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By John Philip Zannaras

John Philip Zannaras (Registered Professional Engineer, Congress, Ariz.)- The authors show in their [Fig. 4] the cumulative results of grinding with two sizes of bails, one 30 mm and the other 20 mm. The Gaudin-Meloy probability for breakage for a single fall used by the authors in their paper is given by their [Eq. 6]. Another form of [Eq. 6] is given by Gaudin-Meloy in their paper as follows: [ ] From the definition of A given by Gaudin-Meloy it is obvious that A30 is greater than A., it therefore follows from the foregoing equation that according to the Gaudin-Meloy formula the probability of breakage for a single fall of all the balls in the 20-mm experiment was more than 2.25 times the probability of breakage in a single fall of all the 30-mm balls which is contradicted by the authors' experimental evidence in [Fig. 4] in which is shown that much more grinding took place with the 30-mm balls. In fact the authors present convincing evidence that the Gaudin-Meloy work is erroneous because their work is based only on a geometric configuration and on ambiguous and uncertain definition of A and disregards the fact that the distribution of fracture depends on other important and indispensable factors including the intensity of stress caused on the feed grain by the balls. That there is an immense and chaotic variation of stresses caused on the feed grains by the balls is shown by a formula, derived by this writer and published in 1955. The derivation of this formula is given in the Appendix of this discussion; it contains the variables in the operation of ball mills and is based on the science of mechanics-not on probabilities. [ ] where T is the unit stress in pounds per square inch produced by the moving load, h is the height in feet through which P has fallen, E is the modulus of elasticity of the rock, P is weight of one ball, and L is the size of the grain (assumed to be a cube of side L). It will be shown by this writer's formula that when a 30-mm ball strikes any size of feed grain it will cause 1.837 times higher stress than the 20-mm ball when striking the same size grain. It will be shown that when the 30-mm ball or the 20-mm ball strikes a feed grain of 0.1 mm it will cause 90 times more stress on the grain than when it strikes a 2-mm grain.

Jan 1, 1974

By Leonard D. Jaffe, Donald C. Buffum

THE importance of temper brittleness in alloy steels has long been realized in Europe, In the United States recognition of its importance has developed within the last several years. Many brittle failures encountered in parts made of alloy steel are undoubtedly attributable, wholly or in part, to temper brittleness. These failures have occurred particularly at low temperatures, under shock loading, and in the presence of notches, restraints and combined stresses. It has been almost universally accepted that plain carbon steels are not susceptible to temper brittleness. As a result, considerable effort has been expended in attempts to discover the manner in which alloying elements introduce temper brittleness. It is desired to raise the possibility that plain carbon steels are not only susceptible to temper brittleness, but are much more susceptible than alloy steels, in the sense that they embrittle much more rapidly. It is suggested that previous views, (that plain carbon steels are not susceptible), are based upon an erroneous interpretation of the experimental results. INTERPRETATION OF PREVIOUS DATA For many years the standard criterion for susceptibility of a steel to temper brittleness consisted of comparison of the energy absorption, in a notched-bar impact test at room temperature, of specimens that had received two heat treatments.1 One specimen (or group of specimens) was quenched, tempered, and quenched from the temper. The other specimen (or group) differed only in having received an embrittlement treatment, which might consist of a slow cool from the tempering temperature, or of an isothermal hold in the range 450-550°C subsequent to quenching from the temper. If the energy absorption of the specimen receiving the embrittlement treatment was lower than that of the specimen not given this treatment, it was said that the steel was susceptible to temper brittleness, If the energy absorptions were the same, it was said that the steel was not susceptible. Several investigators2,3 found that plain carbon steels showed negligible difference in energy absorption in such tests (at least when their manganese content was below 0.60 pct), and concluded that plain carbon steels are not susceptible to temper brittleness. Recently the deficiencies of the criterion mentioned above have been pointed out.4-6 The criterion now generally used for susceptibility to temper brittleness retains the heat treatments used in the earlier scheme, but instead of the notched-bar impact tests being made only at room temperature, they are made over a range of temperatures, covering the transition from ductile to brittle fracture, If the transition temperature of the specimens receiving the embrittlement treatment is higher than those

