The extent to which sizing by sieves should be carried, as a preliminary to the separation, by jigging, of minerals of different specific gravities, has been a matter of controversy for many years. The subject has been investigated by several authorities, yet the ground does not seem to have been completely covered, nor are the questions involved entirely settled. For my present purpose I shall refer to but three investigators—Rittinger, Munroe, and Hoppe.

In seeking additional light, I have gone over part of the old ground which has been considered satisfactorily settled; and since these preliminary tests have thrown light on some points, they have been included in this paper.

In the investigations here described, I have confined myself, for several reasons, wholly to small sizes—grains of 0.1 inch in diameter and less. Rittinger’s work was mainly done upon larger sizes, and there is much need among millmen of information concerning the smaller sizes. Moreover, these sizes brought the investigation within the means at my disposal.

The laws that have been claimed as the laws of jigging by the several authorities are:

1. The law of equal-settling particles.
2. The law of interstitial currents.
3. The law of acceleration.
4. The law of suction.

The first of these has been considered by investigators, generally, to be the most important of all, and the larger part of the work of jigging is thought to be governed by it. But that it does not cover the whole of jigging is clear to all; and to account for the increased efficiency which we may call the extra jigging-catch, the other three laws have been advanced.

The investigation described in this paper was undertaken to determine, as far as possible, to what extent each of the four laws contributes towards the results of jigging. The discussion will be taken up in the order indicated above.

Equal-Settling Particles

If we drop into a deep vessel filled with water an unsized product containing particles, say, of galena and quartz, which have been thoroughly wetted, and all of which will pass through a limiting-sieve of 10 meshes to the linear inch, we shall find that, after the short interval of acceleration, each particle will fall at its maximum velocity towards the bottom. These velocities, if the particles do not interfere with each other, and if they are all cubes or spheres, will depend upon two things, namely, the specific gravity, and the size of the grains. Of two particles of equal size, but different specific gravity, the heavier will fall the faster. Of two particles of like specific gravity, but different diameter, the larger will fall the faster. Evidently, therefore, any larger particle of the quartz will have the same velocity as a certain smaller-sized grain of galena. These two grains are said to be equal-settling particles.

Rittinger gives, in his treatise, four formulas to represent the relation between diameter of grains and rate of falling in water for irregular-shaped grains:

In which V is the velocity in meters per second; D, the diameter of particles in meters, and δ the specific gravity of the minerals.

From the formula for the average, he computes the ratio of the diameters of quartz and galena particles that will be equal-settling in water. Taking the specific gravities, as determined by me, viz., for quartz, 2.640, and for galena, 7.586, and using his formula for the average grain, we should have,

For quartz, V² = 5.9536 D1 x 1.64,
For galena, V² = 5.9536 D2 x 6.586.

For equal-settling particles, we equate the two values of V², and deduce:

D1/D2 = 6.586/1.64 = 4.015.

That is to say, the particle of quartz will have a diameter four times as large as the galena.

The minerals employed in the investigation described in this paper are given in Table I., with their specific gravity, and the multiplier which gives the diameter of the equal-settling grain of quartz, computed from Rittinger’s formula for average grains.

Rittinger (1866) considers the law of equal-settling particles to be the law of jigging, and infers in consequence, that a jig should be fed with particles of galena and quartz, for example, that are in no case equal-settling. To prepare the sands for a series of jigs, then, there will be required a series of sieves graded according to the diameters of their meshes. The ratio for the diameters of these meshes for jigging quartz and galena, for example, will be 1 : 4, and for the other minerals, as the multipliers given in Table I.

Upon this theory, the continental system of close sizing before jigging has been developed.

With a view to studying this question, experiments were instituted upon the rates of falling in water, and for this purpose, a sorting-tube of the size indicated in Fig. 1, and marked at a, b and c, was mounted vertically and filled with water to the top. Each mineral was sized by a series of sieves, the values of the holes in which were obtained with great care.

