During the last few years, one of the great problems in the milling of all ores has been that of grinding. This subject involves not merely the cost of the operation, but also the selection of the proper degree and character of grinding to yield the best metallurgical results on the given ore. Considering the diversity of machinery, one is led to wonder at the variety of grinding methods employed, even when realizing that metallurgy demands varying products.

In an attempt to investigate the relative grinding resistances of a number of ores now being milled in this country and Alaska, the management of the Portland mills requested samples of average mill-run of ore

from various companies. The request met with a ready response, indicating the desire of all operators to gain information on the subject.

The difficulties involved in this investigation were numerous, lack of time for outside problems during this strenuous period being a serious one. Also, we were unable, in the time, to obtain a correct 150-mesh screen; in the screen analyses tabulated and plotted herewith, the 150- mesh screen was used merely to protect the 200-mesh screen, not to ascertain points on the curves.

The experimental grinder was a small iron tube-mill, 8 by 12½ in., in which was placed a definite number (74) and weight (3450 gm.) of ¾-in. steel balls, 1 lb. water and 1 lb. ore. To obtain uniform conditions, each ore was first crushed and screened, and from the sized products a ‘‘standard feed” was artificially prepared, the same standard being adopted for all tests in that particular series. The prepared feed was placed in the little mill, and this was allowed to revolve at 84 r.p.m. for a definite time; the sample was then dried and screened. The whole operation was then repeated for other periods of time.

The mass of data accumulated by these tests is only partially given below, as time at present will not permit a complete analysis. I realize that the method here adopted has its drawbacks, and yet, with all conditions identical, the screen tests of the products should at least give an indication of the relative grinding resistances of the ores.

One objectionable feature is the small size of the grinder, although the labor involved in drying, cutting down, and screening the product of a larger machine would be burdensome. The small size also necessitated a comparatively fine feed.

The method adopted for computing the results is that of Rittinger, based on the law that work done in crushing is proportional to the surface exposed by the operation, or to the reciprocal of the diameter. For plotting the screen tests, the mesh (reciprocal of diameter) and the cumulative per cent, of oversize are used as coordinates. The area between the feed and product curves will be proportional to the “apparent work” done. The apparent work is in turn inversely proportional to the resistance of the ore to grinding; hence the area between the curves is inversely proportional to grinding resistance.

Unfortunately, we are unable to deal accurately with the material below 200 mesh, which is where most of the work done is represented. Microscopic measurements seem to offer the only accurate method. Curves plotted in the area below 200 mesh seem to follow no definite law, as that of a hyperbola. Many operators may feel but little interest in what happens after a certain fineness (say 48 mesh) is reached, but this does not alter the necessity of measuring the total work done on the whole of the ore.

As a method of measuring the work done in the region below 200 mesh, I offer the following suggestion, not asserting that it is accurate as to absolute results, but only that it yields additional evidence as to the relative grinding resistances of ores.

Product work (Rittinger’s law) = H + P + G + a1 + a2 + H ∞ + P ∞ — (H + a1 + H ∞)=P + G + a2 + P ∞. (Sen diagram, p. 237.) For a given ore, assume that the material, in the feed (say 20 per cent.) below 200 mesh has the same value in mesh-tons as the finest 20 per cent, in the product, that is,

a1 + H ∞ = P ∞ + H ∞, or a1 = P ∞

Substituting this value for P ∞, and calling (a1 + a2) = A,

Product work = P + G + A

I have plotted the diameters and cumulative percentages as coordinates. The last definite point in diameter is 0.0029 in. (200 mesh); the curves must also pass through the point corresponding to 100 per cent, retained and zero diameter. The last three known points—0,0082 or 65 mesh; 0.0058 or 100 mesh; and 0.0029 or 200 mesh—are shown

in plots No. 1, 2,3,4. The extension of the curves through the unknown area between 0.0029 in. and zero is made with reference to the known curve section. Subsequent investigation may require some of these curves to be slightly altered. The ratio between mesh-tons of the 5¬min. and the 10-min. products does show a proportion fairly close to 1:2, From the curves thus drawn, I have taken points representing 0.0029 in,. (345 reciprocal), 0.002 in. (500 reciprocal), 0,001 in. (1000 reciprocal), 0.0006 in. (1667 reciprocal), with their corresponding cumulative per cents, and have replotted these as No. 5 and 6 (only the curves for the 10-min. grinding being shown). From these curves, the so-called “product area” G + A, of material below 200 mesh, is

obtained; this, added to the product area P of material above 200 mesh, gives the total mesh-tons to be used for comparison with the mesh-tons of other ores. These totals are recorded in Table 3.

Screen analyses of the products after 5-min. and 10-min. grinding, starting with the standard feed of which the analysis can be observed in the diagrams, are given in Tables 1 and 2. As a matter of further interest, these analyses are plotted according to the Tyler direct cumulative diagram method in Figs. 7, 8, 9, 10.

**Discussion**

**C. Q. Payne, New York, N. Y. (written discussion).**—The method adopted by Mr. Lennox is a very interesting test of the practical application of Mr. Gates’ crushing-surface diagram to a great variety of gold and copper ores. His method of dealing with the material below 200-mesh is also a distinct contribution to the subject, although, as he suggests, it seems likely that some microscopic measurement of this material may be advisable before the mesh reciprocals of its group particles can be dealt with as accurately as can those coarser than 200-mesh.

