Fig. 35. Dolly.
Fig. 35a.Primitive Dolly.
I have seen some rather elaborate dollies, intended to be worked with amalgamating tables, but the usual prototype of the quartz mill is set up, more or less, as follows: A tree stump, from 9 in. to a foot diameter, is levelled off smoothly at about 2 ft. from the ground; on this is firmly fixed a circular plate of ½ in. iron, say 9 in. in diameter; a band of ³/₁₆ in. iron, about 8 or 9 in. in height, fits more or less closely round the plate(Fig. 35). This is the battery box. A beam of heavy wood, about 3 in. diameter and 6 ft. long, shod with iron, is vertically suspended, about 9 in. above the stump, from a flexiblesapling with just sufficient spring in it to raise the pestle to the required height. About 2 ft. from the bottom the hanging beam is pierced with an auger hole and a rounded piece of wood, 1½ in. by 18 in., is driven through to serve as a handle for the man who is to do the pounding. His mate breaks the stone to about 2 in. gauge and feeds the box, lifting the ring from time to time to sweep off the triturated gangue, which he screens through a sieve into a pan and washes off, either by means of a cradle or simply by panning. In dollying it generally pays to burn the stone, as so much labour in crushing is thus saved. A couple of small kilns to hold about a ton each dug out of a clay bank will be found to save fuel where firewood is scarce, and will more thoroughly burn the stone and dissipate the base metals, but it must be remembered that gold from burnt stone is liable to become so encrusted with the base metal oxides as to be difficult to amalgamate.Fig. 35Arepresents another primitive dolly(Plate VI. hand dollying).
Plate VI.—Hand Dollying
Make two St. Andrew’s crosses with four saplings, the upper angle being shorter than the lower; fix these upright, one at each end of the shaft; stay them together by cross pieces till you have constructed something like a “horse,” such as is used for sawing wood, the crutch being a little over 3 feet high. Select a log for a windlass barrel, about 6 in. diameter and a foot longer than the distance between the supports, as straight as is procurable; cut in it two circular slots about an inch deep by 2 in. wide to fit into the forks; at one end cut a straight slot 2 in. deep across the face. Now get a crooked bough, as nearly the shape of a handle as nature has produced it, and trim it into right angular shape, fit one end into the barrel, and you have a windlass that will pull up many a ton of stuff.
This is made by excavating a circular hole about 2 ft. 9 in. deep and, say, 12 ft. in diameter. An outer and inner wall are then constructed of slabs 2 ft. 6 in. in height to ground level, the outer wall being thus 30 ft. and the inner 15 ft. in circumference.The circular space between is floored with smooth hard-wood slabs or boards, and the whole made secure and water-tight. In the middle of the inner enclosure a stout post is planted, to stand a few inches above the wall, and the surrounding space is filled up with clay rammed tight. A strong iron pin is inserted in the centre of the post, on which is fitted a revolving beam, which hangs across the whole circumference of the machine and protrudes a couple of feet or so on each side. To this beam are attached, with short chains, a couple of drags made like V-shaped harrows by driving pieces of rod iron through a heavy frame, shaped as a rectangular triangle(Fig. 36).
Fig. 36.Puddling Machine (Sectional View).
Fig. 37.Puddling Machine.
To one end of the beam an old horse is attached, who, as he slowly walks round the circular track, causes the harrows and drags to so puddle the washdirt and water in the great wooden enclosure that the clay is gradually disintegrated, and flows offwith the water which is from time to time admitted. The clean gravel is then run through a “cradle,” “long Tom,” or “sluice,” and the gold saved. This, of course, is the simplest form of gold mining. In the great alluvial mines other and more intricate appliances are used, but the principle of extraction is the same.
To make a temporary small “draw-lift” pump, which will work down to a hundred feet or more if required, take a large size common suction Douglas pump, and, after removing the top and the handle, fix the pump as close to the highest level of the water in the shaft as can be arranged. Now make a square water-tight wooden column of slightly greater capacity than the suction pipe, fix this to the top of the pump, and by means of wooden rods, work the whole from the surface, using either a longer levered handle or, with a little ingenuity, horse-power. If you can get it the iron downpipe used to carry the water from the guttering of houses is more easily adapted for the pipe column; then, also, iron pump rods can be used, but I have raised water between 60 and 70 feet with a large size Douglas pump provided only with a wooden column and rods.