Table II. shows the manner in which the size of the grains delivered upon each sieve was computed. For convenience the sieves were arranged in a nest, see Fig. 2, so that when the nest was shaken, a sample of mineral placed on the upper sieve delivered all its different sizes, each upon its own sieve. Fall velocities were obtained by allowing a number, perhaps 50, of grains of the same size to fall

the distance of 8 feet from a to c in the sorting-tube, and noting the period required for the passage of the fastest grain, and also the time required for approximately 90 per cent, of the grains to pass. This proportion of 90 per cent, was preferred to the observation of the slowest grain, because the slowest often lags an indefinite distance behind. The results of these tests are given for fastest grains in Table III., for slowest, in Table IV.

The specific gravities are the result of three or four closely agreeing tests. The diameters are given in fractions of an inch; the velocities, in inches per second. In all cases the grains were thoroughly wetted, and in many cases they were boiled in water, before being dropped.

Some remarks are called for by apparent inconsistencies in Table III. In nearly every instance, cassiterite fell faster than antimony, although its specific gravity is lower. I explain the low specific gravity given by the presence of a little quartz in included grains with the cassiterite, while the free grains probably have a higher specific gravity than antimony, and fall ahead of that metal, as they should. The inconsistency between chalcocite and magnetite is due to the shape of the particles; magnetite has rounded or cubical grains ; chalcocite is very flat and scaly. Copper does not lead galena nearly so much as one would expect. This is due to the shape of the particles. The copper was Calumet and Hecla stamp-copper, as free as possible from rock, pieces being all more or less flattened, and the finer particles were to some extent arborescent and leaf-like, while the galena was taken from large pure cubes of Wisconsin mineral. The work upon magnetite broke down at the 60-mesh sieve, sizes below attracting each other so much that the large flakes resulting made a test impossible.

The fall-velocities for the slowest particles, that is, the particles which fell at a period when 90 per cent, (as estimated by the eye) had fallen, are given in Table IV. These are perhaps of less value than those of the fastest particles, since there is a certain personal equation which may vary. But for other reasons, as I think I shall be able to show later, these values are of very great interest and play an important part in the whole ore-dressing discussion. The values marked and all below them in the columns were measured upon 1-foot fall instead of 8 feet, and are therefore somewhat better determinations than the values for the corresponding sizes in the other columns. Towards the lower ends of these columns frequent inconsistencies will be noted. They are, however, not very serious, and are accounted for, partly as in the case of the fastest grains, Table III., and partly by the difficulty in judging the 90 per cent.

That the meaning of the figures in Tables III. and IV. may be more plainly shown to the eye, curves may be drawn representing the fastest and slowest grains for each mineral. The points of actual observation, and those of the corresponding calculated parabola, are shown in diagrams 1 to 13 inclusive.

The parabolas that are plotted in these diagrams with the fall-velocities were calculated as follows: For example, take the fastest grains of galena. A point is selected on the .05 inch diameter line which would apparently bring the parabola well among the observed points. Its velocity, 15.2 inches per second is read upon the upper line. We then fill in the formula for the parabola :

V²/D = C

V= velocity in inches per second.
D = diameter of the grain in inches.
C= a constant.

15.2 x 15.2/.05 = C = 4621.

We then assume different velocities and solve the equation,

V²/D = 4621.

to get the values of D. D and V being known, the plotting of the curve is easily done.

Table V. shows, for these thirteen minerals, both Rittinger’s and the author’s parabolas for fastest and slowest grains.

The discrepancy between the two sets of parabolas is striking. That Rittinger’s values for the slowest grains should be less than mine is natural, since I did not wait to get absolutely the last grain, but marked the moment when 90 per cent, (estimated) had passed. In regard to the fastest grains, however, my method of letting 50 grains fall at a time selects by natural process the fastest grains of the 50, and should yield higher results than the method of picking out compact grains by the eye, and letting them drop one at a time. The test makes a more perfect selection than can the eye. Individual grains were tried, and found to confirm this view.

The computations made by A. E. Woodward and myself from Rittinger’s formulas, and published in our paper on this subject (Trans., xviii., 644), must therefore give place to the present figures obtained by actual test.

