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Collection: Books and Periodicals > Mining & Scientific Press

Volume 12 (1866) (428 pages)

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146 The Wining and Scientific Press. Gonmunications. In Ta1s DErartwent we lnylte the FREE Discussion of proper H Y alone being r he ideas and theories they advance. all for [Written for the MinIng and Sclentific Press.j THE TRAQTORY QOURVE, AND THE PROPERTIES OF GRINDING PLATES, BY W. A. GOODYEAR. [conzINvED FRoM PAGE 130.] ‘Let us now look at some of the points relating to the wear and grinding effect of certain plates as investigated in the Hand Book. Tadopt the two defintttons given under “Laws of Grinding,’ 1 and 2, page 102. Instead, however, of taking, without modification, the law given under 3, as it is there expressed, I will modify its statement as follows: The wear (that is, the thickness of the layer of material worn from the surface) in any direction, at any point of grinding surfaces of uniform hardness, is proportional to the product of the pressure at that point in the given direction, into the distance passed over, provided that the surfaces he of such a form that, this law holding true, the plates can follow each other and remain an contact as they wear away ; otherwise the law does not hold. : Iwill now discuss, to some extent, the proposition attempted to he proved upon page 103 of the Hand Book. If I understand the author correctly, it is there assumed that in tractory conoidal plates, of uniform hardness, the pressure in the direction of the normal to the surface is constant (which is true when the upper plate revolves ), and that, therefore, the grinding surface will wear into one, whose meridian curve is so related in form and position to the meridian curve of the original surface (that is, the tractory), that the distance intercepted hetween the two curves, on the normal to the tractory at the point 2, y, shall he proportional to the ordinate y (which is zot true), and it is then attempted to prove that the distance intercepted hetween these two curves, on a straight line parallel to the axis of 2, is constant, and, therefore, that the secondary curve is a tractory equal to the first. (I still use 2 and y in the same sense as heretofore, viz. as representing the codérdinates of points in the tractory when the origin is at I’, in the figure on page 103 of the Hand Book.) I will now show that if the distance intercepted hetween a tractory and a secondary curve, on the normal to the tractory at the point 2, y, he proportional to the ordinate y of the tractory, then the secondary curve is not a tractory, and therefore that the distance intercepted hetween the two curves, on a line parallel to the axis of x, is not constant; for if it were the curve would hea tractory. Consider a point 2, y, of the tractory, If X and Y he the running codrdinates of the normal at this point, then the equation of the normal is (51) Yoy=—Z >». This normal will cut the secondary curve in a point x, y’, whose codrdinates must, therefore, satisfy (51). Hence, (52) 7 —y=— Pi (z’ — 2). The distance hetween the points x, y, and 2’, y’, is VY (x — 2)?+ (y—y)?. This distance is, hy supposition, proportional to the ordinate y ; therefore, (58) Y (#' — a) + (y¥ —y)? = by, where bis constant. Substitute in (52) the known value of 6 in terms of y, thus, y 6)y—-y=s Vere (2). If, now, hetween (53), (54), and (18), we eliminate x and y, we shall ohtain an equation expressing the relation hetween :c’ and y' , which is the equation to the secondary curve in question. The elimination of # and y in this case, however, involves the resolution of an equation of the fourth degree. If, for example, we ohtain the value of (#’—zx) from (54), and suhstitute this in (53), we are led to the equation (55) By! — at (B—1) ff — 2 ayy + ey? = 0, an equation of the fourth degree in y, which, if resolved, would give us four complex expressions for as many different values of y. If, then, from (53) or (54) the values of x corresponding to these values of y were obtained, and these values of x and y substituted in (18), we should obtain the equation of the secondary curve. I have not resolved equation (55), and have, therefore, not ohtained the equation of the secondary curve, as the operations involved would he tedious, and the resulting expressions would he very complex. The final equation, however, would represent a curve having eight hranches—that is, two hranches for each hranch of the tractory—one lying upon the concave side, and the other upon the convex side of the latter. This is as it should he, since there are two points in the normal at x, y—one on each side of the tractory—which will satisfy the conditions of equations (52) and (53). Let us now consider a single hranch of the tractory and the corresponding pair of branches of the secondary curve, and let us suppose two other tractories described equal and parallel with the first, hut heginning at the points y == 4, © = + 6a, instead of the point y = a, = 0. It may easily he shown, geometrically, hy constructing the curves under the ahove conditions (as I have done for the particular case 6 = 1): first, that the ranch of the secondary