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By Warren Smith

IT has been 5 years since the writer left the Philippine Islands and while in that country his chief work did not lie in this field, though he has visited all but one of the localities mentioned in this article. The principal field studies relating to oil were made by his colleague, Mr. Wallace E. Pratt. The writer's investigations dealt with the general stratigraphy and paleontology of the Philippines. With the exception of the investigations made by Mr. Pratt and the writer very little information on this subject is available. A number of geologists in the employ of large oil companies have visited the Islands from time to time but, following the general rule, the public has scarcely ever been permitted to learn anything of the results. The writer is indebted to the Bureau of Insular Affairs, Washington, for late information regarding recent legislation in the Islands relating to petroleum. All the known oil seeps, petroleum residues, such as ozocerite, and natural-gas emanations are associated with Tertiary sediments. The chief seeps and most promising prospects are located as follows: 1. Bondoc Peninsula (lower end), Tayabas Province, Southeast Luzon. 2. The west coast of the island of Cebú from Alegria north to, and perhaps beyond, Toledo. 3. Central Mindanao not far from Lake Lanao. 4. The ozocerite veins on the Island of Leyte in the northwestern part in the vicinity of the town of Villaba. 5. Natural gas from some deep wells in Tertiary shale formations on the eastern flank of the Cordillera and extending out under the plain on the island of Panay.

Jan 2, 1920

By J. G. EVANS

It is with a certain amount of trepidation that a man considers gathering his family of six, traveling across a continent, two oceans and a sea, and going to live in a foreign land. But "pioneering" is still possible, and a nation is "foreign" only until one has lived in it. We've had eight years of pleasant experiences in South Africa on which to base that contention. It was in January 1938 that my brother first extolled the virtues of South Africa to us, and just three months and a thousand small problems later my wife, two daughters, three sons and I were boarding a ship in New York, bound for Cape- town. We arrived in May, and within a week had found a furnished home with beautiful lawns, tennis, court, a garden, and everything needed for family comfort. The children were soon located in school, and I settled down to the task of entering the importing business, as had been my original intention. The importing business started out slowly but was coming along nicely when on Sept. 3, 1939 the war started in Europe and a declaration of war by the Union of South Africa was made on the following day. With the declaration came import and export controls. In fact we were controlled completely out of business in one stroke. Liquidating the business, I went to Johannesburg intending to find work in one of the mines. Government health and safety regulations require that all underground mine employees have a red ticket from the Miners Phthisis Bureau certifying that they are not susceptible to silicosis, the scourge of the Witwatersrand gold mining industry. I made application to the Bureau, completed a form covering my whole past life, and was given a complete physical examination. The following day I was startled to find that I had not only been refused a red ticket but had been classified with a green ticket which for- ever bars one from working underground in any scheduled mine in the country, and all this in spite

Jan 1, 1949

By John Henry Harden

IT appears that in the earlier days of anthracite coal mining, 1824-25, the Lehigh region mined 76 per cent. of all the coal sent to market. During the same period Wyoming sent 12 and 5 per cent. respectively, whilst the Schuylkill sent 11 and 18 per cent., the number of tons marketed being in those days very small indeed. In the year 1828 the Schuylkill region mined over one-half of all the coal sent to market, and continued to do so for thirty years (with the exception of the year 1831), until 1858 ; since that date the pro¬duction has declined very steadily in comparison with the other regions, until, in 1876, it was only 34 per cent. Wyoming, in the year 1820, was mining 40 per cent., but the production of all the regions was very small ; in six years it declined to 5 per cent., increased to 34 per cent. in 1831, declined to 10 per cent. in 1838. Since which time the increase has been gradual, until 1873-75 Wyoming produced over 50 per cent. of all the anthracite coal sent to market. In 1867 the production exceeded that of Schuylkill, and has continued to do so since that time. In the year 1876, during the existence of the " coal combination," Wyoming lost 9 per cent. ; during the same time Lehigh gained 7 and Schuylkill 2 per cent. over their relative production of the preceding year, the decrease of Wyoming being two and a half million tons, the increase of the Lehigh one million, the decrease of the Schuylkill nearly three-quarters of a million. The extraordinary production of the Lehigh region at a time of decreased demand and in opposition to an agreement with the other regions to limit the supply to the supposed demand was the cause of the disagreement which ultimately broke up the combination of the great coal-producing and carrying companies. The Lehigh region produced very steadily, from 1829 to 1854, an average of about 22 per cent. of the whole production. From 1854