For squeezing amalgam, strong calico, not too coarse, previously soaked in clean water, is quite as good as ordinary chamois leather. Some gold is fine enough to escape through either.
The mercury extractor or amalgam separator(Fig. 38)is a machine which is very simple in construction, and is stated to most efficient in extracting quicksilver from amalgam, as it requires but from two to three minutes to extract the bulk of the mercury from one hundred pounds of amalgam, leaving the amalgam drier than when strained in the ordinary way by squeezing through chamois leather or calico. The principle is that of the De Laval cream separator—i.e., rapid centrifugal motion. The appliance iseasily put together, and as easily taken apart. The cylinder is made of steel, and is run at a very high rate of speed.
The general construction of the appliance is as follows: The casing or receiver is a steel cylinder, which has a pivot at the bottom to receive the step for an upright hollow shaft, to which a second cylinder of smaller diameter is attached. The second cylinder is perforated, and a fine wire cloth is inserted. The mercury, after passing through the cloth, is discharged through the perforations. When the machine is revolved at great speed, the mercury is forced into the outside cylinder, leaving the amalgam, which has been first placed in a calico or canvas bag, in a much drier state than it could be strained by hand. While not prepared to endorse absolutely all that is claimed for this appliance, I consider that it has mechanical probability on its side, and that where large quantities of amalgam have to be treated it will be found useful and effective.
Fig. 38.Mercury Extractor.
I am indebted to Mr. F. W. Drake for the following account ofsluice plates, which I have never tried, but think the device worth attention:
“An addition has been made to the gold-saving appliances by the placing of what are called in America, ‘sluice plates’ below the ordinary table. The pulp now flows over an amalgamating surface, 14 ft. long by 4 ft. wide, sloping 1½ in. to the foot, and is then contracted into a copper-plated sluice 15 ft. long by 14 in. wide, having a fall of 1 in. to the foot. Our mill manager (Mr. G. C. Knapp), advocated these sluice plates for a long time before I would consent to a trial. I contended that as we got little or no amalgam from the lower end of our table plates, there was no gold going away capable of being recovered by copper plates; and even if it were, narrow sluice plates were a step in the wrong direction. If anything, the amalgamating surface should be widened to give the particles of gold a better chance to settle. His argument was that the conditions should be changed; by narrowing the stream and giving it less fall, gold, which was incapable of amalgamation on the wide plates, would be saved. We finally put one in, and it proved so successful that we now have one at the end of each table. The percentage recovered on the sluice plates, of the total yield, varies, and has been as follows:—October, 9·1 per cent.; November, 6·9 per cent.; December, 6·4 per cent.; January, 4·3 per cent.; February, 9·3 per cent.”
To ascertain the width of a difficult gorge, a deep river, or treacherous swamp without crossing and measuring, sight a conspicuous object at the edge of the bank on the farther side; then as nearly opposite and square as possible plant a stake about five feet high, walk along the nearer margin to what you guess to be half the distance across (exactitude in this respect is not material to the result), there plant another stake, and continuing in a straight line put in a third. The stakes must be equal distances apart and as nearly as possible at a right angle to the first line. Now, carrying in hand a fourth stake, strike a line inland at right angles to the base and as soon as sighting over the fourthstake, you can get the fourth and second stakes and the object on the opposite shore in line your problem is complete. The distance between No. 4 and No. 3 stakes is the same as that between No. 1 and the opposite bank(Fig. 39).
Fig. 39.Measuring Inaccessible Distances.
Measure 40 ft. on the line to which you wish to run at right angles, and put pegs at A and B(Fig. 40); then, with the end of the tape held carefully at A, take 80 ft., and have the 80 ft. mark held at B. Take the 50 ft. mark and pull from A and B until the tape lies straight and even, you will then have the point C perpendicular to AB. Continue straight lines by sighting over two sticks in the well-known way.
Fig. 40.
Fig. 41.
Another Method.—Stick a pin in each corner of a square board(Fig. 41), and look diagonally across them, first in the direction ofthe line to which you wish to run at right angles, and then for the new line sight across the other two pins.
Fasten a common carpenter’s square in a slit to the top of a stake by means of a screw, and then tie a plumb-line at the angle so that it may hang along the short arm, when the plumb-line hangs vertically and sights may be taken over it. A carpenter’s spirit-level set on an adjustable stand will do as well. The other arm will then be a level(Fig. 42).