To compare further the results obtained by the fall-tube with those of Rittinger, the ratios of diameters of the particles of the several minerals to those of equal-settling particles of quartz, were determined as follows: A number of velocities were assumed, and corresponding diameters of the fastest grains for each mineral were taken from the curves of free-falling particles. These values are here tabulated. (See Table VI.)

From these figures for fastest grains were computed multipliers to be used in obtaining the diameters of equal-settling particles of quartz. These are given in Table VII., in the final column of which Rittinger’s multipliers for average grains are also given.

Upon inspection of the curves, for free-falling grains, in diagrams 1 to 13, three facts are noticed :

1. The lines of fastest grains, and of slowest grains, depart very considerably from the parabola, particularly on the smaller sizes.
2. The space between the two lines of fastest grains and slowest grains is a wide zone or belt.
3. The width of the zone may vary greatly, depending upon the shape of the particles—for example, the copper zone is much wider than that of the galena.

With regard to the first point, Rittinger makes note of the fact that his formulas fail for finer sizes. These curves, therefore, place on record the degree to which they have failed with the minerals here tested. We see that the velocity of any mineral which tends to break into flat scales, or elongated grains (for instance, copper or chalcocite), is so modified as to change its class entirely. Thus, the

curves for fastest grains of galena and copper are almost identical, although their specific gravities are widely different.

Each mineral has, therefore, its own “ personal equation,” and minerals cannot be classed by specific gravity alone. Hence, no formula can be founded on specific gravity and sieve-size only. It must be modified by the coefficient of each mineral for practical use.

The second point, also, was recognized by Rittinger, as is shown in his formulas for fastest grains and slowest grains already quoted in this paper. But the deduction which followed from adopting a mean value for these grains has been somewhat of a puzzle to me.

Let us take an example from the curves of sphalerite (blende) and quartz. A mean grain of quartz, of .07 inch diameter, will fall 6.7 inches in one second. Following down the sphalerite curve, we find that a mean grain of sphalerite of .039 inch diameter settles 6.7 inches in one second. If then, we were to use these mean

values, as Rittinger recommends, for obtaining our sieve-scale, we should conclude that, with two sieves, one having holes of .07 inch diameter and the other of .039 inch diameter, the fastest grain of quartz between these two sizes has less speed in settling than the slowest grain of the sphalerite, and therefore this product would be jiggable, according to the law of equal-settling particles. But, in fact, the fastest grain of quartz falls about 8.5 inches in one second, while the slowest grain of sphalerite settles only 5 inches in one second ; hence, the product is un-jiggable according to the law of equal-settling particles. Indeed, these zones of quartz and sphalerite lap over on each other, even on a single sieve; and if the law of equal-settling particles were the only law of jigging, sphalerite and quartz could not be sized closely enough to prepare them for jigging.

The converse seems, therefore, evident, namely, that under no circumstances is the law of equal-settling particles the whole law of jigging.

Interstitial Currents

Professor H. S. Munroe tested, in 1889, the effect of confined space upon falling particles. He timed different sizes of lead shot, or spheres, falling in a narrow glass tube filled with water, Fig. 3a. If d equals the diameter of the shot, and D that of the tube, he found that the larger the fraction d/D the greater was the retardation or loss of velocity by the shot. When this fraction equals unity, the shot stops. He applies this principle to the question of equal-settling particles as follows : If particles of quartz, for example (Fig. 3b), are represented by the larger circles, and those of equal-settling galena by the smaller circles, then, when these mixed particles are settling en masse, or are held in suspension by a rising current of

water, each particle may be considered to be falling in a tube, the walls of which consist of the surrounding particles. Substituting a circle in each case for the imaginary tube, we have Fig. 4, representing the conditions for galena and quartz, the outer circle representing, in each case, the imaginary tube. A glance is sufficient to show us that the fraction d/D is much smaller for the galena particle than it is for the quartz. The galena particle will, therefore, be less impeded in its fall than the quartz, and, in consequence, the particles of galena that are found adjacent to the particles of quartz will be smaller than the ratio which the law of equal-settling particles would indicate. Professor Munroe infers that these interstitial currents account for the fact, made use of in the mills, that a jig will save galena which is much finer than would be the case if the law of equal-settling particles was the only law of jigging. And he finally proves, by equating his formulas, that the ratio of diameters for the quartz and galena, after the interstitial currents have brought the grains to equilibrium, will be as 30 : 1.