Jan 1, 1877

By R. A. Pasternak, B. Evans

A dynamic technique for the determination of solubilities of gases in metals has been explored, using the N-Nb system as a test case. An initially clean sample, maintained at constant high temperature, is exposed to the gas at low pressure: the rate of sorp-tion and the corresponding change in sample resistance are measured continuously. A pronounced decrease in the slope of the resistance concentration curve is observed at the terminal solubility. The rate of gas uptake by the sample was determined in an ultrahigh-vacuum flow system equipped with a servo-control which maintains constant pressure in the sample chamber; the system and the technique have been described in detail elsewhere. 1,2 The sample was held at constant temperature during sorption by maintaining approximately constant power input into it; this results in constant temperature, since the emissivity of a metal is independent of moderate concentrations of dissolved gas. The simple electrical circuit used both for heating and for resistance measurement is shown in Fig. 1. The power input into the filament is where R is the filament resistance, RL is an adjustable resistance in series with the filament, and VT is the constant dc potential of the power source. If RL is set equal to R at the beginning of an absorption run, the power input becomes insensitive to subsequent resistance changes; for example, an increase of 20 pct in sample resistance is accompanied by a decrease in power input of less than 0.8 pct; i.e., the

Jan 1, 1967

J. E. Stead, Middlesborough, England (communication to the author): Prof. Howe's valuable paper on cast-iron brings forward most prominently the correct explanation of the part played by combined carbon in pearlite and cementite, in determining the strength and hardness of cast-iron. On a previous occasion I haveoshown that castings made by melting a white Cleveland iron and glazed iron, one containing 1.5 and the other from 4 to 5 per cent. of silicon, and each about 3 per cent. of carbon, were stronger than those made of ordinary foundry-iron; the difference in the final castings being a differ-

Jan 1, 1902

[OFFICERS AND COMMITTEES J. W. Woomer, President A. B. Cummins, President-elect S. D. Michaelson, Past President C. E. Lawall, Eastern Regional Vice-President D. W. Scott, Central Regional Vice-President J. D. Forrester, Western Regional Vice-President R. B. Ladoo, Treasurer John Cameron-Fox, Secretary]

Jan 1, 1961

R. H. THURSTON, Cornell University, Ithaca, N. Y. (communication to the Secretary): The " tri-axial diagram" was, I think, first employed by me in the work of the " U. 8. Board Appointed to Test Iron, Steel and Other Metals." A model was exhibited to the American Association for the Advancement of Science, and the diagram was first published, and the model described, in a paper presented to the same society at its Nashville meeting in 1877." The problem then presented to its inventor was to find a method of planning a research involving proportions of ternary compositions in such manner that, a limited number of such compositions being tested, the results should give the law of variation in the physical properties of all possible combinations of the three elements, and the actual numerical values of such as were important to the investigator. The investigation of the binary alloys, copper and tin, copper and zinc, and tin and zinc, had been completed and satisfactorily discussed, employing the usual bi-axial diagram, of which the ordinates represented the one, and the abscissæ the other, of the characteristic properties to be studied, the composition being commonly indicated by the abscissæ. In these cases it was easy to ascertain, by the study of a limited number of compounds, the law of variation in strength, ductility, etc., with composition; but, for a long time, the ternary alloys were not attacked, because no simple and satisfactory method presented itself of securing results significant for the whole field by the investigation of a comparatively small number of alloys. The tri-axial diagram was finally hit upon as a means of representing and interpreting results, and researches were at once begun, and in due time satisfactorily completed.

