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Collection: Books and Periodicals > Mining & Scientific Press

Volume 12 (1866) (428 pages)

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162 The Mining andl Scientific Press. Gonmnniontions. In rH18 DEPARTMENT we invite the FREE DISCUSSION i dents alone being r of all Proper nT for he ideas and theories they advance. {Wrltten for the MinIng and Scientific Press.j THER TRACTORY CURVE, AND THE PROPERTIES OF GRINDING PLATES, BY W. A. GOODYEAR. [conTInDED FROM PAGE 146.] It is easy, however, to show analytically that in the hranch of the secondary curve which lies upon the concave side of the original tractory, there are always values of y/ that are greater than a, that is, that the hook, above the line y = a, is always formed, whatever be the value of 4, (provided 5 he not ahsolutely 0, in which case there is no secondary curve,) and, therefore, that this curve is never a tractory, since in the latter no value of y can he greater than a. To show this, let us find the point where the normal to the tractory, at the point 2, y, erosses the line y= a. Represent the coordinates of this point hy 2”,y’. Now, since the point x”, y’’, is in the normal to the tractory at the point 2, y,its codrdinates must satisfy equation (51). Therefore, we have ! a, dey ea a, 2). the point 2”, 7’, is also in the line y =a, its codrdinates must satisfy this equation also. Hence, (57) o/’ =a. If, now, we substitute the Since kuown value of = in (56), and then ohtain y from (56) and (57) the value of 2’’ in terms of x and y, we have * (58) a =a aa (58) -y \i in (58) 2 and ystill represent the codrdinates of points in the tractory,we know that hy taking y as near @ as we please, we can make x as near 0 as we please. Therefore, (58) shows that hy taking yas near a as we please, we can make x2’ as near 0 as we please. In other words, that by taking points in the tractory as near the point y =a, % = 0, as we please, we can make the normal at the poiut 2, y, eross the line = a, as near the point y = a, x — 0, as Now, since we please. Therefore, however small 4 may be (provided it he not ahsolutely 0), there are still points in the tractory so near the point y== a, «= 0, that their normals cross the line 7 =a, at a less distance than ba from the point y= a,2—0. There are, therefore, always points in the secondary curve whose ahscissas are less than da, and whose ordinates are greater than a, and which, therefore, lie ahove the line y =a. The hovt referred to is, therefore, always formed, however small 6 may be. That the hook is always formed when 6 is large, is sufficiently evident. The secondary curve, then, is never a tractory; and this heing the case, the distances in a direction parallel with the axis of x, from the original tractory to the secondary curve, are not constant. The demonstration given upon page 108 of the Hand Book is faulty, inasmuch as in the figure there used, the lines 0 ¢ and o! ¢’, which are made to represent the wear perpendicular to the tangent, and are proportional to tbe ordinate, are not drawn perpendicular to the tangent at the point of contact, where this wear would actually take place, if it could take place at all, hut at a distance from it, so that the figure does not answer to the conditions of the prohlem there handled. I may remark here, that although we cannot conveniently ohtain the equation itself of the secondary curve ahove discussed, we can yet, without difficulty, ohtain the differential coefficient of y/ with respect to zx in terms of y, and hy means of this, demonstrate one or two other points in relation to the curve. The value of this differential coefficient is the following: (59) oa * 2b —abtaya—y 2b baYa—#/ From (59) we see that if we make y= a, But from the conditions af = under which the curve is formed, we know that when y = a, y/ also = a, and a’ — ba. Therefore, at the initial point 7’ = a, 7 = ba, of the secondary curve, its tangent is perpendicular to the axis of ahseissas, and the curve itself is tangent to the tractory which hegins at the same point. then di Again, if we make ee 0, we shall ohtain the point or points where the tangent of the secondary curve is parallel to the axis ers) daz! can can he satisfied in two ways, viz., hy making y = 0, or hy making (60) 2by—a?b+ay/ae—y=? Now, we know that when y = 0, then 7’ also == 0, and 2 and 2’ are hoth infinite. Therefore the axis of ahscissas is also an asymptote to the secondary curve. Equation (60) gives a I — (61) yt avs (4480-14781). Therefore, at the point in the secondary curve, corresponding to the point in the tractory, where ey 4 Hl ee Y—= 55 7 4F—-1+ 8+), ‘the tangent of the secondary curve is also parallel to the axis of ahscissas. It is very evident that this curve is not a tractory. Let us now consider some of the conditions of grinding, If two grinding plates, of tractory conoidal or any other form, rest uniformly the one upon the other without motion, the pressure hetween the two, in direction as well as in amount, is determined solely hy the weight of the upper plate, and