Prof. Munroe says further (Trans., xvii., 650):

“We see, therefore, that if the material to be treated is sized between the limits of 1 mm. and 30 mm., it will be possible to separate the quartz from the galena. All the spheres of galena will have a greater falling-velocity than the 1 mm, grain; and all the spheres of quartz will rise more readily and fall more slowly than the 30 mm. grain.”
I have recently attempted to ascertain by experiment to what extent this law of interstitial currents acts upon irregular particles. For this purpose, I constructed a pointed tube of the form shown in Fig. 5, which consists of a tin cone, a, with an overflow, f, united to a pointed tube of glass, b, by a rubber connector, c, and having a water-supply, d, regulated by the cock, g, and a bulb, e, joined by a rubber connector, h. If this apparatus be filled with water, and a sample of mixed sands, which pass through a ten-mesh sieve (an ordinary 8-ounce bottleful represents the quantity used), be charged gradually at the top, and a slight upward current of water be admitted through the tube, d, the sands will rapidly assume a condition of approximate equilibrium. Here we have sands, say, of two specific gravities, and of sizes ranging from ten-mesh to dust, which are held in gently-moving suspension by the slow upward current. This device presents, therefore, the conditions necessary to test the limits of interstitial currents.

By means of this pointed tube, the behavior of the minerals named in Table VIII., taken by pairs, has been tested.

Each of these pairs was treated in the pointed tube (Fig. 5) by allowing from one half hour to two hours for the grains to come to equilibrium; and since the larger part of the sorting is done in the first minute, we may consider that the work is practically completed in half an hour.

While the sands are still kept in gently-moving suspension, the current is slightly slackened by means of the cock, g, and the heavier grains are allowed to find their way down into the bulb, e. When the bulb is full, the rubber connector, h, is pinched with the thumb and finger, and the bulb is replaced with a new one, which has been completely filled with water, care having been taken to remove the bubble of air from the neck. In like manner the second bulb is filled and removed, and a third, a fourth, and so on until all the sand, to the finest slimes, has been drawn off. The overflow will be found to contain very light particles, and also a few particles carried over by greasy flotation. This should be caught, and may be called the last bulb or drawing.

Each of these drawings, which were ten in number, was carefully dried and then sized in the nest of sieves (Fig. 2). The sizes, for example, in the galena series (see Plate II a), in the fifth flask, were found to be perfectly pure quartz down to the 30-mesh sieve. The 40-mesh contained a little galena; the 50-mesh was nearly all galena, with a little quartz; and all the sizes below 50 were pure galena.

The twelve pairs of minerals were all treated in this way, and the photographs (Plates I. to XII. inclusive) show the results obtained in the form of a graphical plot of the actual grains. The vertical columns Nos. 1, 2, 3, 4, etc., represent the successive bulbs. The horizontal lines indicate groups of particles resting upon like sieves.

This series of photographs shows very prettily what can be done with a pointed tube in the way of water-sorting, preparatory to sizing. A series of tables (Tables IX. to XXI inclusive) has been prepared to accompany the photographs. These tables, giving the estimated percentage in every hill of the mineral which was to be concentrated, will be found convenient in interpreting the photographs.

In the galena-quartz photograph (Plates II. a, II. b) there are scarcely any mixed grains until slimes are reached. The ninth and tenth drawings are much mixed, and always will be so, coming from the apparatus here described. Their separation will be the subject of another paper.

The same is true of the copper-quartz photograph (Plate I.), except that the sample contained none of the very finest slimes, and therefore the ninth and tenth drawings are practically pure quartz.