Jan 1, 1899

By Robert L. Gower, John H. Cash

Interconnections for integrated circuits operating at rnicrowaue frequencies rzust be formed as microwave transmission lines. This paper describes the fabrication of one type of microwave transmission line known as microstrip, which can be fabricated on momlithic integvated circuits by deposition of 0.1- to 2.0-mil-thick metal and dielectric films. A microstrip line consists of a narrow conducting strip separated from a gvound plane by a dielectric material. Thick films of good conducting materials are required for low loss at high frequencies. Vacuum-evaporation methods for depositing aluminum and silver films are described. The narrow conducting strip forming the top conductor is defined by photoresist-etching techniques after the thick rnetal film is deposited. Gold plating with a photoresist-masking technique is also used to forrrz thick metal conductors. The microstrip dielectric layer is formed by deposition of suitable dielectric films 0.1 to 2.0 mils thick. Several deposition techniques were investigated. Electron-beam evaporation of quartz is described. Electrical characteristics of deposited microstrip lines at microwave frequencies are included and the microwave power attenuation as a function of conductor and dielectric thickness is given. It is concluded that the deposition of microstrip transmission lines is a practical way to achieve low-loss interconnections in monolithic integrated circuits. CONNECTIONS between devices in low-frequency and digital circuits are usually made by connecting the devices with a length of conductor such as a metal lead oi- a wire. If this method were applied to microwave integrated circuits, the reactance of the connection due to the series inductance and parasitic capacitance would be very high, in fact too high to permit successful circuit operation. In addition, resonance and antenna effects would occur at high frequencies, especially when the connections approach the wavelength.' Connections which are sections of transmis- sion line will overcome these difficulties. The electromagnetic field is confined to the volume of the transmission line, parasitic effects are not present, and circuit design utilizes familiar transmission-line techniques. TRANSMISSION LINES One type of transmission line geometrically adaptable to integrated circuits is known as micrstri. A microstrip line can be generated from a coaxial line as shown in Fig. l(a). The outer conductor of the coaxial line is distorted into an ellipse (b) and finally separated at the extremities of the ellipse to form the strip transmission line shown in (c). One of the ground planes is then removed, leaving a conducting ground plane and a narrow conducting strip separated by a dielectric. Two configurations of the microstrip line were considered in this investigation, Fig. 2. Type (a) is fabricated from a semiconductor slice with the ground plane and top conductor deposited on each side of the slice. The semiconductor slice serves as the die lec-

Jan 1, 1967

By Blamey Stevens

(Butte Meeting, August, 1913.) THE following paper aims to make a full explanation of the phenomena of rock jointing: It may be unnecessary to give any general description of what are termed joints in rocks, but Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given. for introducing the following and other quotations into this paper "Almost all rocks are traversed by vertical or highly inclined divisional planes termed joints. These have been regarded as due in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure and movement within the crust." 1 General Explanation.-In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of the porous material may be considered to be separately compressed by the water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from moving freely by other material around its boundaries. The mass of rock thus becomes broken up. This phenomenon is known as '" shrinkage " jointing. The term " shrinkage " is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.-The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting. .

Jan 7, 1913

By T. A. Rickard

The notion prevails that writing is a knack, that the skilful use of the pen is a gift of nature. This is an error. Dogberry may be responsible for it; he said: "To be a well-informed man is the gift of fortune, but to write and read comes by nature". Because Dogberry said it, we may be sure that Shakespeare thought otherwise. Ability of any sort may be partly innate, but my own observation and experience lead me to conclude that most of the easy writers have become so by constant practice. As I recall the names of men successful with the pen, I remember that most of them have written a great deal and have taken particular pains to improve their style. The suggestion that proficiency in the difficult art is a happy accident provokes a sardonic smile. The larger part of the great writing in our literature is the result of persistent effort. An easy fluency has been the undoing of many; their flamboyant and fantastic scribbling has proved as perishable as froth. This criticism applies to technical writing also; in order that a technical description or discussion may hold the interest of the reader, at least long enough to cause him to read it to the end, the writing must be done carefully and systematically; otherwise it will fail in its purpose of conveying information. Clearness is absolutely essential. "It is not enough to use language that may be understood; it is necessary to use language that must be understood."* The purpose of writing, at least of that which is meant to be read by others, is not only to express ideas but to communicate them. Lack of perspicuity may prove as %ad as

Jan 1, 1931

By L. G. Austin, P. T. Luckie, R. R. Klimpel, R. S. C. Rogers

1. INTRODUCTION The Bond method(1.2) for sizing tumbling ball mills has been used successfully for many years. The primary purpose of the Bond calculation is to predict the mill size and mill power to give a desired capacity (Q tph) from a wet overflow ball mill in normal closed circuit operated with a circulation ratio of 2.5. The input to the calculation is the make-up feed size characterized by the 80%-passing size in micrometers (xG), the desired circuit product size characterized by the 80%-passing size (xQ), and an empirical grindability number (the standard Bond Work Index) determined by a standard test. A series of empirical correcting factors(2) are used to convert the results to open-circuit or dry grinding in grate discharge mills. The Bond method has two major engineering advantages: (i) it is very simple; (ii) experience has shown that it works for many circumstances, as a reasonable approximation, because it is based on direct conversion of test data to results measured on industrial mills. There are four main disadvantages of the Bond method. First, there will be a range of error for any specific mill and material and set of operating conditions because the method does not explicitly include several variables which are obviously important: (i) recycle ratio and classifier efficiency (ii) mixture of ball sizes in the mill (iii) variations of residence time distributions with mill geometry and slurry density (iv) lifter design (v) slurry rheology (vi) different underfilling or overfilling of the mill as flow rate is changed. Second, the Bond method explicitly assumes that specific grinding energy E is not a function of ball load, whereas industrial practice and laboratory tests(3) show that the specific grinding energy (to go from a specified feed to a specified product) is less for lower ball loadings than the ball loading for maximum mill capacity. Third, the method uses only the 80% passing size of circuit feed and product to characterize the size distributions, whereas mill capacity in general must depend on the shape of the feed size distribution and the product size distribution. The prime example of this is the use of the reverse closed circuit which removes some fraction of the make-up feed before it is

