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By Albert Sauveur

THE senior author of this paper has expressed the belief that when gamma iron transforms into alpha iron on reaching the A3 point, each gamma grain does not change bodily into one or more alpha grains but that the alpha phase forms first at the boundaries and along the crystallographic planes of the austenite grains.1 To quote: On cooling through the point A, at about 900° C., iron passes from the gamma condition to a. new allotropic form generally designated as alpha. This transforma¬tion, however, is not instantaneous. There are good reasons for believing that it begins at the grain boundaries and along the octahedral planes of the crystals and that it progresses until each grain of gamma iron is changed into a grain of alpha iron, the resulting structure being similar to that of gamma iron. Were it possible to retain at room temperature pure iron but partially transformed, it seems probable that a Widmanstättian structure, or rather, as later explained, a martensitic structure would be observed (Fig. 1), consisting of alpha iron at the boundaries and at the octahedral planes, and of a groundmass of gamma iron. In order to confirm, if possible, the accuracy of that view, a number of experiments were conducted. Polished samples of electrolytic iron were heated in a vacuum, maintained in the gamma range for several hours and quenched in different media. It was hoped by such means to produce and retain on the polished surfaces a pattern which would reveal the mechanism of the allotropic transformation. The samples were placed in evacuated quartz tubes, heated to 1000° C. and held 2 hr. at that temperature. The tubes were then immersed in the quenching bath. Iced brine and liquid air were used first. The polyhedral austenitic structure existing at the time of immersion was very clearly revealed (Fig. 2). This is generally ascribed to iron volatilizing at the grain boundaries.

Jan 1, 1929

By R. P. McLaughlin

In most branches of the mining industry it is a well-recognized fact that care must be taken to protect the mineral deposit from undue physical injury. It is comparatively easy to grasp this idea when the mineral is a solid and the lives of workmen depend directly upon the care with which it is removed from its natural position, but when the product is a liquid drawn up from pools several thousand feet beneath the surface of the ground through openings only a few inches in diameter, it requires some imagination to picture underground conditions and the changes which must often occur. The development of the petroleum deposits of California has been attended by numerous accidents, the results of which are readily noticed at the top of the wells and in the profit and loss accounts of the operators. Determination of the cause of these accidents has been the subject of considerable study, which naturally has fallen upon men familiar with technical methods. The greatest damage to the oil deposits of California has resulted from water finding its way into the oil-bearing sands, and it is the purpose of this paper to set forth briefly this phase of the oil industry. Much of the material here presented has previously appeared in publications issued by the California State Mining Bureau, which, under the direction of State Mineralogist Fletcher McN. Hamilton, has investigated the subject and taken steps toward improvement of conditions. The writer, having been in charge of this branch of the Bureau work, has gained considerable knowledge of existing conditions. Generally speaking, the oil-bearing formations of California are soft, unconsolidated sand beds, separated by clay strata, which are also soft. Some of the sand beds carry water instead of oil. All of the beds are more or less separated, probably being of lenticular shape. Very few of the beds in the oil fields lie flat or undisturbed over any great area. Folding and tilting are common, and faulting also occurs in some of the fields. The accumulation of oil is not confined to any single structural feature, such as the anticline, but occurs in many other structural features. Water-bearing strata occur in practically every oil field in the State. Complete data are not at hand for a comparison of the damage

Jan 1, 1916

By Bradley Stoughton

(Cleveland Meeting, October, 1912.) [SECRETARY'S NOTE.-To avoid repetition of foot-notes, references to authorities are made in this paper by means of figures, referring to a numbered list in the appendix.-J. S.] INTRODUCTION. THIS paper gives the results : first, of a research into the somewhat extensive literature of titanium; and second, of a series of original tests upon the effect of titanium on iron castings. New investigations have also been made upon the effect of titanium on steel, but I hope to treat this subject in an independent paper at some later date, and, therefore, will not discuss the experiments in detail here. The combined results of this study, which extended over a period of more than two years, can be briefly summarized as follows: 1. Steel or cast-iron, in which the titanium is properly proportioned, and which has been properly treated, is improved in strength, toughness, and durability against wear, such as, for example, the wear of railroad-rails, of steel and chilled-iron .rolls, car-wheels, etc. 2. These improvements seem to be caused, not so much by the direct effect of titanium on the metal, as by its cleansing influence in removing harmful impurities, such as oxygen and oxides, nitrogen, occluded slags, and perhaps also sulphur. It appears also to reduce segregation, which would contribute to the same end. 3. In order that its effects may be fully realized, the treatment of steel or iron with titanium must be correctly performed. There are a few simple, but essential, details to be observed; if they are neglected, the best results cannot be expected. To illustrate by an example : A series of tests on cast iron