curve lying upon the convex side of the original tractory hegins at the point y =a, = — éa, where it is tangent to the tractory which begins at the same point, hut that the halance of this branch of the secondary curve, though lying helow the line y == a, does not coincide with the tractory to which it is tangent, hut lies upon the convex side of it; second, that the hranch of the secondary curve, lying upon the concave side of the original tractory, hegins at the point y= @, «=a, hut that heginning here, it immediately rises above the line y = a, forms an unclosed loop or hook, and then descending, crosses the line y = a, and continues on, lying then between the original tractory and the one which hegins at the point y= e, z =2e, instead of coinciding with the latter. The construction which I have made then (and which any one else can make at pleasure), shows that at least in the case where 6 = 1, the secondary curve is not is not a tractory. ‘The question now arises, whether for other values of 6 the case may not he different. Erratom.—Instead of x in equation (35) read +. [fo be Continued.] Tue two kings that rule America—Jo-king and Smo-king. [Written for the Mining and Scientifie Press. ] From Our Regular Correspondent. Enirors Press: This place, which has been my center of operations for the pasttwd weeks, isa respectably decayed mining town of the olden time, still retaining its name and organization ; hut whose glory has long since passed away, with the richness of the gulches and river placers, which once made it famous throngbout the State and the whole coast. Bat though I speak of it as decayed, I do not wish to say that business has entirely deserted the place, or that its streets are lined with empty houses like some of the ex-mining towns of the present day. The glory of tbe ancient placers is still perpetuated, though feebly, by numerous deep shaft claims, and a few hydraulic diggings, which together with its being the county seut of Calaveras county, keep up quite a respectable show of business. It is only respeciably decayed. The principal] mining now being carried on in tbis vicinity is deep placer mining; the gold being obtained from deposits of gravel supposed to be the beds of an ancient system of rivers, now covered by deposits of lava and other voleanic debris. The most important entarprise of this kind is the “ American Shaft,” owned by Messrs. Paul, Larnard & Holbrook,
located on Chili Gulch, two miles below this place. ‘The channel was strnck at a depth of 100 feet, at which depth a large stream of water was tapped which compelled the owners to suspend operations for some time. and was only removed at an epxense of over $30,000. When the water was once checked, there was no turther trouble, and the mine is now in successful operation, employing upwards of thirty men, and ten stamps for crushing the cement. The hoisting, pumping, and stamping machiuery, are all driven by tbe steam engine. The daily prodnet of the ming is from $150 to $200 per day, yielding a very handsome profit to the owners. ‘The deepest shaft in this section is that on the claim of SQUIRES & COMPANY, Which is about 165 feet in depth. Tbe hed of cement gravel in which the gold is found varies from a few inches to four or five feet in depth, averaging about two feet, and pays about ten dollars per ton, by washing in sluices, The width of the channel is uncertain, but is known to bs upwards of fifty feet , tbe rock on which it rests being ordinary slate. Some of these claiins are opened by tunnels driven into the sides of the hills, often at great expense. Among thoss now in progress may be mentioned THE INDIAN RAVINE TUNNEL, Which is being driven into Stockton Ridge, about three miles below Mokelumne Hill, by Messrs. Pau] & Haerschner, and other citizens of thistown. Itis estimated that to reach the channel a rim of slate 1,100 feet in thickness will have to be penetrated. The work has been going on nearly two years, and the tunnel is now in 430 feet, the rock having been very hard thus far. It is estimated that it can be finished in two years more,as the slate is expected to be softer, as the work progresses. ‘There area few hydraulic claims also at work and many of them are doing quite well, one of these, tbat of Messrs. Shaw & Co., is immensely rich. It is situated on the west side of Chili Gulch, about a mile anda half below Mokelumne Hill. THE “OPAL CLAIMS” OF STOCKTON HILL. Considerable excitement has been awakened at different times by the discovery on Stockton Hill, near this place, of soms beautiful concretions, believed at the time, to be opals, but which subsequent observations have proved to be agates, some of which are of marvelous beauty, and doubtless of considerable value, though there is no market for them in this country. A company was finally organized amonz the French residents of Mokelumne Hill and vicinity, and the search commenced inan earnest and systemitic manner. The work is done by a Mr. Neven, who shuwed me the excavations, and explained the different processes employed. The claim of the company is known as the Occulis Mundi, (light of the world), and is 5,000 feet in extent along the northern slope of Stockton Hill, and extends