Fig. 42.
Fig. 43.Levelling Instruments.
Another very simple, but effective, device for finding a level line is by means of a triangle of wood made of half-inch boards from 9 to 12 ft. long(Fig. 43). To make the legs level, set the triangle up on fairly level ground, suspend a plummet from the top and mark on the cross-piece where the line touches it. Then reverse the triangle, end for end, exactly, and mark the new line the plumb-line makes. Now make a new mark exactly half way between the two, and when the plumb-line coincides with this, the two legs are standing on level ground. For short water races this is a very handy method of laying out a level line.
Take a stake about your own height, and walking from thebutt of the tree to what you judge to be the height of the timber portion you want, drive your stake into the ground till the top is level with your eyes; now lie straight out on your back, placing your feet against the stake, and sight a point on the tree (seeFig. 44). AB equals BC. If BC is, say, 40 ft., that will be the height of your “stick of timber.” Thus, much labour may be saved in felling trees the timber portion of which may afterwards be found to be too short for your purpose.
Fig. 44.Measuring Height of a Standing Tree.
This should be used more for ascertaining relatively large differences in altitudes than for purposes where any great nicety is required. For hills under 2000 ft., the following rule will give a very close approximation, and is easily remembered, because 55°, the assumed temperature, agrees with 55°, the significant figures in the 55,000 factor, while the fractional correction containstwo fours.
Observe the altitudes and also the temperatures on the Fahrenheit thermometer at top and bottom respectively, of the hill, and take the mean between them. LetBrepresent the mean altitude andbthe mean temperature. Then 55000 × (B-b / B + b) = height of the hill in feet for the temperature of 55°. Add ⅟₄₄₀ of this result for every degree the mean temperature exceeds 55°; or subtract as much for every degree below 55°.
Fig. 45.Aneroid Barometer.
1. Set up vertically a stick of known length, and measure the length of its shadow upon a horizontal or other plane; measure also the length of the shadow thrown by the object whose height is required. Then it will be:—As the length of the stick’sshadow is to the length of the stick itself, so is the length of the shadow of the object to the object’s height.
Place a vessel of water upon the ground and recede from it until you see the top of the object reflected from the surface of the water. Then it will be:—As your horizontal distance from the point of reflection is to the height of your eye above the reflecting surface, so is the horizontal distance of the foot of the object from the vessel to its altitude above the said surface.
Read the vertical angle, and multiply its natural tangent by the distance between instrument and foot of object; the result is the height.
When much accuracy is not required vertical angles can be measured by means of a quadrant of simple construction, represented inFig. 46. The arc AB is a quadrant, graduated in degrees from B to A; C, the point from which the plummet P is suspended, being the centre of the quadrant.
Fig. 46.
Whenthe sights AC are directed towards any object, S, the degrees in the arc, BP, are the measure of the angle of elevation, SAD, of the object.
Rule:—Square the number of seconds a stone takes to reach the bottom and multiply by 16.
Thus, if a stone takes 5 seconds to fall to the bottom of a shaft—
5² = 25 and 25 ° 16 = 400 feet, the required depth of shaft.
Where water is scarce it may be necessary to use it repeatedly. In a case of this kind in Egypt, the Arab miners have adopted an ingenious method, which is shown inFig. 47, and may be adapted to almost any set of conditions. Atais a sump or water-pit;bis an inclined plane on which the mineral is washed and whence the water escapes into a tankc;dis a conduit for taking the water back toa;eis a conduit or lever pump for raising the water. A certain amount of filtration could easily be managed during the passage fromctoa.
Fig. 47.
Mercurial ointment mixed with black cylinder oil and applied every quarter of an hour, or as often as expedient. The following is also recommended as a good cooling compound for heavy bearings:—Tallow 2 lb., plumbago 6 oz., sugar of lead 4 oz. Melt the tallow with gentle heat and add the other ingredients, stirring until cold.
When, through carelessness or unpreventable causes, plummer blocks and other detachable portions of machinery become cloggedwith sticky deposits of grease and impurities, a simple mode of cleansing the same is to take about 1000 parts by weight of boiling water, to which add about 10 or 15 parts of ordinary washing soda. Keep the water on the boil and place therein the portions of the machine that are to be cleaned; this treatment has the effect of quickly loosening all grease, oil, and dirt, after which the metal is thoroughly washed and dried. The action of the lye is to form with the grease a soap soluble in water. To prevent lubricating oil hardening upon the parts of the machinery when in use, add a third part of kerosene.