Jan 1, 1948

By C. E. Birchenall

DaVIES and Richardson1 have measured composition changes for Mn1-Owith variation in the equilibrium partial pressure of oxygen at 1500°, 1575°, and 1650°C, where 6 is the deviation from the simple stoichiometric ratio. No trend in this relationship with temperature was observed, so these remarks apply to the whole temperature range. The experimental values and their spread are shown by the bounded straight-line segments in the figure. Davies and Richardson assume that the stoichiometric oxide shows Frenkel disorder, given by the equation Mn2+Mn2+ + Mn" [1] where Mn2+ is a normal lattice ion which moves into an interstitial site (Mni2+) leaving a vacancy (Mn,"). The superscript dashes indicate that there is an excess charge on the anions surrounding the vacancy. Schottky disorder, in which a perfect crystal acquires equal numbers of cation and anion (Ov") vacancies according to leads to equations of exactly the same form in the analysis below. In view of the neutron diffraction results of Roth,2 which shows extensive Frenkel disorder in Fe1-o, Eq. [I] seems more appropriate. The deviations from stoichiometric composition, MnO, result from the addition of oxygen according to In effect Davies and Richardson ignore the variation of Mn3+in constructing equilibrium constants. This approximation might not appear to be very serious if the excess positive charges are really free posi- tive holes (P+) and if the intrinsic conductivity is high as a result of the reaction where e- is a conducting electron. However, the calculations of Buessem and Butler3 indicate that the partition functions of the free charges make a large contribution to the equilibrium constant, and this approximation would not be a desirable one. Furthermore, Morin4 shows that the positive holes are probably localized in MnO and therefore are described better by the mass action principle than by a degenerate gas model. Davies and Richardson's considerations require that activity corrections be applied beyond a 6 value of about 0.005. It is proposed to show here that the dissociation pressure curve can be calculated reasonably well over the whole composition range studied without activity corrections by choosing appropriate equilibrium constants for reactions 1 and 2. As stoichiometric composition The mass action constant, Ks, for reaction [I.] and the equilibrium constant, K,, for reaction [2] are given by where the concentrations which do not change significantly have been absorbed into the constants. The brackets denote concentrations. The deviation from stoichometric composition is given by gardless of [Mni2 ]. Substituting Eq. [7] in [6]

Jan 1, 1961

By C. P. Mangelsdorf

Introduction The use of frequency of vibration measurements to determine tension has long been accepted by industries that use electrical or stranded cables of wire ropes in their operations. In contemplating how to determine the tension in chords of a roof truss, it seems almost inevitable that a similar approach should be investigated even though there are some important dissimilarities in physical behavior between a chord of a rod-type Birmingham truss and a stretched wire rope. While the dominant feature of both types of behavior is the existence of tension, the bending resistance of the vibrating truss chord cannot be ignored. And it is common to have attached to the chord, pieces of hardware (turnbuckles, extension sleeves, wedge boxes) that represent concentrations of mass not usually found in a vibrating wire rope. Analytical solutions to the problem of vibrating wires or beams can be found in the literature on vibrations (Timoshensko, 1955; Den Hartog, 1956). But in every case, at least one of the ingredients of the vibrating truss chord is missing. The presence of axial tension, or bending resistance, of concentrated masses and of end conditions peculiar to truss chords is a combination that appears not to have been dealt with before, although the techniques for dealing with it are commonly known. The purpose of this note is to report the results of a project to measure and calibrate such frequencies. The work was conducted by the University of Pittsburgh under the sponsorship of the US Bureau of Mines. Field observations Tests were conducted on 24 different truss installations. The first 18 trusses were installed in shale roofs above Kentucky No. 9 seam and Illinois No. 6 seam. The remaining six were placed against the competent sandstone over the Pocahontas No. 3 seam in West Virginia. Chord tension was determined by two electrical resistance strain gages, in series, applied diametrically opposite to one another on the rod before tensioning. Due to the combined effects of inexact gage placement, rod bending and residual torsion in the chord due to tightening, errors in tension as high as 1780 N (400 lb) were reasonably possible. Due to faulty soldering or damage, three of the first 18 trusses and one of the final six were rendered completely unreliable. In addition to strain, the first natural frequency of vibration was observed to the nearest 0.1 Hz. Dimensions recorded included the span between contact points at the bearing blocks (Fig. 1) and the locations and amount of excess rod and rod gap at the wedge box and turnbuckle, respectively.

Jan 1, 1986

By R. J. Wasilewski

The resistivity of single crystal and of polycrystalline metal has been determined between 77° and 1500°K. At comparable purity, the resistivity of the poly crystalline metal differs from that calculated from the axial resistivity values. The observed anisotropy is briefly discussed. A zone refined titanium rod was obtained from F. J. Darnell.1 The hardness of this material varied between 52 and 64 Bhn, indicative of its high purity. Single-crystal specimens were cut out from a few large grains, elongated predominantly along <1120>. Resistance measurements were taken with specimens immersed in liquid nitrogen, solid CO,, and acetone, and at ice point, and then recorded continuously between room temperature and 1200" to 1250°C, throughout at least one full heating and cooling cycle at a rate of l° to 3°C per min. Four probe measurements were taken using spot-welded Pt wire 0.003 in. in diam as potential terminals, and the electromotive force drop was determined poten-tiometrically. A standard resistance, in series with the specimen, served to determine the dc current (generally about 80 ma) in the circuit. In order to eliminate spurious thermal electromotive forces, the circuit polarity was automatically reversed at 5-min intervals, and the mean of the two adjacent readings taken as the true electromotive force value. The discrepancy between the readings at reversed polarities was generally of the order of a few µ v, as all the spot-welded joints were contained within a volume of some 5 mm cube. The relative resistance (R T/R 273o) variation with temperature is tabulated below, and shown in Fig. 1, as measured during the first heating run. The discontinuous drop in resistance, corresponding to the a — ß transformation, started for both initial orientations at 1170°K; i.e., some 15°K above the accepted value of 882°C (1155°K). Judging by the temperature ranse of transformation—some 30°K for the single crystal and 20°K for the polycrystal-line specimen—this difference is believed caused by the solution of the oxygen present initially on the surface of the specimens. The general trend of the resistance vs temperature shown in Fi,;. 1 is in qualitative agreement with that previously reported for polycrystalline titanium metal. 2,3 Significant anisotropy is, however, indicated by the crossing over of the curves for <1120> and <0001> orientations at 273°, 650°, and 1000°K. This difference is most startlingly shown in Fig. 2, where instantaneous temperature coefficients (l/R273 x dR /dT) are plotted for both the first heat-