Nov 1, 1912

By T. W. Beck

Roof bolter occupations in underground coal mines continue to experience overexposure to respirable dust. One potential source of dust in roof bolting operations is the exhaust from the roof bolter dust collection system. A wet exhaust conditioner (water box) has been developed to reduce dust emissions from the exhaust of the vacuum dust collection system on roof bolting machines. The exhaust conditioner consists of a muffler chamber and a water chamber with four internal partitions to direct airflow over the surface of the water. The National Institute for Occupational Safety and Health conducted a series of laboratory tests to assess the respirable dust capture ability of this device as compared to the standard exhaust muffler. To determine the dust collection efficiency, both devices were placed in the exhaust stream of a simulated roof bolter dust collection system. Gravimetric samplers were operated upstream and downstream of the exhaust conditioner and muffler to evaluate the ability to capture both respirable coal and limestone dust. Researchers observed a 41 % reduction in dust concentrations for the water exhaust conditioner in the laboratory configuration. Significant levels of dust deposition in the sampling chambers may have contributed to this effective capture rate.

Jan 1, 2012

THE. extraordinary volume of work done in this period, and the multiplicity of subject matter, make a year-by-year historical account undesirable, if the account is not to be an assembly of unrelated fragments. We shall, instead, undertake to narrate the development in this period of each of the branches of the subject separately, hoping that their interrelations will be self-evident. There is a certain arbitrariness in the selection of subject matter in the following sections. The development of important engineering alloys-for example, high-speed steel-is disregarded, for it is the primary purpose of this account to relate the advances in ideas, the growth of the science of metals; other historical accounts relate these parallel advances. Nor are advances in techniques stressed, though occasionally the most important are noted; nor is the progress described in allied fields such as welding, cutting, etc.; for though these developments have very frequently made possible the advances herein related, they are far too numerous to recount in anything short of a ponderous volume. There is a more serious arbitrariness, however; it is not an easy matter to draw the boundaries of physical metallurgy, and some contiguous subjects have been omitted that perhaps should have been included, such as, for example, corrosion, gases in metals, the magnetic behavior of metals and alloys, and certain other fields in the physics of metals. REACTIONS IN ALLOYS--DIFFUSION Many of the reactions occurring in alloys proceed by the operation of the process of diffusion in the solid state: the annealing of mixed powders to form alloys, the homogenization of castings or forgings, the freezing of alloys, the treatment of clad metals, the loss

Jan 1, 1948

AT the meeting of the Board of Directors held on June 25, 1926, and in response to numerous in-dividual suggestions for changes, a committee on Re-vision of the Constitution and By-Laws of the Insti-tute was appointed, consisting of C. F. Rand, Archi-bald Douglas and H. Foster Bain. Various confer-ences were held, much correspondence conducted and a preliminary draft was prepared. It proved imprac-ticable to complete the work in time to submit the matter to the membership for approval or disapproval at the annual meeting in 1927, and the Committee was continued with instructions to prepare a report as a basis of action in 1928. After Mr. Rand's death George Otis Smith was appointed in his place and the tentative draft herewith submitted has been pre-pared in its present form by Messrs. Smith, Douglas and Bain, though not differing in any material mat-ter from an earlier draft approved by Mr. Rand. In preparing this the Committee has kept in mind primarily the desirability of simplification and of making the By-Laws conform to the actual practice of the Institute as worked out through experience. The Constitution and By-Laws adopted in 1912, and which with minor amendments only still govern the Insti-tute, are full of specific provisions regarding pro-cedure; such as that laid down for guidance of the Papers and Publications Committee. Many of these have proved unworkable and in practice have not been always strictly followed. It now seems wise to write into the Constitution and By-Laws only the general fun-damental principles to he followed and to provide for such easy change in methods of following them out as will permit efficient conduct of the business. It is this thought that has guided the Committee in rewrit-ing many of the sections. With this in view also the Constitution, as such, has been shortened to the brief-est feasible statement of fundamentals. All matters relating to means of making these principles effec-tive have been put into the By-Laws or in the hands of committees whose work is subject to control and whose rules are subject to approval or disapproval by the Board of Directors. Many suggestions for changes have come to the Committee that have not been incorporated in this draft. Some of these are in themselves excellent but have not been incorporated here because the Commit-tee discovered no sentiment for them such as would be likely to secure their approval, or found them out of harmony with the general plan followed herein.