Jan 1, 1982

By H. F. Beardmore

PETROLEUM consumption during 1946 broke all previous records and further increases are expected during 1947. U. S. consumption amounted to an average of 5,280,000 bbl a day, of which 4,745,000 bbl was domestic crude oil, with the rest from natural gasoline production and crude oil imports. World consumption during the past year, excluding Russia, is estimated at 7,200,000 bbl daily. Forecasts for 1947 indicate a U. S. consumption of 5,425,000 bbl daily of petroleum products. This is expected to be made up of 4,655,000 bbl of domestic crude oil production, 340,000 bbl of natural gasoline production, 400,000 bbl of crude oil imports, and the rest from stocks. Petroleum's principal use is still as a fuel. The field remains highly competitive, but petroleum has been continuously progressing. Less than fifty years ago, oil supplied only one twentieth as much of the nation's total energy as coal, but today it supplies over half as much.

Jan 1, 1947

By H. A. J. Wilkens, H. B. C. Nitze

At the Atlanta meeting of the Institute in October,' 1895, some brief remarks were made by Mr. Wilkens on the above subject. It is the object of this paper to set forth the substance of these previous statements, embodying therewith additional information gained since that time, and a brief illustrated description of the method and means of the separation.* Lack of time will unfortunately not allow as complete a resume of the subject in all its phases, especially those relating to the scientific side of the question, as its novelty and importance would warrant, so that even this paper must be considered a preliminary one. It is hoped that at some future meeting of the Institute we may find an opportunity of presenting supplementary data of interest. The paradoxical title above used requires some explanation. The term " non-magnetic material " is applied to such substances as have heretofore been considered non-magnetic in the arts, more especially in the practice of ore-concentration. Scientifically, it has been shown by Faraday, Plucker, Wiedemann and other physicists that magnetism is an inherent property common to all substances, solid, liquid and gaseous, i.e., all suhstances are either attracted or repelled by the poles of a magnet, although ill the great majority of cases the manifestation of this

Jan 1, 1897

By L. R. van Wert

CAREFUL research into the nature of the metallic state has yet to discover, with any certainty, its essential quality. We do riot yet know, for sure, what it is that makes the metallic elements different from, if not actually unique among, all created things. We do know, of course, that metals have certain more or less characteristic properties-they are hard, strong, and tough, and good conductors of heat and electricity, and these so-called metallic properties provide a definition of a sort. How- ever, it is the structure rather than the behavior of the metals which gives the really fundamental information necessary to the understanding of metallicity. But this information is not easily obtained. Nature has a way of keeping secrets. But happily we do possess some knowledge of how a metal is built up, and it is this matter, rather than the presentation of a formal definition, that will be discussed here.

Jan 1, 1937

By J. V. W. REYNDERS

FIRST of all let me express my affectionate gratitude for the cordiality and good will of your reception. On the part of the men I venture to interpret the character of your greeting, not only as a recognition of the position to which you have been good enough to elect me, but also as an expression of your friendly attitude. However, I cannot pass over the tribute of the ladies so casually: Nor does it seem possible to do justice to my sentiments in addressing them collectively. I would feel more equal to the task if I could have the opportunity to talk to them singly, in doing which I know I may count upon their good sportsmanship not to compare notes. There has been some discussion between Mr. Kelly and myself as to our respective duties on this occasion: The precedents are not clear as to whether the retiring or the incoming president is expected to speak at length. Mr. Kelly's argument was that as the incoming president confines himself to promises for the future his field is a broad one and his opportunities for extending his remarks correspondingly unlimited.