if the latter he of uniform thickness in a vertical direction, the pressure 7” a vertieal direetion is uniform, or constant. If the plates he curved (whether they he of tractory conoidal or any other curvilinear form), the vertical pressure at any point may he resolved into two components, one of which is parallel and the other perpendicular to the tangent of the meridian curve at the same point. of ahscissas. But the equation The component parallel to the tangent is ‘taken up hy the hody of the plates themselves, and hecomes null in effect. The other component remains; and it is easy to show that in tractory conoidal plates, if the upper plate he of uniform vertical thickness, this last component varies as y, and, in fact, is equal at any point to R Z, if R denote the constant vertical pressure. These conditions hold so long as the plates remain motionless. If the upper plate hegins to revolve, the conditions of pressure are then changed, and in a manner depending upon the form and relative hardness of the different portions of the plates. [To be Continued.] Ay old man anda little child stand upon the threshold of time, the. two looking different ways. {Written for the Mining and Scientific Press.) From Our Regular Correspondent, Enrrors Press: After a trip in the north: eastern part of the county, I find myself enjoying the kindly hospitality of Mr. Bever of the Rich Guleh Hotel, and having spent most of this time ina highly interesting, but rather unappreciated section of country, I am led to believe that some account of my ‘‘ wanderings and short comiugs” therein may be of interest to the public. Leaving Mokelumne Hill on the afternoon of the 16th instant, I reached the residence of Colonel Rust, three miles above which place, about sunset, and accepted his kind invitation to spend the night. ‘The Colonel is one of the pioneer newspaper men of the coast, having been at one time editor of the Marysville Eapress, and having heen at different times connected with many enterprises of the kind in our mountain towns. He is fond of relating his experiences in those early days of newspaper work, and I was equally fond of listening ; so
between ns two, the evening passed quite pleasantly away. The next morning I started quite early for West Point, where I arrived about one o’clock, having met on the way many of those whose acquaintance [had made last spring, in all of whom 1 found friends and helpers. The most of my time was spent in West Point and Sandy Gulch districts, which lie hetween the north and sonth forks of the Mokelumne river, and are separated by the widdle fork. WEST POINT DISTRICT Lies on the north side of the middle fork of the Mokelumue, and is at present the most prosperous and enterprising quartz-mining district in the county. Itis well supplied with wood and water, both being abundant and cheap, thus offering every facility for working, at small cost, the rich auriferous ores which the numerous ledges so abundantly yield. The veins of this district are situated in a granite formation, and are quite irregular in width above the water line; at which point they were heretofore supposed to disappear, none having been worked below thatline until withina yearortwo. They are also frequently cut hy dykes or “elvans” of granite, trap or slate, which gave rise to the helief that they were generally of insignificant extent, longitudinally. The explorations on the Mina Rica and Sacoterre, and the Cummings and Hadley veins in this district. and the Belding in Amador county, which is alsoon the same range and in the same formation, have proved almost heyond doubt that the veins in this district are as permanent, though not so extensive, as any inthe State. The width of the veins vary from two to three inches to as many feet, and the yield of the ore is fram 20 to $200 per ton ; quartz paying less than twenty dollars not being considered rich enough for profitable working. Owing to the belief that the ledges, or “ bunches,” as they are here called, were not extensive, but few mills have been built for #he working of any particular leads; but most of the quartz is crushed at custom mills, whose charges vary from five to seven dollars per ton; the latter price being charged for working in an arastra; that process being quite popular with some classes of the population. The principal custom mills now at work in this district are Henry’s of five stamps, on the Middle Fork, one mile south of town; Schmidts, of five woodeu stanips and two arastras, on the same stream, some 400 yards above Hendy’s; the Belcher mill, of eight stamps and two arastras, abonta mile above Schmidts, and the Skoll Flat mill, at Skull Flat, two miles northeast of town, of eight stamps, all of which were more fully described iu my letter from this place in April last. Besides these may he mentioned Carlton’s mill, sitnated one and a half miles below West Point on the Middle Fork, consisting of three wooden-stem stamps and two arastras, driven hy water power, with an overshot wheel. This is one of the most substantially huilt mills of the kind that I