Graphite “black-lead” added to the water in a boiler prevents scaling and priming. My method is to paint the inside of the boiler with a good coat of graphite mixed with water to the consistency of thin gruel, and let it stand till dry. It will not be amiss to give a second coat before getting up steam. Even if slight scaling has already taken place, the graphite particles will penetrate and the scale come away gradually.
Where the water contains a large amount of mineral in solution, the pipes, particularly the small ones, inch to two inch, quickly become useless because of the rapid deposition of scale. I have seen in West Australia tons of small pipes thrown on to the scrap heap after a few months use, because of this difficulty. The treatment now indicated, which is my own invention, will make such pipes as good as new at small expense. Have a brick trough a little longer than your pipe. In this put a fire of wood, charcoal, coke, or a mixture of such fuel. Lay the pipes, a few at a time, in this. Heat slowly to cherry red. Then with pinchers suddenly immerse in a second trough of cold water, supporting one end above the water level. Most of the scale or incrustationwill be violently ejected. With a long pipe, if the heat has not been regular, some may still adhere. Then usually tapping with a hammer will detach it. If not, a second heating and immersion will do so, leaving the interior as clean as when made. It is hardly necessary to add that ’tis best to stand clear of the ends when the explosion takes place.
For use on cams and stamper shanks, which will be harmless should it drop into the mortar or stamper boxes, is graphite (black-lead) and soft soap. When the guides are wooden, the soft soap need not be added; graphite “black-lead” made into a paste with water will act admirably.
Oxalic acid 1 oz., rotten stone 6 oz., powdered gum arabic ½ oz., sweet oil 1 oz. Rub on with a piece of rag.
It is often very difficult, and sometimes impossible, to remove rust from articles made of iron. Those which are very thickly coated are most easily cleaned by being immersed in a nearly saturated solution of chloride of tin. The length of time they remain in this bath is determined by the thickness of the coating of rust. Generally from twelve to twenty-four hours is long enough.
The following method is but little known, although it deserves preference over many others. Add 7 oz. of quicklime to 1¾ pints of cold water. Let the mixture stand until the supernatant fluid is entirely clear. Then pour this off, and mix with itenough olive oil to form a thick cream, or rather to the consistency of melted and recongealed butter. Grease the articles of iron or steel with this compound, and then wrap them up in paper, or if this cannot be done, apply the mixture somewhat more thickly.
Take 1 oz. of camphor, dissolve it in 1 lb. of melted lard; mix with it (after removing the scum) as much fine graphite as will give it an iron colour; clean the machinery, and smear it with this mixture. After twenty-four hours rub off and clean with soft, linen cloth. This mixture will keep machinery clean for months under ordinary circumstances.
An excellent fire-lute is made of eight parts sharp sand, two parts good clay, and one part horse-dung; mix and temper like mortar.
A short splice is made by unlaying the ends of two pieces of rope to a sufficient length, then interlaying them as inFig. 48(upper cut), draw them close and push the strands of one under the strands of the other several times as shown in the lower cut.
Fig. 48.
This splice makes a thick lump on the rope and is only used for slings, block-straps, cables, &c.
Zimmermann’s rule for finding the lost part of a vein on the other side of a vein, is as follows:—
Lay down upon paper the line of strike of lode and the line of strike of the fault (cross-course), and by construction ascertain the horizontal projection of the line of their intersection; from the point where the cross-course was struck by the lode, draw a line at right angles to the strike of the former and directed to its opposite wall. Notice on which side of the line of intersection this perpendicular falls, and after cutting through the cross-course, seek the “heaved” part of the lode on that side.
Fig. 49.
