Relative efficiency of certain stamp-mills in Gilpin County, Colorado. I have taken from the report the names of mills, number of stamps running, weight of stamps, fall in inches, number of drops per minute, and tons of ore crushed per day. To these columns I have added one giving the total horse-power developed and one giving the tons of ore crushed daily per horse-power developed. These figures are obtained by separate calculations for each mill. At the bottom of the table certain totals and averages have been added. The total number of stamps explains itself. The total weight is arrived at by multiplying the number and weight for each mill, and then aggregating these products. The total horse-power, again, is a simple addition. The methods of obtaining averages require more detailed comment. In several columns the numerical differs decidedly from the dynamical average; thus, if we multiply the number of stamps in each mill by their fall, add these products, and divide the sum by the total number of stamps, we obtain a numerical average of the fall; and a similar process gives us a numerical average of the number of drops per minute; but if we should attempt to deduce from the total number of stamps, their average weight and (numerical) average fall and speed, the total horse-power developed, we should obtain a result different from that which is arrived at by simply * Estimated, generally from maxima and minima given. Thus 15 to 20 is put at 178. adding the totals given in the column of horse-power developed. The reason is obvious. In taking a merely numerical average we leave out of account the weight of the different stamps; it is therefore necessary to multiply the number and weight of stamps of each mill into the drop and to divide the sum of these products by the aggregate weight of all the stamps of all the mills. In calculating the average speed the drop, as well as the number and weight, must be included. This can be best illustrated by an example, comprising, for the sake of simplicity, only two mills. I take, almost at random, Nos. 2 and 11 from the table, viz: Black Hawk: 60 stamps, 850 pounds, 14 inches, 15 drops, 27 horsepower. Bates: 8 stamps, 425 pounds, 12 inches, 30 drops, 3.1 horse-power. The totals would be 68 stamps, 54,400 pounds, and 30.1 horse-power. The numerical averages are obtained as follows: 31.68 horse-power, whereas the aggregate horse-power, as we know by calculating it separately for each mill, is 30.1 horse-power. The dynamical averages, on the other hand, are obtained as follows: Fall.-60 x 850 = 51,000 51,000 × 14714,000 Average speed=11,934,000-754,800-15.81 drops per minute. 13.87 If now we calculate the total horse-power upon these dynamical averages, we have 54,400 X x 15.81 33,000-30.1 horse-power, which agrees with the total from the table. 12 A third set of averages, which I call, for convenience, gross averages, is obtained by disregarding the number as well as the weight of stamps, and considering only the number of mills. Thus, in the case just given, the gross averages would be 637.5 pounds, 13 inches, and 22.5 drops. This has little value for accuracy; but it is the usual manner in which casual observers estimate the matter, and it shows what is the fashion or prevailing custom among owners of mills. Bearing these distinctions in mind, we have the following results, based on a comparison of thirtythree mills: Total number of stamps, 656; average number in each mill, 19.88; total weight of stamps, 396,110 pounds; average weight, 603.83 pounds; average weight reckoned by mills, without reference to their size, 580.27 pounds; average fall in inches, reckoned from the number of stamps only, 15.34; average fall in inches, reckoned from the number of mills only, 13.41; average fall in inches, reckoned from number and weight of stamps, or average fall of the average stamp of 603.83 pounds, 13.53; average speed by stamps, 29.69 drops per minute; average speed by mills, 30.82 drops per minute; average speed of the average 603.83pound stamp, falling 13.53 inches, 28.31 drops per minute; total horsepower developed, 383; average per stamp, (obtained by dividing by the total number of stamps,) .58; horse-power developed by the average stamp at average fall and speed, (calculated from the dynamical averages,) .58, which necessarily agrees with the foregoing; average per mill, 11.60 horse-power; total number of tons crushed daily, 537; average per stamp, .82; average per mill, 16.27; total number of tons crushed by the development of thirty-three horse-powers, one in each mill, 51.16; average per mill or stamp, numerically, 1.55; actual daily product per horse-power developed by the average stamp, 1.40 tons. These figures admit of further profitable discussion. The difference between the gross and dynamical averages of weight of stamps indicates that the larger