Following through the various minerals and gravities, we see a general set of features possessed in common, but changing a little with each successive photograph. First, we have in copper a range of clean, pure quartz hills from No. 4 on 12 to No. 9 on 100. We also have a clean range of copper hills from No. 1 on 12 to No. 8 slimes, and, between the two, a valley almost destitute of grains, which is widest from No. 4 on 20 to No. 5 on 30, and narrows very much at No. 8 on 120.

In arsenopyrite (Plate VI.), the valley is gone on the 100-mesh line, and we have a plateau instead. In chalcocite (Plate VII.), the plateau has reached up to the 50-mesh line. In pyrrhotite (Plate IX.), it has reached the 40-mesh line. In epidote (Plate XI.), the plateau has disappeared below 24-mesh, and a single wide range of hills has taken its place.

The above features are due to the convergence, towards the hill marked No. 10 slimes, of the two approximately parabolic curves.

A single plate (Plate XIII.) is given to illustrate a three-mineral separation, in which slate (specific gravity, 2.735), barite (specific gravity, 4.127), and galena (specific gravity, 7.586) are the three minerals. Table XXII. accompanies it, giving estimated percentages in the hills.

The weights of the hills for three columns of each of Plates I. to XII. inclusive (except VIII.) will be found in the following Tables, XXV. to XXXVI.

They are absolute weights in every case except where a hill contained a mixture of two minerals. In such a case the total weight was obtained, the relative proportions of the two minerals were estimated by the eye, and the total weight was divided between them in accordance with this estimate.

In order to, throw light upon the question of interstitial currents, it was necessary to obtain the ratio of diameters for the particles of quartz and galena, for example, when the two minerals had arrived at equilibrium through the action of the upward current. The values given in Tables XXV. to XXXVI. for the whole series of minerals were used for this purpose.

The particles in any given column may be assumed to be in equilibrium because the light and heavy materials there drawn out together have had ample time to choose their partners.

The mode of computation for any given column or bulb, may be shown by taking as an example Plate II. b, and bulb No. 5 of

Tabie XXVI. Here the average diameter of the quartz particles was obtained by multiplying all the quartz-weights in column 5 by their diameters, and dividing the sum of the products by the sum of the weights. The galena figures in column 5, treated similarly, give an average diameter for the galena particle. This diameter of quartz is then divided by the diameter of the galena. In like manner computations were made upon all of the eleven minerals, and these interstitial factors are given for all the minerals except magnetite in Table XXXVII.

Lest the proportions of the two minerals (equal volumes) used in the pointed-tube tests (Plates I. to XII.) might have influenced the results, a trial-test for comparison with Plate II. b, was made, using a quantity of galena equal to about one-sixteenth of the volume of

quartz, instead of equal volumes of the two minerals. The 4th, 5th and 6th bulbs were sized, and gave hills apparently at the same points as shown in Plates II. a, and II. b. To demonstrate the point still further, weights and computations were made upon the 4th bulb (Table XXVII.), and yielded the ratio of the diameter of the galena particle to that of the quartz,

1: 5.966.

This ratio is practically the same as those given in Table XXXVII. for galena and quartz, and therefore demonstrates that the relative quantities of the two minerals have nothing to do with the law of interstitial currents. The ratio of diameter is fixed.

The foregoing experiments show that, under the conditions existing in the pointed tube, the diameter-ratio of galena and quartz in equilibrium together, when interstitial currents have done their whole work, is about 1 : 6 for particles ranging between 10-mesh and 100-mesh. They further show that interstitial currents have a real existence, and have decidedly advanced the ratio from the equal-settling particles of the free-falling test which is given by Rittinger as 1:4, and which has been found in this investigation for 10- to 12-mesh quartz as 1 : 3.75. My tests do not, however, substantiate the claim made by Prof. Munroe, that galena and quartz will not come to equilibrium in interstitial currents until a ratio of 1:30 for their diameters has been reached.

One or two interesting facts may be noted here, although they are one side from the main thread of this paper.