Jan 1, 1962

By D. A. Woodford

A number of observations have now been reported where the steady-state creep rate is apparently linearly dependent on the applied stress at high temperature and low stresses. This results in a creep rate greater than that predicted by extrapolation of high-stress data and has obvious practical implications. However, some of these observations are open to question. For example, the analysis by Harris and Partridge17 of the data of Greenfield et a1.18 was dependent on strain rates which, according to the original authors, were too low to be measured. Dr. Bernstein appears to have demonstrated a linear stress dependence at low stresses in two zirconium alloys. There are, however, a number of discrepancies in his treatment of the data and the subsequent theoretical analysis which require clarification. 1) It is incorrectly stated that steady-state conditions are revealed by a slope of unity on a plot of log i vs log (time). This objection is trivial if the author meant to say a slope of zero, although it is unclear how subsequent extrapolation was made to determine the steady-state creep rates at low stresses for the zircaloy-2. If the plot used was actually log c vs log (time), it is unlikely that a slope of unity would represent a constant creep rate. A plot of log (c - co) vs log (time), where c0 is the extrapolated intercept sf the steady-state creep rate on the strain axis, would have a slope of unity during steady-state creep. However, eo cannot be determined unless is is already known. 2) The author chooses to interpret his results based on the equation: where A, and B, are structure-sensitive parameters, Ql and Q, are the activation energies for the particular creep process, and n describes the sensitivity of the creep rate on stress. The first term represents a slip creep process and the second a diffusion creep process. However, it is stated later that "two distinct processes acting in parallel are involved". Eq. [I] surely represents two processes in series since each reacts to the total applied stress and t, is the sum of the individual creep rates. If the processes are acting in parallel, then the effective stress in each would be less than the applied stress. The component stresses would be given by sl + s2 = a but it is not clear how the magnitude of either, or the corresponding stress exponent, could be determined.

Jan 1, 1969

By Sylvan Z. Beer

Aluminum phosphide was synthesized and grown in solution of excess aluminum using a modified two-temperature technique. An inversion in the density difference between ALP and molten aluminum takes place at about 1100°. Dispersed nuclei can act as sources for further crystal growth in a manner resembling ripening. Advantage was taken of this phenomenon by introducing a stirring motion into the molten liquid. This was done with a split-phase 10-kH2 rotating magnetic field produced by four horizontal coils placed symmetrically about the furnace at the level of the molten metal. The method also prevents the formation of a surface film which would impede the reaction. By this technique vastly improved yields were obtained and flat crystals 5 by 5 by 0.5 mm were grown at lower temperatures and at greater rates than heretofore. THE family of III-V intermetallic compounds has received much attention since the prediction of their semiconducting properties in the early 1950s. Of the family, A1P has perhaps the highest band gap of those compounds normally possessing the zinc-blende structure. But it has been least studied because it is difficult to handle and grow. The handling difficulties have been dealt with elsewhere and it is sufficient to say here that, by various techniques, many of the difficulties can be overcome.&apos; The difficulties encountered in crystal growth can be related to the refractory nature of A1P and in turn to its high band gap. Because of the anticipated high melting point of the material and the accompanying high phosphorus vapor pressure, the reported work on synthesis and growth was done by epitaxial synthesis-growth via chlorine2 and iodine3 transport and from solution of excess aluminum by the two-temperature technique.4&apos;5 The transport-grown crystals take on the dimensions of the substrate but do not grow easily in thickness. In the usual two-temperature technique as applied on the synthesis of Alp, the temperature of the molten aluminum is kept at 1000° to 1250°C while the phosphorus is maintained at 1 to 20 atm. A thin film of aluminum phosphide and oxide form immediately, impeding the reaction and affecting the yield. Attempts to grow the Alp from such solutions by the methods used to grow Gap and InP from excess gallium and indium have not been successful. As discussed in the preceding paper,5 the yield can be greatly increased

Jan 1, 1969

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

IN 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group -SO4- or _S03- are excellent collectors for cassiterite and promise to be selective.1 The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000gram Denver cell. EXPERIMENTAL METHODS Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously described.5-10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these tests determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver Submachines.--Melbourne tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By A. A. Collins