Jan 1, 1925

By S.S. Clarke

The sheet-ground deposits of the Tri-State district, because they are fairly uniform in thickness (7 to II ft.)—rather flat, with an easy dip to the west—and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. Developing Tractors and Trailers A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Tig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½-in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the spring: could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dud. After four months of use, the .tires are beginning to show signs of failure.* In

Jan 1, 1943

By S. S. Clarke

The sheet-ground deposits of the Tri-State district, because they are fairly uniform in thickness (7 to II ft.)—rather flat, with an easy dip to the west—and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. Developing Tractors and Trailers A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Tig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½-in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the spring: could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dud. After four months of use, the .tires are beginning to show signs of failure.* In

Jan 1, 1943

By A. W. Ambrose, C. E. Beecher

It is the purpose of this paper to summarize data on unitization projects in Oklahoma and Kansas as obtained from replies to questionnaires sent out by the A. I. M. E. committee for these states. The information received indicates that unitization is growing rapidly in this area, but has not been in operation for a sufficient length of time to develop production history. It was impossible to obtain a record of all unitization projects in the time available. The magnitude of such projects is indicated by the fact that reports were received covering a total of 171,420 acres in Kansas and 49,350 acres in Oklahoma. Most of these units have been formed during the past 2 years, the greater number having been completed in 1929. It is anticipated that even more will be formed during the present year. The following important facts have been emphasized by answers to the questionnaire and discussion with various operators: 1. Unitization is growing rapidly, as evidenced by the number of units and the large total acreage now included in units as compared with practically no acreage 2 years ago. 2. Operators are convinced that unitization is reducing development and operating cost and they anticipate greater reductions as experience is gained in unit operation. 3. Producing units have not been in operation for a sufficient length of time to give significant production history from which to estimate the ultimate recovery of oil, but the general opinion seems to be that more oil will be recovered. 4. In view of the benefits to be derived from unitization, many operators are refusing to carry on wildcat operations unless a unit has been formed. If this attitude continues to grow there will be no large pools developed in Oklahoma and Kansas in the future except under unit control. Summary The following tabulation gives a condensed summary of the information received on unit operations in Oklahoma and Kansas, but does not include all units, because many were not reported.

Jan 1, 1930

By W. J. Keep

Some explanation of methods of testing will be given before presenting the record of a series of physical tests of aluminum, other metals and alloys. I. The Methods Employed and Meaning of Diagrams. The test-bars used, 12 inches long and 4 inch square, are cast in green sand, with chills bedded in such a way that the ends of the bar run against them. By splitting the ends of the bar the depth of chill can be measured. The chills being held in the mould 121/8 inches apart, the space between the end of the bar and the face of the chill, after both are alike cold, is the amount of shrinkage, and is recorded in thousandths of an inch per foot.

Jan 1, 1890

By George A. Grandy, D. W. Fuerstenau

Simulation of nonlinear grinding systems is discussed in the context of the size-discretized batch-grinding model. A linear approximation of environment-dependent (or nonlinear) selection functions is postulated for systems which exhibit feed grinding orders less than unity. For this, a convex linear combination of zero and first-order selection function forms is used to obtain an analytical solution that can be used for simulation. An example in which marked nonlinear behavior occurs is rod-mill grinding. Accordingly, a series of grinding experiments was carried out in a batch laboratory rod mill to test these techniques; agreement between experiment and the model was found to be very good. Recently, significant progress has been made in the simulation of linear grinding systems by using a population balance mathematical model. Herbst and Fuer-stenaul presented a parameter estimation scheme that can be used with the size-discretized batch-grinding model, and Gumtz and Fuerstenau3 have extended these techniques to the simulation of locked-cycle grinding. Grandy et aL." summarized the simulation of linear systems and noted important alternate solutions to the batch-grinding equation. Kelsall et a1.'-" discussed the dynamic simulation of linear batch grinding, as well as linear open and closed-circuit grinding. In all of these, the key word is linear, which certainly restricts the engineer trying to simulate a variety of grinding systems. This paper discusses an approach for the simulation of non-linear grinding systems, particularly those which exhibit grinding orders less than unity. Experimentally, dry rod-mill grinding is used to evaluate the technique presented. Batch Grinding Model The size-discretized batch-grinding model has been discussed in detail by Mika et al.'.' and by Herbst and Fuerstenau,' and therefore, will only be briefly developed here. The model is formulated by making a differential mass balance of each size fraction in such a manner that the equation parameters are precisely defined in terms of selection and breakage functions,' which can be either calculated'.' or estimated1 from experimental data. The model is phenomenological because it averages all stress-application events in the system and, therefore, does not distinguish the manner in which individual particles are stressed.' For this average environment, the resistance of all particles in a size fraction to breakage is defined by that size-frac-tion's selection function; and when fracture occurs from an average event, the breakage product size distribution is defined again by that size-fraction's breakage function. The model is deterministic and is derived in terms of a continuous time variable and a discretized size variable,' i.e., the n mass fractions associated with the n defined size intervals (see Table 1 for nomenclature).

Jan 1, 1971