Thus let AB(Fig. 49)represent, at any depth, the line of strike of a fault or cross-course dipping east, and CD the line of strike of a lode dipping south, and we will suppose that in driving from C to D in a westerly direction, the fault has been met with at D. Knowing the dip of the lode and that of the fault, it is easy to lay down on any given scale, AₖBₖ and CₖDₖ, the lines of strike of the fault and lode respectively at a certain depth, say 10 fathoms, below AB. The point Dₗ, where AₖBₖ and CₖDₖ meet, is one point of the line of intersection. Join D and Dₗ, and prolong on both sides. The line MN represents the horizontal projection of the line of intersection of the two planes.At D erect DE at right angles and directed towards the opposite wall of the fault. As DE falls south of MN, the miner, after cutting through the fault, would drive in a southerly direction and eventually strike the lode again at F. It will be at once understood that if the miner were following the lode frombto F, the perpendicular would lie to the north of the line of intersection, and following the rule, he would drive in that direction, after cutting through the fault. When several faults in succession dislocate a lode, very great complications may arise.
Having finished the survey of a metalliferous mine, the surveyor is sometimes called upon to calculate the quantity of ore reserves in that mine. Various methods are employed for this purpose.
[4]Bennett H. Brough’s “Treatise on Mine Surveying,” sixth edition, p. 165.
[4]Bennett H. Brough’s “Treatise on Mine Surveying,” sixth edition, p. 165.
Indeed, different surveyors will not agree within wide limits as to the amount of ore reserves in the same mine. Sometimes the amount of ore in sight will be considered to be a rectangular block, limited by the outcrop of the vein, the depth of the shaft, and the extreme points of the levels, diminished by the amount extracted. Other surveyors would avoid so excessive an amount, and take but one-third of that amount.
The following method is recommended by Mr. J. G. Murphy, an experienced American mining engineer, as the fairest and most trustworthy:—
Let it be required to calculate the ore reserves in a mine opened up on a vein with a mean cross section of 6 feet; a cubic foot of the vein matter in place weighing 150 lb. The ore stopes are generally very irregular. In this case, however, it may be supposed that the stope faces are 11 feet apart and 8 feet high. There is an inclined shaft, 10 feet by 6 feet, following the dip of the vein, and six levels, each 7 feet by 6 feet, 100 feet apart. The lengths of the levels are—
The longest level west is 350 feet, and the shortest 100 feet.
Assuming the bounding line of the area of available ore to be at a distance west of the shaft—
If the longest level east is 400 feet, and the shortest 100 feet, the bounding line in this direction, calculated in a similar way, will be at a distance of 250 feet from the shaft.
The inclined shaft has opened up the vein for 670 feet. Deducting, say, 15 feet for the irregularity of the surface, the quantity of ore in sight will be a rectangular block 655 feet deep, 225 + 250, or 475 feet long and 6 feet wide, that is 1,866,750 cubic feet.
From this quantity, however, must be deducted the quantity of ore extracted, namely:—
This quantity, deducted from 1,866,750 cubic feet, leave 1,684,750 cubic feet. Divided by 13½, the number of cubic feet required for a ton, this gives 124,797 tons of ore in sight.
The quantity of ore discovered in a mine may be estimated from its specific gravity and the average size of the vein. The specific gravity of the ore, with that of water taken at 1000 for standard is equal to the number of ounces in a cubic foot. Great cautionis necessary to determine the proportion of the vein which may be considered solid ore. A vein 6 feet square and 1 inch thick, contains 3 cubic feet, therefore, in order to find the number of cubic feet per square fathom of a vein, it is merely necessary to multiply the thickness in inches by three.
The following example illustrates the method of finding the weight of any ore per square fathom in a vein. What quantity of galena will be produced per square fathom from a mineral vein 6 inches in width? One quarter of the vein consists of galena, the remainder of zinc-blende. One-twentieth must be allowed for cavities in the vein. The specific gravity of galena is 7·5, and a cubic foot of water weighs 1000 ounces; therefore a cubic foot of galena weighs 7500 ounces.
The vein being 6 inches thick, there are 18 cubic feet in a square fathom. One quarter of that amount, or 4·5 cubic feet, consists of galena. The weight of galena in ounces is therefore:
or 17 cwt. 3 qr. 15 lb. as the weight of lead ore per square fathom.
In testing a gold mine with a view to purchase, it should be remembered that as a rule the intersections of leaders or small veins with the main ore body are usually the richest portions of the lode. This the experienced prospector knows, and generally his shafts and cuttings are made at such points. For the ordinary mining investor, when inspecting with a view to purchase, these are places to avoid if endeavouring to form a correct estimate of the value of the ore in bulk. Take samples across the lode from place to place, break down and bag personally, and mark bags. Test the rich portions separately and average, estimating quantity of both.