OF widespread interest to all lead metal¬lurgists is a dross smelting process that will consistently give mattes and speiss of low lead and high copper contents. It is -a problem that has intrigued operators through the years. In the past few years, with increased amounts of copper and overcrowded metallurgical furnaces, it has been almost imperative to evolve some method. Experience at El Paso has shown that high copper-to-lead ratios can be consistently attained by use of the new soda process.* OLDER METHODS Three older methods; i.e., I. Dross plus siliceous ore and limestone, 2. Dross plus one fourth blast-furnace speiss and siliceous ore, 3. Dross plus sulphides and siliceous ore and scrap iron, do not give consistent results and the products are higher in lead and lower in copper than those produced with the soda process. Any radical changes in the blast-furnace drosses will throw any of these older methods into a tailspin. For almost ten years, El Paso used the third method, with varying results. It was noted that as the arsenic and antimony contents of the dross increased, the speiss and matte steadily increased in lead and decreased in copper. A dross containing four parts of copper to one part of arsenic was considered to be ideal. At times this balance of copper to arsenic was almost impossible to obtain, especially when handling copper Cottrell dusts, which vary so greatly in copper and arsenic. Custom smelters like El Paso, handling a great variety of dusts, concentrates and ores, are apt to have anywhere from 1 to 15 pct copper on charge, with a variable in arsenic of from 0.5 to 2 pct. With such conditions, and drosses varying from 12 to 40 pct copper, an operator using the older dross reverberatory practices would find it just about im¬possible to control the reverberatory operations and to produce a good product low in lead and high in copper. These conditions prevailed at El Paso from the year 1940 to the present. In May 1942 it, was decided to experiment with the soda process. THE SODA PROCESS After considerable work the soda method was finally evolved to the present state. It has never failed to produce a good product even under the most adverse conditions. It might be well to remember that many men of thought in the smelting industry have at one time or other suggested the removal of all copper, arsenic and antimony from the lead blast-furnace charge as an aid to better metallurgy.

Jan 1, 1947

By Coleman D. Hunter, George M. Straughan

Oil and gas development as well as extensive leasing in Kentucky during 1940 has shown a marked improvement over the past three years.$ The most noticeable improvement is the gas development in eastern Kentucky and the deep tests being drilled by major oil interests. In western Kentucky, 406 wells were drilled, of which 173 were oil producers, 12 were gas wells and 221 were dry or abandoned. The number of dry tests was large, because no important, new oil or gas pool was discovered and many of the dry holes could be considered wildcat tests. However, with either oil or gas possibilities from Pennsylvanian formations on through Mississippian, Silurian, Devonian, and Ordovician, this percentage of dry holes seems rather high. Many of the dry tests possibly should have been tested in deeper horizons before being abandoned: namely, Silurian and Ordovician ages. In eastern Kentucky, 213 wells were drilled, of which 113 were gas producers, 61 were oil wells, and 39 were dry holes. Of these wells, 117 were drilled in the most important Big Sandy gas field, in Floyd, Pike, Knott and Martin Counties, and of this number 103 were gas producers, 5 were oil wells, and 9 were dry holes. In the Big Sinking oil field of Estill, Lee and Powell Counties, 70 of the remaining 96 wells were drilled, j6 being oil producers. During 1940, four deep tests were drilled in eastern Kentucky. One test penetrated the Knox dolomite in Knox County and was dry; no St. Peter sand was encountered. Another test in Lee County had some gas in what might be called St. Peter sand, according to the State Department, and also some gas deeper in the Knox dolomite. In Wolfe County, a small oil well was completed in the Ordovician, which was undoubtedly of Trenton age. ilt the present time, four deep tests are being drilled, all of which will go to the Knox dolomite. In Elliott County, on the Burke dome, the Inland Gas Co, is drilling at 3650 ft. In Magoffin County, on the Paint Creek uplift, the Cumberland Petroleum Co. is drilling at 3800 ft. In Clark County, in the Ruckerville fault area, W. 0. Allen is drilling at 1800 ft. In Laurel County, on the Sinking Creek dome, the Globe Oil and Gas Co. is drilling at I750 ft. If production is encountered in the Trenton, St. Peter, or Knox dolomite in any of these tests, eastern Kentucky will experience a marked increase in deep development.