have ever seen. It is capable of working two and a half tons of ordinary quartz daily, the rock being first broken by the stamps into pieces of the size of filberts, agai which itis ground and amalgamated in the arastras. ‘The old Nestor mill, now owned by Mr. Lidstrom, of Masnn’s brewery, San Francisco, and ran by Mr. Fred Morris, formerly in charge of the Mina Rica mine and mill, consists of three stamps and two arastras, driven like the last hy water power; but is in a very dilapidated condition, as is also Bryant’s mill of two stamps and one arustra, situated near. The owners of the latter, however, inform me that they intend improving their mill soon. Both these mills are located on a small stream called Bear creek, about a mile east of town. The principal mill of the district, is that of the MINA RICA NE LAS FLORES MINING COMPANY, Located at Camp Flores, one and a half miles east of West Point. ‘This mill consists of ten heavy stamps driven bya steam engine of thirty hnrse power, and is well and substantially built. Amalgamation is performed in small pans into which the pulp rans directly from the hatteries. ‘The tailings are again ground, aud amalgamated in one of Baux & Guind’s amalgamators, by which means the yield of the quartz is increased from twelve to fifteen dollars per ton. ‘Lhe average yield of the rock is from thirty to thirty five dollars; at least this is the estimate of the superintendent. This conipany own two veins, the Mina Rica and the Lockwood. On the formera shaft has heen sunk to a depth of 130 feet, showing a well defined vein of quartz lroin fourteen inches to two feet in width, and much of it heavily charged with sulphurets. At a depth of 112 feet, drifts have heen run lengthwise of the vein a distance of eighty feet, disclosing a large vein of rich ore. ‘The course of this vein, like that of all others in this range is nearly north and south, with a very shght dip to the westward. As Ihave before stated, the surface of this district is all of granite formation, hut on reaching a depth of 100 feet, the hanging wall of this vein is of talcose slate. while the foot-wall remains granite all the way down. ‘This is the only instance of the kind which has come under my ohservation, and I should like to see some explanation nf the case hy geologists. ‘The Lockwood has heen explored to a depth of 100 feet, and by drilts along the vein a distance of filty-nine feet. It is from eighteen inches to three feet thick and yields quartz of a character very similar to the Mina’ Rica. ‘The rock is hoisted from both of these mines by horse power, the mining being done by Corbishmen, on contract, at fixed prices per foot for sinking or driftiug. The richest lode yet discovered in the district, is believed to he THE CUMMINOS & HADLEY, Owned by the parties whose name it bears, and who sre making a vigorous effort to tes‘ its permanence and value, and with very fair proapects of success in developing a valuable mine, ‘This vein is crossed hy two dykes of hard slate about ten fect apart, between which the shaft has been sunk to 2 depth of ninety feet. No attempt has been made to drift through that onthe north side, and its thickness is not known, but the ore on the south side of the sha{t, has been found to be about three feet wide at the top, and to narrow gradually as it goes down, until atthe depth of ninety feet it almost disappears, and the two portions of the vein are almost united. The vein at the hottom is about four feet in width, while its average thickness is fully twenty inches. 1 visited the mine on Saturday afternoon, the 17th instant, in company with Mr. Robert Briggs of West Point. We were informed that the rock from this vein, worked at Carltou’s mill, which is ahout halfa mile distant, had averaged from $140 to $150 perton. A short distance south of this is the Aino lead, owned by Messrs. Carlton and Fischer, which has been opened to a depth of 100 feet. It dips to the west,at an angle of thirty-three degrees, and is about one foot inaverage width. The quartz differs from most of that in the district in containing no sulphurets. It has yielded ahout $85 per ton in free gold. On Monday morning I started to visit the mines in the neighborhood of Skull Flat, and nn the way, fell in with Mr. A.M. Harris, of Sandy Gulch, who was visiting Skull Flat on business. The oldest and most productive mine in this vicinity is LA SACOTERRE, Sitnated about half a mile sonthwest of the Skull Flat mill, and owned hy the Cassner Bros., who are also owners of that mill. ‘The lead was first discovered in 1855, since which time over $100,000 are said to have been © taken out. It has been opened bya shaft to a depth of 120 feet, while on the level of the bottom of this shaft a tunnel has been driven into the hill a distance of 300 feet, eighty feet of which is on the vein. Its usual width is from fifteen inches to two feet, though I was told that at the bottom of the deepest shaft, its width wag three feet. The average yield of the rock worked from this vein for the past . eleven years is set down at $80 per ton. \ -.