Plate VII.—California Pump.
Any handy man or rough bush carpenter can make a California Pump. The prospectors in the illustration(Plate VII.)are using a home-made contrivance, which is quite effective for raising water from shallow depths for “long tom,” or ground sluicing—a wooden frame-work and open wooden wheel with handle. Over the wheel is run a belt of canvas, say, six inches wide, with wood stops about a foot apart—a long sloping box, dipping into the water, up which the stopped belt travels—and you have a California Pump which, if not a highly scientific device, is at least very serviceable.
An imperial gallon of water weighs, at 62° F., 10 lbs. avoirdupois. Gallons × ·1606 = cubic feet. Cubic feet × 6·288 = number of gallons.
Gallons × 277·46 = cubic inches. Cubic inches × 0·003604 = gallons. Cubic feet of water × 62·28 = number of pounds weight. Pounds of water × 0·0166 = cubic feet. Gallons of water × 0·004464 = number of tons. Tons of water × 224 = gallons of water. Cubic feet of water × 0·0278 = number of tons. Tons of water × 35·97 = cubic feet of water.
A pipe 1 yard long holds approximately (actually, 1·52 per cent. less) as many pounds of water as the square of its diameter in inches; thus a 6-inch pipe holds approximately 36 lbs. of water in each yard length.
Ten feet head of water gives a pressure of 4⅓ lbs. per square inch approximately.
If H = head of water in feet, P = pounds pressure per square inch:
H = P × 2·311 P = H × ·4326
Horse-power required to Pump Water.—One h.-p. indicated will raise about 3000 gallons of water per hour 50 feet high.
To pump 1 gallon of water per minute against a pressure of 4 lb. per square inch, requires:
p × ·0007 H.-P.
Rock is bored with jumpers of 10 lb. to 18 lb., used alone, or with boring bars and hammer. The former are more effective, but can only be used perpendicularly, or nearly so, and with rock of moderate hardness; they require more skill.
The boring bars may be made of 1¹∕₈ inch bar iron of various lengths, with steel bits up to 3 inches. A bit should bore from 18 feet to 24 feet with each steeling, and requires to be sharpened once for every foot bored.
per day of 10 hours in hard granite.
The average duration of flat, wire ropes is usually taken at one year, and that of round ropes at half a year.
This drill is applicable to sinking a borehole for prospecting for minerals or water, shafts, &c., or blasting under water.
It consists of a circular row of “carbonados,” a species of diamond, set in a circular steel ring. This is attached to a hollow steel tube which is kept rotating at about 250 revolutions per minute, pressed forward by a force varying from 400 to 800 lb. according to the nature of the rock. Water is supplied through the tube which washes out thedébrisand cools the diamonds.
Granite and the hardest limestones are penetrated at the rate of 2 to 3 inches per minute, sandstones 4 inches, quartz 1 inch.
The diamond drill is not effective in soft strata such as clay, sand, and alluvial deposits.
Boreholes have been made at the following rates:
In Ironstone formation:
Or an average of 12 feet a day.
In Coal measures:
Or an average of 7½ feet a day.
To find Solidity of Round Timber.
When all dimensions are in feet: Length × (¼ mean girth)² = cubic feet.
When length in feet,girth in inches: Length × (¼ mean girth) ÷ 144 = cubic feet.
When all dimensions are in inches: Length × (¼ mean girth)² ÷ 1728 = cubic feet.
To find Solidity of Square Timber.
When all dimensions are in feet: Length × breadth × depth ﹦ cubic feet.
When one dimension is in inches: Length × breadth × depth ÷ 12 ﹦ cubic feet.
When two dimensions are in inches: Length × breadth × depth ÷ 144 ﹦ cubic feet.
For board measure, depth always equal 1 inch.
To find surface in square feet, proceed as per rules for solidity of square timber.
1.In Squares.—Extract the square root of the desired content,reduced to square chains (ten square chains equal one acre). The result will be the length of the required side in chains.
Thus if we wish to find the side of a square block containing 25 acres, we first reduce the acres to square chains: 25 × 10 = 250, the square root of which is 15·81, or 15 chains 81 links; the side required.
By reference to the tables of square roots on page 189, the required sides of square block for a large number of acres can be read off at once.
One acrelaid out as a square must have its side made 316¼ links, or 208-71/100 feet, or 69-57/100 yards, 70 paces being a near approximation.
