of belt in feet per second. F = force in pounds transmitted by belt.

The first rule gives good practical results where there is no great inequality in the diameter of the pulleys.

Double Belts transmit 1½ times as much as single belts.

Splicing Belts.

Rules for Double Leather Belting.

A = covered area of driven pulley in square inches.

V = speed of belt in feet per minute.

H = indicated horse-power.

W = width in inches.

H = ^AV⁄_66,000 A = ^{66,000 H}⁄_V. W = A/L, where L = length of belt on driven pulley in inches.

Another authority simply says H = {70 to 80} × ^WV⁄_33,000.

And a third says W = ^{36,000 H}⁄_6VL, where L is here in feet.

Evan Leigh’s rule is W = ^{66,000 x IHP}⁄_{L x V}.

L = length of arc of contact upon smaller pulley in inches.

V = velocity of rim in feet per minute.

A belt transmits its motion solely through frictional contact with the surfaces of the pulley. The lower side of the belt should be made the driving side when possible, as the arc of contact is thereby increased by the sagging of the following side. Increase of power will be obtained by increasing the size of pulleys, the same ratio being retained. Wide belts are less effective per unit of sectional area than narrow belts. Long belts are more effective than short ones. The proportion between the diameters of two pulleys working together should not exceed six to one. Convexity of pulleys to receive belt = ½ inch per foot wide. The width of pulley should equal 1·2 times width of belt.

Speed of Belts.

Belts have been employed running over 5000 feet per minute. Nothing, however, is gained by running belts much over 4000 feet per minute. About 3500 feet per minute for main belts agrees with good practice; lathe belts from 1500 to 2000 feet per minute. The life of a belt may be prolonged and its driving powers increased by keeping it in good working order. To ensure this it should be dressed on the back with castor oil every few weeks, more or less according the dryness of the atmosphere in which it works.

WEIGHT AND BULK OF MATERIALS.

The weight of a cubic foot of any material is its specific gravity multiplied by 62·425, or the weight of a cubic foot of water in pounds. To find the specific gravity of a stone, divide its weight in air by loss of weight in water of temperature of 60° F. = specific gravity.

Thus:

Then:

^293·7⁄_113·6 = 2·59 = Specific gravity of quartz.

One ton of quartz when solid occupies 13 cubic feet, but when broken, about 20. Rocks when solid, as compared to the same when broken, usually increase in volume in the ratio of 1 to 1·5 or 1 to 1·18, the increase depending on size and form of fragments.

A dwt. of gold in a cwt. of ore = 1 oz. of gold per ton of ore.

For approximate calculation a grain of gold = two pence, and a dwt., four shillings.

In the following table of the chemical elements the standard of sp. gr. is hydrogen for the gaseous elements (hydrogen, oxygen, &c.) and water for the others.

The Chemical Elements, their Symbols, Equivalents, and Specific Gravities.

The figures indicating the proportions by weight in which the elements unite with one another are called the combining or atomic weights, because they represent the relative weights of the atoms of the different elements. Since hydrogen is the lightest element, it is taken as the standard, and its combining or atomic weight = 1.

To find the proportional parts by weight of the elements of any substance whose chemical formula is known:

Rule.—Multiply together the equivalent and the exponent of each element of the compound; the product will be the proportion by weight of that element in the substance.

Example:—Find the proportional weights of the elements of Alcohol C₂H₆O.

Of every 46 lb. of Alcohol, 6 lb. will be H; 16, O; 24, C.

To find the proportions by volume, divide by the specific gravity.

Common Names of Chemical Substances.

Thermometer.

The following are the formulæ for the conversion of degrees of one scale to those of another:—

Freezing, Fusing, and Boiling Points.

Heat Values of Fuels.

Pounds of water evaporated by 1 lb. of fuel as follows:—

SIGNS AND SYMBOLS USED IN EXPRESSING FORMULAS.

= Sign of equality, denoting that quantities so connected are equal to one another; thus, 3 feet = 1 yard.

+ Sign of addition, signifying plus or more; thus, 4 + 3 = 7.

- Sign of subtraction, signifying minus or less; thus, 4-3 = 1.

× Sign of multiplication, signifying multiplied by or into; thus, 4 × 3 = 12.

÷ Sign of division, signifying divided by; thus, 4 ÷ 2 = 2.

{} () [] Brackets, denoting that the quantities between them are to be treated as one quantity; thus, 5 {3(4 + 2)-6(3-2) = 5 (18-6) = 60.

Letters are used to shorten or simplify a formula. Supposing we wish to express length × breadth × depth, we may put the initial letters only, thus, l × b × d, or, as is usual when algebraical symbols are employed, leave out the sign × between the factors, and write the formula lbd.

When division is to be expressed in simple form, the divisor is written under the dividend; thus (x + y) ÷ z = (x + y) / z

° ’ ” are signs used to express certain angles in degrees, minutes, and seconds; thus 25 degrees 4 minutes 21 seconds would be expressed 25° 4’ 21”.

√ This sign is called the radical sign, and placed before a quantity indicates that some root of it is to be taken, and a small figure placed over the sign, called the exponent of the root, shows what root is to be extracted.

Thus ²√ a or √ a means the square root of a
∛ a                      ”    cube      ”
∜ a                      ”    fourth    ”

ρ This sign is used to denote the force of gravity at any given latitude.

π The Greek letter pi is invariably used to denote 3·14159, that is, the ratio borne by the diameter of a circle to its circumference.

When the figure 2 is affixed to any number, as diameter² or 12², the number is to be squared, as 12 × 12 = 144, the square; and with ³ affixed, the number is to be cubed—i.e., multiplied twice by itself, as 6³ = 6 × 6 × 6 = 316, the cube of 6.

ENGLISH WEIGHTS AND MEASURES.

Measures of Length.

Square Measure.

Solid or Cubic Measure.

Avoirdupois Weight.

Troy Weight.

Apothecaries’ Fluid Measure.

Gallon (C) = 8 pints (O); 1 pint = 20 fluid ounces (oz. weight of water). Ounce (f ℥) = 8 drachms (f ʒ) = 480 minims (♏) = 720 drops (gtt.).

One wine glass = 4 tablespoonfuls = 16 tablespoonfuls = 2 ounces.

Symbols.—f. or fl. fluid; s.s. one half; a.a. for each. Thus f℥ss. ½ a fluid ounce.

Apothecaries’ weight, formerly used for dispensing medicines, superseded in 1864. 20 grains = 1 scruple; 3 scruples = 1 drachm; 8 drachms = 1 ounce; 12 ounces = 1 lb. (troy).

Liquid Measure.

FRENCH WEIGHTS AND MEASURES.

Weights.

Lineal Measure.

Superficial Measure

Measures of Capacity.

Solid Measure.