to the top of the same. Several tunnels bave been driven at different points along the hill-side, the longest of which is in 150 feet. The stones are found in a ledge of grayish colored gravel orclay, from three to six inches in thickness, having a slight inclination to the northwest, of about two degrees from a_horizontal plane. Hach stone.is eocased in a brittle white substance, supposed by Mr. Neven and others to be produced by the decomposition of the stone itself by the action of chemical agents contained in the water in the hill. Throughont the whole extent of the claim the same regulnr formation exists, the line of the Strata being easily traced, and perfectly straight and parallel, Above the ledge is a belt of “ trachyte” which is traversed at a hight of five feet above the ledge, hy two strata of white fieldspathic clay, each: about one inch in thickness. giving to the sides of the tunnel a regnlarity of appearance, as if they had been purposely striped by the hand of man. ' Some very beautiful stones have also been found in another hill east of town, and about a mile from the Occulis Mundi. These are principally “ moss-agates,” many of which are exceedingly heautiful. They are found in veins traversing a stratum of hard ferruginous, volcanic rock, in which they are so firmly imbediled . aa often to break before they will be separated 1 from it. Many of the stones from hoth these . claims have been cut and polished by Dr. H. M. Stuart, of Mokelumne Hill, to whom the company are indebted for the beuutiful dis) lay of cut stones made by them last fall, at the Mechanics’ lair at San Francisco. One of these, a fine “imoss-agate” of about two carats in weight, is now worn in a ring by Mr. Geo. \, Leger, one of the owners ofthe Occulis Mundi who takes great pleasure in exhibiting it to the i curious. J am indebtedto the Superintendent, . Mr. Neven. for some very fine specimens of { the stones from these claims, some of which J expect to preserve during life, as pleasing reminders of a day very agreeably spent. On the third day of my stay at Mokelumne Hill started in company with a young friend, a son of Mr. Thomas Loutlett of this place, to 4 visit the mine of the “Campo Seco Copper : Mining Company,” situated near Campo Seco and fourteen miles from here. A walk of eight Wy) miles brought us to the residence of the Messrs. . Young, near the Calaveras linie-kilns, who very kindly volunteered to furnish us with saddle-horses for the remainder of our journey, which offer, after such a walk, we were not at all loth to accept, and after visiting the mine, and the smelting works near, we came back a little after dark, to ths residence of the Messrs. ‘Yonng. where we were very hospitably entertained for the night. and returned to town on ths following day, well pleased with our trip, and with what we had seen. THE CAMPO SECO COPPER MINE i Ts owned by a joint stock company of the same name, and is superintended by Mr. D. L. Morril, onder whose able manngement, the mine . is now more than paying its expenses, nnd will probably soon be in a dividend-paying condition. It is opened at present to a depth of . 200 feet, at which depth the vein of ore, a : solid mass of sulphides of iron and copper, unmixed with slate, is twenty-three feet in width, ahout one-sixth of which is estimated by Mr. M. to be shipping ors, assaying from twelve to twenty-three per cent. copper. ‘Ihe lower grades of ore are sold to the proprietors of the smelting works located near. The shaft is not sunk on the vein, but west of it, and drifts are run from it to the vein at points where it is desired to open levels. The~body of ore in the 150-foot level, is forty feet east 9) of the shaft, and is twenty-three feet in width, ) and is divided nt the end of a drift extending 9) eighty-five feet northward from the shaft by a . “horse” of slate. This horse is not fonnd in the lower level, but the vein is of uniform width and character throughout tbe extent of its drift. Besides the twenty-three feet: of ore, the vein contains a massof slate somewhat cupriferous, of unknown width, the we-tern or f “hanging wall.” having never been reached. It is believed that another hody of ore will be found onder this wall, and acting under this belief, a drift has been started on the 200-foot level for the purpose of reaching it. This drift has been continued 120 feet, and is still in the vein It has cut a few narrow strata of rich 7 copper ore, but hag not as yet developed any f very important deposits. One thousand tons of ore were shipped from this mine during the past year, averaging 16 to 17 per cent., and if is confidently believed that the amount will be much increased during the present one. The hoisting works are driven by water power and are capable of raising thirty tons of ore daily. It is intended to erect steam works in a short time, as the present machinery is entirely insufficient for the wants of the mine. After passing through the mine we went in company with Mr. Morril to visit the works of THE TAUNTON SMELTINO COMPANY, Located on the Mokelumne river, three-fourths of amile beluw the Campo Seco mine, with which they are connected by a railroad, on which the cars are drawn by a horse. The . ® .