Jan 1, 1941

By George M. Straughan, Coleman D. Hunter

Oil and gas development as well as extensive leasing in Kentucky during 1940 has shown a marked improvement over the past three years.$ The most noticeable improvement is the gas development in eastern Kentucky and the deep tests being drilled by major oil interests. In western Kentucky, 406 wells were drilled, of which 173 were oil producers, 12 were gas wells and 221 were dry or abandoned. The number of dry tests was large, because no important, new oil or gas pool was discovered and many of the dry holes could be considered wildcat tests. However, with either oil or gas possibilities from Pennsylvanian formations on through Mississippian, Silurian, Devonian, and Ordovician, this percentage of dry holes seems rather high. Many of the dry tests possibly should have been tested in deeper horizons before being abandoned: namely, Silurian and Ordovician ages. In eastern Kentucky, 213 wells were drilled, of which 113 were gas producers, 61 were oil wells, and 39 were dry holes. Of these wells, 117 were drilled in the most important Big Sandy gas field, in Floyd, Pike, Knott and Martin Counties, and of this number 103 were gas producers, 5 were oil wells, and 9 were dry holes. In the Big Sinking oil field of Estill, Lee and Powell Counties, 70 of the remaining 96 wells were drilled, j6 being oil producers. During 1940, four deep tests were drilled in eastern Kentucky. One test penetrated the Knox dolomite in Knox County and was dry; no St. Peter sand was encountered. Another test in Lee County had some gas in what might be called St. Peter sand, according to the State Department, and also some gas deeper in the Knox dolomite. In Wolfe County, a small oil well was completed in the Ordovician, which was undoubtedly of Trenton age. ilt the present time, four deep tests are being drilled, all of which will go to the Knox dolomite. In Elliott County, on the Burke dome, the Inland Gas Co, is drilling at 3650 ft. In Magoffin County, on the Paint Creek uplift, the Cumberland Petroleum Co. is drilling at 3800 ft. In Clark County, in the Ruckerville fault area, W. 0. Allen is drilling at 1800 ft. In Laurel County, on the Sinking Creek dome, the Globe Oil and Gas Co. is drilling at I750 ft. If production is encountered in the Trenton, St. Peter, or Knox dolomite in any of these tests, eastern Kentucky will experience a marked increase in deep development.

Jan 1, 1941

By R. L. Sandefur

Professor Kim&apos;s excellent review article1 on ultimate pit planning contains a statement of the apparently widely held but incorrect belief that "kriging provides information on the confidence limits around the estimate which no other extension technique is capable of supplying." If a geostatistical approach is valid, there are several good reasons for using kriging but uniquely provided confidence limits is not among them. If kriging is possible, then confidence limits can be calculated for any other linear estimate. Kriging is the procedure which finds the weighing coefficients which minimize the estimation variance [ ] is the variance of blocks like the one being estimated. wi is the covariance of the estimated block and the i-th sample. oij is the covariance of the i-th sample and the j-th sample. Ai is the weighing coefficient for the i-th sample. N is the number of samples. The formula for estimation variance can also be used to calculate confidence limits on blocks estimated by any linear combination of sample grades including: 1) Polygons a. Hole nearest block centroid is assigned weight 1. All other holes are assigned weight 0. b. Polygonal area weighing. The samples are assigned weights directly proportional to their polygonal areas of influence within the block. The weights sum to 1. 2) Inverse distance weighing. The samples are assigned weights directly proportional to the reciprocal of their distance to some power from the block centriod. The weights sum to 1. Often only holes nearer than a certain distance and/or the nearest hole in each octant is considered. If there is an antisotropy to the ore body, an elliptical transformation often gives more accurate results. The most popular inverse distance weighing function is inverse squared distances (IDS). 3) Simple average. All samples within a certain distance are assigned the same weights which sum to 1. As an example of the applicability of the above formula to any linear estimate an internal verification on copper grade of 665 blast holes on the 1040 bench at Utah&apos;s Island Copper mine is presented. Internal verification is simple and applicable to non-linear estimates as well. Any sample (drill hole, bulk, trench, or chip) is dropped out, the value of the dropped sample estimated and compared with the actual value. If this is done for all samples, a measure of confidence limits is obtained. Internal verification is used in Cominco&apos;s MEPS system4 and in the BLUEPACK system.5 Comparison of block values against estimates697 is not dissimilar to internal verification. Results of the internal verification are presented below:

Jan 1, 1980

By T. Koulomzine

The theory of the Askania mag-netometer, as well as a complete discussion of all factors influencing magnetometer readings, is very ably described by J. Wallace Joyce.1 We will assume that the reader is thoroughly familiar with this theory and we will use whenever possible the same notations for the physical values involved in the theory. On the other hand, we believe that the principal formulas of the magnetometer can be deduced much more easily by the use of differential calculus than by the methods employed by Joyce. Consequently, we are presenting herewith a resumé of the theory of the vertical magnetometer in order to determine the correct formula of the temperature coefficient which we propose to compensate. Short Theory of the Vertical Magnetometers We shall accept the following notations: m = total mass of the magnet system, in grams. g = acceleration of gravity, in dynes. a = projection on the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. h = projection on the perpendicular to the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. M = 2pL = M, magnetic moment of the magnet system. Z = vertical component of the earth&apos;s magnetic field. ? = deflection angle of the magnet system. = focal length of objective lens in the optical system S = scale reading. In a vertical magnetometer the axis of the magnet system is kept horizontal within 2". Therefore, referring to Fig 1, we see that the magnetic torque of the magnet system influenced by Z must be counterbalanced by the gravity torque. MZ cos ? = mga cos ? + mgh sin ? or dividing by cos ? MZ = mga + mgh tan ? If we now move to another magnetic station and the temperature conditions change, the values of all the variables will change also: M, a, and h under the influence of temperature. 2, both with time and space. ? and S, as a result of all the above changes. Taking increments in Eq 2 we obtain: (Mo + ?M)(Z + ?Z) = mgao + mg?a + mg(h + ?h) tan (? +??) but tan (? +??), because ? is small, can be replaced by tan ? + tan ??; in fact tan (?+ ??) = sin ?.cos ?? + cos ?.sin ??/ cos ?.cos ?? — sin ?sin ?? but sin ? sin ???0 tan (8 + ??) ? tan ? + tan ??. Fur-thermore, neglecting all terms of the equation containing two differentials becomes: or a differential and a tan ??, Eq 3