In examining the general results shown in Table 3, it is somewhat puzzling to perceive why Calumet & Hecla jig tails should show a crushing resistance 3½ times greater than that of the ore from the Ray Consolidated copper mine. The latter is, I believe, an altered Pinal schist containing over 70 per cent, silica, and the composition of the former probably does not differ greatly in this respect. I also note that the crushing resistance of Calumet & Hecla jig tails compares with that of Miami ore in the ratio of about 2 to 1. Hardinge mills are now being employed to crush Calumet & Hecla conglomerate, and also Miami ores on a very large commercial scale, and it is interesting in this connection to note that M. K. Rodgers gives the relative crushing duty of 1 hp. on C. & H. conglomerate and Miami ore as 1:3.75, the feed in both cases being ¼ in. size. The inverse of the above figures would represent the relative crushing resistances. At a later date Mr. Gates pointed out that the crushing-surface diagrams of the two ores, on material coarser than 200 mesh, give for C. & H; conglomerate 12.5, and for Miami 34.0 mesh-tons per hp.-hr. This would indicate the relative crushing resistance of these ores to be 2.72:1. However, this difference in the crushing resistance of these two ores, as measured by Mr. Lennox’s small -tube mill and by the Hardinge mill may be due to the fact that the crushing-surface diagrams in the two cases are not comparable.

A possible question in connection with these tests is whether the determination of the crushing resistance of an ore may not be difficult to measure owing to what may be called “screen resistance.” Of two ores which may have the same crushing resistance when measured by a 4- or 8-mesh screen, for example, one may show a much greater crushing resistance than the other when measured by a 200-mesh screen, owing to the presence of a certain amount of mica or other flaky mineral unlocked at, say, 50 mesh, but only reduced to pass a 200-mesh screen by very prolonged grinding. The micaceous ore would thus show a different crushing-surface diagram from the granular ore, although the same amount of energy might have been expended in crushing it. The proximity on the scale of crushing resistance (Table 3) of such a hard and tough ore as the Homestake to a comparatively soft ore like that of the Nevada Consolidated for example, has suggested the idea that a difference in the “screen resistance” might perhaps here have counteracted a greater difference in the crushing resistance than the results actually show.

The interesting and valuable work done at McGill University by Professor Bell seems clearly to establish Rittinger’s law as a better measure of the energy absorbed in crushing than Kick’s law. The method of recording the work of crushing by the crushing-surface diagram, which has been developed and illustrated by Mr. Gates, also marks a very notable contribution to the subject. The crushing-surface diagram is fascinating from its very simplicity. But are we not expecting too much from it until we have corroborated it, and perhaps corrected it, by means of certain more exact physical measurements on a wide range of minerals and ores? Many ores consist of a more or less loose aggregate of different minerals, and it may help toward clear thinking if we subdivide the subject, and apply the laws of crushing only to the breaking up of aggregates, as performed by coarse crushing, in which surface areas can be accurately measured by screen analysis; and then apply the laws of grinding to the reduction of small-sized particles of homogeneous composition, the surface areas of which are difficult to measure by screen analysis alone.

For illustration, if we knew the number of heat units developed, and therefore the energy absorbed, in grinding 100 gm. of a given ore or mineral, so that it would all pass a 200-mesh screen, could we not then develop an energy unit which would be a physical constant for that particular ore or mineral? With a number of such physical constants determined for various ores, we would then have more accurate means of measuring not only the grinding resistance of the ores, but also the mechanical efficiencies of different machines employed in grinding them. Such an energy unit as I have suggested might require some other method than screen analysis to estimate the surface exposed, since the unit should be independent of the habit of crystallization of the component ore minerals, and should be directly related to their molecular structure, on which their coherence and mechanical resistance to grinding must ultimately depend.

The establishment of accurate methods for measuring the energy absorbed in crushing and grinding ores is a matter of great importance. Most mining engineers realize the backward state in which the art of crushing now lies, largely for lack of accurate units of measurement. Considering the subject broadly, and including the crushing of cement rock and clinker and pottery materials, it is probable that the average efficiency of crushing as a whole does not exceed 20 to 25 per cent. When we recall that the efficiencies reached in the concentrating, cyaniding, and flotation of ores frequently exceed 90 per cent., it is evident that the first step in the ore-dressing and allied industries is worthy of more serious attention than it has yet received.

**Luther W. Lennox (author’s reply to discussion)**.—Mr. Payne calls attention to the relative grinding resistance of Calumet & Hecla and Miami ores, as pointed out by Mr. Rodgers and by Mr. Gates in comparison with the figures obtained in my Table 3. As pointed out by Mr. Gates, the relative grinding duty of one horsepower on Calumet & Hecla and Miami ores as 1 to 3.75 obtained by Mr. Rodgers takes into consideration only the tonnage and power, and ignores the mesh of the product and also the feed, except that it passes ¼-in. mesh. After plotting, Mr. Gates arrives at figures that indicate a relative grinding resistance of 2.72 to 1 instead of 3.75 to 1.

In this connection I wish to call attention to work on “Hardinge Mill Data” by A. F. Taggart in which are published tests on various ores, among them being Calumet & Hecla, Miami, and Arizona copper. Plotting feeds and product and taking into consideration only the plus 200-mesh zone, combined with the data on tonnage and power in these tests, we find the following relation: Card No. 34, Calumet & Hecla relative grinding resistance being assumed as 1.33. From the three tests Nos. 107, 108, and 80 Miami become 0.41, 0.81, and 0.45, respectively, as the relative grinding resistance, while Arizona copper, card No. 142, gives 0.64. The standing of these three ores in my Table 3 will be found to be 1.33 for Calumet & Hecla, 0.62 for Miami and 0.61 for Arizona copper, where only the plus 200-zone is considered.

Two factors might easily enter into the tests as printed by Mr. Taggart and those referred to by Mr. Payne, either one of which could alter the apparent grinding resistance of these ores. The ores might or might not be typical of the present ores. Then again the tests referred to were not necessarily run under such conditions that it would be fair to compare the ores with reference to grinding qualities. The results on Miami would indicate this, as they do not give consistent data.