2.In Rectangles.—Divide the content by the length or breadth, according to which factor is known, and the result will be the required side.
Thus 5 acres, or 50 square chains, if 10 chains long, will require to be 5 chains wide.
If the content only is given, and the length is to be a certain number of times the breadth, the content in square chains divided by the ratio of the length to the breadth, and the square root of the quotient, will give the length of the shorter side. Thus, if we wish to lay out 72 acres as a rectangle twice as long as broad: 72 acres = 720 square chains, divided by 2, the ratio given, = 360, the square root of which is 18·97 chains, the length of the shorter side. The length of the other side is therefore 18·97 × 2 = 37·94 chains, or 3794 links.
To find the area of a triangle when the base and perpendicular height are given: Multiply the base by half the height, orvice versâ.
To find the area of a triangle when the three sides are given: Take half the sum of the sides, subtract each severally from this sum, then multiply this and the three remainders together, and take the square root for the area.
To find the area of a rectangular figure: Multiply the length by the breadth, the product will be the area.
To find the area of a trapezoid: Multiply half the sum of the two parallel sides by the distance between them.
To find the area of a parallelogram whose angles are not right angles: Multiply the length of any one of the sides by the perpendicular.
To find the area of a trapezium: Divide it into two triangles and find the areas of the latter by the first rule.
To find the area of an irregular polygon: Divide the polygon into triangles and find the area of the latter.
To find the area of an irregular figure: Draw the figure on fine cardboard or thin sheet metal, cut the same carefully out and weigh with an accurate balance. Then this weight, compared with the weight of a piece of the cardboard or metal of a definite size, say one square inch, gives at once the area required.
It would be futile to profess, in the limits of a small work of this kind, to instruct the beginner fully in the principles and practice of mine surveying, especially as the most elaborate treatise can only be of service when some actual practical experience and knowledge of instruments have been obtained.
For an exhaustive and well-arranged work on the subject, Brough’s “Treatise on Mine Surveying” can be strongly recommended, and should be carefully studied by all wishing to learn the best methods of accomplishing the accurate results that any mine-surveying worth the name demands.
The following methods of connecting underground and surface work are therefore addressed to such as are thoroughly acquainted with a dial and the method of traversing.
1.To find where a shaft should be sunk to connect with any part of the underground workings.
Should the mine be one opened by an adit, there is no difficulty in doing this, as the dial can be set up at the mouth and a sight taken to a light; this can then, by means of the vertical arc, be prolonged up the hill, and the remaining bearings and distances are then easily laid down to the desired point. When a starting-point has been obtained, the chief difficulty in these caseshas been overcome. If a single shaft is the only connection to the underground workings, the magnetic bearing of the first line at bottom must first be carefully ascertained, and the position of the first station brought to the surface by means of a plumb-line, made of copper wire preferably, the plummet being put into a dish of water to steady it. The dial is then set exactly over the end of the line at the surface, and the first bearing and distance laid off.
Should it be impossible to set the instrument over the point at surface, a spot must be found by trial outside the shaft which is in the correct course. The dial is set up in the supposed direction of the line and repeated sights taken to the first point till the instrument and it are exactly in the required line, when the length of the first line can be measured along it, and the new lines proceeded with.
As local attraction frequently affects the needle at the bottom of the shaft, and so vitiates the surface survey that depends on its swinging the same at both points, a method of dispensing with the needle must be resorted to. This is the suspension of two plumb-lines from opposite sides of the shaft, the plummets hanging exactly over as much of the first underground line as the width of the shaft will allow.
The two plummet lines at surface then give the direction, and by trial the dial must be put exactly in line with them in order to prolong it correctly.
If there are two or more shafts sunk on the workings, it will be an easy matter to ascertain if the needle can be depended on for laying out any further surface work, as the underground survey connecting the shafts can be laid down on the surface, or the direct bearing and distance calculated, when its correctness is tested by the terminating point of the survey.
2.To find depth of shaft at any point, to cut a vein whose dip is known.
Rule:—Multiply natural tangent of angle of dip C (Fig. 50.) by the distance from outcrop to proposed shaft AC. The result is the depth required, AB.
By Protractor and Scale.—Rule on paper a line AC of the required distance, then at C set off the angle of dip and drawAB at right angles to AC. Then scale off AB = depth of shafts.