Jan 1, 1950

Discussion of the paper of Dorsey A. Lyon and Robert M. Keeney, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 80, August, 1913, pp. 2117 to 2149. C. D. WOODWARD, Butte, Mont.:-We constructed a small blast furnace, and used first carbon electrodes and an alternating current of about 50 to 75 volts. We were able to smelt the material which was fed to the furnace, but we did not carry on experiments far enough to see just exactly what the power consumption was and compare it with the amount of material treated. We found that the blast seemed to help materially in reducing our charge and cutting down our power consumption. There were several other experiments tried at the time, and I do not call to mind now just what they were. We were trying to do away with the carbon electrode and replace it with an iron one, and it also seems to me we tried to use the ore for an electrode; but I believe that the electric furnace in the reducing end is simply a question of British thermal units per kilowatt-hour compared with British thermal units in a pound of coke. Now, if a pound of coke costs us 0.5 c. and a kilowatt-hour costs us in the neighborhood of 1.5 c., I think there is a big advantage in using coke instead of the electrical current for copper reducing. We tried steam, and a number of other methods, to throw copper down, but it has been some time ago and I am not very familiar with them now. The outlook of the experiments did not seem to be very promising, and we took it more as a thermal problem than an electrical one. PROF. JOSEPH W. RICHARDS, South Bethlehem, Pa.:-Mr. Woodward has spoken of the question as a thermal problem. I would call attention to the fact that electric furnaces usually utilize the heat of the electric current at from four to ten times the efficiency with which the heat generated by fuel is utilized; so it will not do simply to compare by thermal units generated. Your total thermal units may cost much less from coke than from electricity, yet you will find the electrically generated thermal units utilized in a properly designed furnace from three to ten times more efficiently than in the combustion furnace. You must make that allowance is comparing the cost of thermal units generated electrically and thermal units from coke.

Jan 11, 1913

By James Norman, O. C. Ralston, John Dasher

Most mineral products are used in the finely divided state, but some are sold in larger sizes. Coal, gravel, metallurgical fluorspar, phosphate rock, hematite, chro-mite, and other products are sold in sizes coarser than can be treated by many mineral-dressing methods. Gravity separation of coarser sizes by log washing and jigging is probably as ancient as any process now in use. The performance of jigs on a feed with sufficient difference in density of the minerals is excellent, but many families of minerals are too similar in density to be separated effectively by this method. The use of heavy suspensions of fine solids to separate coarse coal from bone and slate has been in use for some years. This separation by sink-and-float was limited until recently to light minerals. Development of galena and ferrosilicon as suspension media, by Minerals Beneficia-tion, Inc., at Mascot, Tenn., Pitcher, Okla., and Crosby, Minn., under patents granted during and since 1938, has permitted excellent results to be obtained on minerals of very similar densities up to 3.3. This process has been put In the hands of American Cyanamid Co. for exploitation, and further research now in progress may increase the density of suspension obtainable so that separations at a density of 4.0 may be practicable before this is published. The Huntington-Heberlein dense-medium process, developed in England, is also being commercialized in the United States by Sink and Float Corporation. Du Pont has developed a sink-and-float separation using halogenated hydrocarbons as parting liquids; at this writing, the method is used commercially only on coal but has been successful in the pilot plant on many other minerals using tetrabrom-ethane at densities up to 2.95. While these processes were being developed to extend the range of separation by difference in density to the coarser sizes, the Bureau of Mines was engaged in developing a process that will extend the range of separation by difference in wettability up to 2-in. size. War work has pushed aside its further development indefinitely. The results are published here with the hope that some use may be suggested that will justify post-war development, and so that readers that may be able to make immediate use of the scheme may have the information. Earlier Work It has been known since the time of Herodotus (B.C. 484(?)-425) that water-repellent particles will adhere to sticky surfaces. That early historian reports the recovery of gold from the mud of a lake