mills carry, on the whole, heavier stamps. The difference between the gross and dynamical averages of fall is slight, while both of these are considerably less than the numerical average, showing that the larger mills, on the whole, adopt a greater fall than the gross average, but the greater aggregate weight of metal in the smaller mills nearly restores the dynamical average to the prevailing fashion, as shown by the gross average. The differences in the averages of speed are more difficult to explain. It appears that 30.82 drops per minute is the fashion, and that the few large mills running at 15 and 16 do not reduce the numerical average below 29.69. But when the fall is taken into consideration, it appears that the slow-running stamps (as might be expected) drop further, thus increasing their effect, and reducing the real effective average speed to 28.31 drops per minute. The difference between the dynamical and numerical averages of daily product per horse-power shows that the mills developing less than 11.6 horse-power crush, on the whole, slightly more in proportion than those of greater capacity; but in view of the very great variations in the final column of the table, this residual difference is comparatively insignificant, and it may be assumed that deficiencies in economy are pretty equally divided between the two classes. If the matter turned upon the daily management only, the larger mills being presumably under more skillful management, might be called upon to show better results; but the conditions here discussed are mainly those of original construction; and some of the largest mills in this table are among the oldest and the worst. How far is this exhibit invalidated by the conditions of discharge, size of screens, etc., and hardness of rock, not included in it? By the former, I think, not to any great extent, as it may safely be assumed that these conditions have been made as favorable in every case as the form of the battery and the necessities of amalgamation will allow, and, moreover, that the mortars and screens are of one general pattern, the California high mortar not being in favor, and Russia iron, punched, being preferred to wire screens, and slits to needle-holes. . Variations in the diameter of shoes are, I must confess, more common, and constitute an element which I have disregarded only because the data are wanting. But this element, if included in the discussion, would strengthen the conclusions arrived at, since the mills having the largest diameter of shoe, as the Black Hawk and Gregory, which have 9-inch shoes, do not reach on that account even the average efficiency. It may be inferred, therefore, that in crushing average quartz the conditions of weight and speed are more influential than slight variations in the crushing surface. The hardness of rock is a serious disturbance to the calculations. Surface rock differs considerably from the deep quartz in this respect, and doubtless affects unfavorably the apparent results of the larger mills. It should be distinctly understood, therefore, that the general conclusions deduced from the table at the beginning of this chapter are modified by special conditions. If any mill shows a considerable departure from the average effectiveness, it is fair to inquire what kind of rock it is crushing before concluding that its superior or inferior capacity is due to the weight, drop, and speed of the stamps. With these qualifications, we may assume that the average or normal stamp of Colorado weighs about 600 pounds, drops about 13.5 inches, about 28 times a minute, and crushes 82 tons daily, or about 1.4 tons per horse-power developed. This is probably less than the average efficiency, measured in the same way, of California stamps. It is, indeed, somewhat in excess of the estimate of Mr. Ashburner, whose observations some five years ago led him to fix upon 1.25 tons daily per horsepower, as the average result of the stamp-mills of California, but improvement of construction since introduced have increased their capacity. The mill at Lone Pine, Inyo County, (p. 22 of my last report,) is said to crush per horse-power, daily, 3.81 tons, with 650-pound stamps, dropping 8 inches, 60 times per minute. The table of quartz mills in Tuolumne County, California, (Ib., p. 26,) gives the following results when reduced: The stamp-mills of Sutter Creek mining district, in Amador County, California, (Ib., p. 34,) show, by a similar calculation, the following results: The table of quartz mills in Eldorado County, California, (Ib., p. 37,) yields, under discussion, the following results: The quartz mills of Colfax district, Placer County, (Ib., pp. 39, 42,) show: Some of the quartz mills of Nevada County, California, show the following results, (see report of 1870, pp. 44, 200; and report of 1869, pp 23, 26, 27, 29 :) * Estimated. H. Ex. 10-25 |