In the first galena trial (Plate II. a) it was found that fine galena appeared in the first drawing below 30-mesh. This may be attributed wholly to particles abraded during the subsequent sifting operation. To test the question, the galena-quartz lot was mixed up thoroughly and run over again (Plate II. b); and this time the fine galena, below the main range of galena hills is much reduced, proving the conjecture to be substantially correct.

Again, the fall-velocities of these different heaps were taken in a tube, Fig. 6, designed by C. Le Neve Foster, in which by inverting the tube the measure may be taken over and over. The results are here given. They show that, for example, on the 18-mesh line, grains of galena in No. 1 are faster than No. 2, and No. 2 than No. 3; also that the quartz Nos. 4, 5, 6 and 7 fall in that order, 4 being the fastest, and 7 the slowest, 4 containing the 18-mesh grains that are nearest to a cube, and 7 being the flat oyster shells that fall much slower. Results of these trials are given in Table XXXVIII.

In this test a group of 20 or 30 grains was timed. When the average grain passed the upper and lower marks the time was taken. The results are therefore averages. In the light of these facts the remarkable resemblance between these two tests of galena and quartz (Plates II. a and II. b) becomes more interesting; for it

is probable that, with certain latitude, the particles of the first test found their way back to the same identical heap in the second test. This principle of almost absolute predestination of particles for their own appointed places in ore-dressing is very important. It was mentioned by me in Chicago last summer, in discussing the paper of Oberbergrath Bilharz, under the heading “ Once Middlings, Always Middlings” (Trans., xxii., 700).

It will be noticed that the light color of the slimes of No. 9, in Plates I. to XII. is almost always marked when compared with its neighbors on the right and left of it. This being a truly sorted product, the finer dark mineral hides itself beneath the coarser light mineral. This shows in all the sets except copper, which had no slimes, magnetite, which had almost none, and epidote, the fine powder of which is extremely light colored, and of which the 10th slimes are therefore as light as the 9th.

The ultimate effect of an upward current of water upon sands of two specific gravities is shown in Plates I. to XIII. inclusive. This, then, is the ultimate equilibrium, which is approached but never quite reached by the pulsion-movement of a jig. The ideas conveyed by these photographs may be represented geometrically by Fig. 7, in which each cone stands for a column of particles of a single mineral species, as they would be arranged in an upward current of water. The heaviest grain with the largest diameter is represented by the diameter of the base of the cone, m; the lightest and smallest is represented by the apex of the cone, n. Two cones placed together, as a and b, represent two minerals of different specific gravity treated together in a pointed tube. Their vertices will be together, because the finest dust of the two will settle at almost the same rate; that is, with almost no velocity.

The largest particles, represented by the bases of the two cones,

will settle at very different rates, and the relative lengths of the cones may be chosen to represent the relative positions in the pointed tube of the coarsest particles of each of the two minerals. For example, the cone, b, may represent galena, and a, quartz, as they would appear when in equilibrium in a pointed tube. The cones, d and e, may represent quartz and arsenopyrite, and g and h may represent quartz and epidote. From these main facts the conclusion is natural. The particle, c, of galena, which is adjacent to a of quartz, is very small. It is much smaller than the interstices between the quartz particles, a. The same relation holds between all the adjacent particles of cones, aj and ej. The particle, f, of arsenopyrite is larger than e; it is about equal to the interstices between the particles of quartz, d; and consequently all the particles of arsenopyrite in the little cone,fk, will bear the same relation to the adjacent quartz particles, they all being equal to the interstices in the cone, dk. The particles, i, of epidote will be larger than the interstices between the quartz particles, g, and this relation will hold all the way up for adjacent particles in the cones, gl and il.

The ultimate result of the pointed tube, the Spitzlutte, the Lake Superior separator, and of the pulsion action of the jig, is to associate together particles of the two minerals that are to be separated, in which the ratio of the grains lies in one of these three classes:

1. The lesser, higher specific gravity grain is smaller than the quartz interstices.
2. The lesser, higher specific gravity grain is equal to the quartz interstices.
3. The lesser, higher specific gravity grain is greater than the quartz interstices.

These laws are important, and should be recognized and duly considered when mills are planned.