Jan 1, 1943

Geostatistics originated as an application of a classical statistical concept, multivariate linear regression, to the solution of a practical problem, estimation of reserves in the South African gold mines. In this respect, geostatistics should only be considered as one statistical method among many that can be used to evaluate mineral deposits. R.F. Shurtz has studied possible applications of power spectrum analysis to the same problem, and these studies may result in future improvements over the presently accepted geostatistical methodology. The intention of R.F. Shurtz&apos;s paper, as stated by the author, is to "relate geostatistical doctrine to classical statistical and mathematical concepts." However, in this comparison the "geostatistical doctrine" appears to include only the simplest among the geostatistical concepts advocated by G. Matheron, while "classical statistical and mathematical concepts" are limited nearly exclusively to power spectrum analysis. The author attempts to compare the two methods, and to prove the theoretical superiority of power spectrum analysis. Unfortunately, a number of errors and incorrect statements are made concerning both the theory and application of geostatistics, which invalidate the comparison and the conclusions drawn from it. The errors made in this comparison are understandable since few scientists can claim to have expertise in two theories as diverse as those compared here. In many respects, this paper is reminiscent of polemics which occurred 15 to 20 years ago when geostatistics and trend surface analysis were compared. Each method has its own merit and limitations, and none can claim absolute superiority. The most misleading statements found in R.F. Shurtz&apos;s paper are: The definition of the semivariogram given on page 1923 is incorrect. If the maximum difference between two assays is 1, the maximum value of the semivariogram is not 1, as stated, but 0.5. The comparison of geostatistics and linear regression made in the section entitled "Insufficiency of Classical Statistics?" is not valid. The semivariogram of the sample values given in Table 1 (page 1919) has a parabolic shape indicative of a linear drift. When such a semivariogram is observed, the simplest method of geostatistical estimation (linear kriging with unknown mean) is not applicable. Universal kriging must be used that takes trends into account. On page 1921 it is stated that the use of trends "is officially disparaged in geostatistics." Again on page 1924 mention is made to "Matheron&apos;s commitment to random process (intrinsic) models and his present categorical rejection of deterministic (trend) models for mineral deposit evaluation." Indeed, from articles published by geostatisticians in the 1960s one could infer that geostatistical methods are not compatible with the presence of trends. However, even the simplest

Jan 1, 1984

By O. Vartianen, R. T. Hukki

A preliminary investigation of the collecting effects of various fatty acids in tall oil has led to a conclusion that the collecting power of fatty acids used in flotation increases with increasing un- saturation of the hydrocarbon chain. Linoleic acid was found to be an excellent collector for oxide minerals. TALL oil is a mixture of fatty and resin acids extracted as byproducts in the sulphate pulp industry. In the field of flotation a well-known example of this type of product is Reagent No. 708 of the American Cyanamid Co. Its successful use as a flotation collector with many nonsulphide minerals has been described by Falconer and Crawford.&apos; The composition of crude tall oil varies within wide limits.&apos; " By a number of methods the crude oil may be refined to produce a variety of refined products. This investigation presents a preliminary comparative study of collecting properties of the fatty acids in tall oil. In Finnish tall oils these constituents are primarily palmitic, oleic, linoleic, and linolenic acids.:&apos; The first is a saturated fatty acid having 15 carbon atoms in its hydrocarbon chain, plus one in the carboxyl group. The others have 17-carbon-atom chains and are unsaturated. It is of particular interest to note that palmitic, oleic, lino-leic, and linolenic acids represent increasing degrees of unsaturation with 0, 1, 2, and 3 double bonds, respectively. To test the collecting properties of the four fatty acids separately, the vacuum flotation technique described by Schuhmann and Prakash4 was used. By this method the boundary between flotation and non-flotation conditions was approximately delineated, with the use of ilmenite and several other minerals. Collector concentration and pH were the principal variables. On the basis of information obtained, actual flotation tests were run on an ilmenite-bear-ing ore in a laboratory flotation cell. Through the courtesy of P. Kajanne from the Department of Chemistry, Finland Institute of Technology, the following reagents were obtained for this investigation: 1—Palmitic acid, of Judex, had a purity of 95 pct as determined by parallel iodo-metric and spectrophotometric measurements. 2— Oleic acid, product of May and Baker Ltd., indicated purity of 98 pct. By iodometric and spectrophoto-metric determinations the oleic acid content was found to be 83.8 pct. In addition, it contained 6 pct linoleic, 1 pct linolenic, and 9.2 pct saturated fatty acids.&apos; 3—Linoleic acid was prepared from soybean oil by low-temperature crystallization. Its linoleic acid content was 95 pct by the methods indicated above. 4—Linolenic acid was prepared from linseed oil by low temperature crystalIization. Its linolenic

Jan 1, 1954

By James Norman, O. C. Ralston, John Dasher

Most mineral products are used in the finely divided state, but some are sold in larger sizes. Coal, gravel, metallurgical fluorspar, phosphate rock, hematite, chro-mite, and other products are sold in sizes coarser than can be treated by many mineral-dressing methods. Gravity separation of coarser sizes by log washing and jigging is probably as ancient as any process now in use. The performance of jigs on a feed with sufficient difference in density of the minerals is excellent, but many families of minerals are too similar in density to be separated effectively by this method. The use of heavy suspensions of fine solids to separate coarse coal from bone and slate has been in use for some years. This separation by sink-and-float was limited until recently to light minerals. Development of galena and ferrosilicon as suspension media, by Minerals Beneficia-tion, Inc., at Mascot, Tenn., Pitcher, Okla., and Crosby, Minn., under patents granted during and since 1938, has permitted excellent results to be obtained on minerals of very similar densities up to 3.3. This process has been put In the hands of American Cyanamid Co. for exploitation, and further research now in progress may increase the density of suspension obtainable so that separations at a density of 4.0 may be practicable before this is published. The Huntington-Heberlein dense-medium process, developed in England, is also being commercialized in the United States by Sink and Float Corporation. Du Pont has developed a sink-and-float separation using halogenated hydrocarbons as parting liquids; at this writing, the method is used commercially only on coal but has been successful in the pilot plant on many other minerals using tetrabrom-ethane at densities up to 2.95. While these processes were being developed to extend the range of separation by difference in density to the coarser sizes, the Bureau of Mines was engaged in developing a process that will extend the range of separation by difference in wettability up to 2-in. size. War work has pushed aside its further development indefinitely. The results are published here with the hope that some use may be suggested that will justify post-war development, and so that readers that may be able to make immediate use of the scheme may have the information. Earlier Work It has been known since the time of Herodotus (B.C. 484(?)-425) that water-repellent particles will adhere to sticky surfaces. That early historian reports the recovery of gold from the mud of a lake

Jan 1, 1943

By W. F. Dietrich

Mineral fillers are relatively inert chemically under the conditions of use but have physical properties* that modify those of the materials • The properties. uses, and other data on 15 classes of important *The pro listed in the second edition of Industrial Minerals and Rocks.l A third edition of this reference is in preparation. in which they are incorporated. The mineral fillers considered in this article are asbestos, barite, clays, diatomite, crushed limestone, limestone whiting and lime, mica, silica, talc and soapstone, and pyrophyllite. Slate and stone, other than limestone and its derivatives, are excluded because, even though used in large quantities, they are exceptionally low-cost materials generally produced close to the area where they are used. Carbon black is excluded because it is manufactured from natural gas and more than 90 pct of the output is used in rubber; hence the factors for estimating requirements are easily evaluated. OVERALL GROWTH FACTORS Table I gives the population, retail sales, and value added by manufactures in the U. S. and in the eleven western states in 1954. These data are rough guides to the proportionate part of total U. S. markets for products containing mineral fillers that may be expected in a given area. For example, the population of the eight Mountain states in 1954 was 3.6 pct, and retail sales in these states were 3.8 pct of the U. S. total, but the value added by manufactures was only 1.3 pct of the U. S. total. On the other hand, the three Pacific Coast states, with 10.3 pct of the total population, had 12.0 pct of the retail sales and produced 9.6 pct of the value added by manufactures. On an industry-by-industry basis the correlation between the three guideposts will not be as close as shown in the 1954 data for the Pacific Coast states, but in the long-term view the continuing rapid population growth in the western states is certain to result in expanded industrial production at an even more accelerated pace, which will shorten the gap between local consumption and production in most major groups of manufactured consumer goods. Of course, there will always remain favorable areas for production of specific products. Such special situations must be individually analyzed. Fig. 1 compares the population trends in the U. S., the western states, and California with Real Gross National Product from 1910 to 1957, with forecasts to 1970. It is estimated&apos; that the U. S. Real Gross National Product, as measured by the value of goods and

Jan 1, 1960

By Brison Robertson, W. P. Fishel

THE carbide-forming tendencies of the various steel-alloying elements, or their affinities for carbon, is a subject that has received considerable attention, but little more than a probable arrangement of the elements as to their carbide-forming tendencies has been proposed. The physical properties of alloy steels depend upon the relative proportions of the elements present and their combinations. One important phase of this subject is the distribution of carbon between the various elements present. The distribution of carbon between iron and other elements evidently will depend upon: (I) the affinity of each for carbon; (2) the relative atomic masses of the elements present; and (3) the possible formation of compounds between the alloying elements and iron and between the elements themselves. In ternary steels the case is simplified, especially in systems in which the element and iron form no compounds. In such systems iron and the alloying element are competing for the carbon present. In this work the distribution of carbon between titanium and iron has been studied by measuring the relative amounts of iron carbide and titanium carbide present in a series of annealed steels in which the ratio of titanium to carbon extended from 0.527 to 4.61. EXPERIMENTAL PROCEDURE Ten Fe-Ti-C alloys, weighing about 250 grams each, were prepared by melting under a vacuum, in an induction furnace, Armco iron, carbon-free ferrotitanium (25 per cent Ti), and pure carbon. Vacuum melting prevented the formation of titanium oxides and nitrides, which would complicate the problem. The melts were made in graphite crucibles lined with sintered magnesium oxide. The ingots were cooled in the furnace under a vacuum and were then completely annealed at 950°C. The determination of the amount of titanium carbide present was based upon the established insolubility of titanium carbide in boiling dilute (I :4) sulphuric acid, and the complete solubility of free titanium and titanium-iron compounds in this acid. High-carbon ferrotitanium, which had been treated to remove free Ti and Fe, was found to be completely insoluble in the acid; and the carbon-free ferrotitanium used in making the alloys was found to be completely soluble. Others 1,2 have reported the insolubility of titanium carbide in sulphuric and hydrochloric acids. Turnings from the ingots were digested with boiling sulphuric acid (1:4) until all action had ceased. The carbide residue was filtered off and analyzed for titanium, and in some cases for carbon. This represents the titanium that was united with carbon. The filtrate from the carbide residue contains the portion of the titanium that wasin solid solution in the ferrite. Titanium

Jan 1, 1944