Jan 9, 1927

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 Charles H. Foreman, James F. McCarthy

The orebodies of the Hecla mine are from 3 to 40 ft. wide, dip not less than 70°, and in most cases are nearly vertical. The Hecla and Intermediate orebodies are generally associated with a lamprophyric dike, usually about 2 ft. wide, but which attains a maximum width of 7 ft. The ore appears on either or both sides of the dike. The country rock is Burke quartzite with no definite walls and a tendency for nearly horizontal, but irregular, quartz stringers to run from the lode into the walls. This latter condition prevails almost entirely in the hanging wall, causing a natural tendency for portions of the wall to "offset" and resulting in an extremely heavy side pressure. The fact that there are no definite walls causes a great variation in the width of the stopes, as stringers will run into the walls for irregular distances. The ore occurs as galena in varying widths and grades. It is often necessary to mine a face having a " horse"' of waste between two stringers of ore. This block of waste might be 6 or 7 ft. wide but with the Hecla method it is necessary to mine the entire face. In this case an effort is made only to shatter the waste, allowing for easy sorting underground. The Hecla mine requires a flexible system allowing for the extraction of ore from varying widths, with the necessity of close filling to give the needed protection from side weight. About 15' per cent. of the material broken in the face is sorted as waste, either at the face of stope, or in the sorting plant. Shafts, Drifts and Crosscuts The outside dimensions of the shaft are 19 ft. 4 in. by 7 ft. 2 in. The shaft consists of three working compartments, two for the hoisting of ore and one for auxiliary work. The working compartments are 5 ft. 2 in. by 4 ft. 4 in. inside measurement. The rest of the shaft is used for pump column, electric cables, and ladderway. (See Fig. 6 for framing of timbers.) The shaft is about 700 It. from the orebody for topographical reasons. Solid formation was not reached in shaft for 80 ft. Timbers in this section became alternately wet and dry on account of seasonal changes

Jan 1, 1925

By JOHN R. SUMAN

IT appears now that the conflict with the totalitarian states will be a long-drawn-out struggle. The course of this war up to now indicates that this may well be the first major conflict where man power has not been the vital and determining factor. Mechanized warfare has made it possible for relatively small, well-equipped groups to outmaneuver and defeat large armies which lack the necessary modern equipment. Under these circumstances, ultimate victory becomes a matter of resources and productive ability. The important question is not how many soldiers can he put into the field, but the volume and speed in producing the armaments essential to ensure a victory. The resources available to the opposing nations and the efficiency of their systems of enterprise and production will be primary factors in determining the ultimate outcome. Germany had a head start of eight years in the armament race, and it is not easy to overcome such an advantage overnight.

Jan 1, 1942

By Paul M. Tyler, Carle R. Hayward

DOES it pay to do really good work? Quite likely the practical millman will answer that it does not. The preparation of ores for market is primarily a business enterprise, and by and large the individual operator does not bother his head about squandering our national resources or making easier the job of the smelterman. Having accepted such ore as he may get fro111 the mine, his job is to make the best possible showing with his mill fro111 the standpoint of financial return. His success is measured in dollars and cents, and he has no rightful reason to expect more than scant acknowledgment of any other achievements from the stock- holders of his company who in the last analysis are his employers.

Jan 1, 1936

By Frank J. Tolonen, Nicholas H. Manderfield, Paul Jasberg

EARLY in the study of the low grade iron formations of Michigan, wide variations in their structure and texture became evident. Because of these variations no simple method of concentration is possible, and those portions of the formations that can be exploited profitably under a given stage of metallurgical progress and existing economic conditions must be searched for carefully. Both structure and texture of the formations have an important bearing on their amenability to beneficiation. By structure is meant the banding planes of easy fracture, the porosity, and the degree of leaching. Texture, which includes grain sizes, shapes, and degree of interlocking, determines the amount of grinding necessary to liberate the mineral grains. Structure determines the liberation of portions richer in one mineral. Structure and texture may be termed the gross features of the formation

Jan 11, 1957

By N. G. W., Cook

When an excavation is made underground the original rock stresses are removed from the surfaces of the excavation. These surfaces converge to partially close the excavation and the superincumbent rock mass moves down towards the excavation. If the convergence of the surfaces of the excavation were controlled, energy generated by their motion against the controlling forces could be extracted. Since the total forces in the rock mass are not significantly affected by the excavation, stress concentrations arise around the excavation, which compensate exactly for those stresses no longer transmitted through the excavation. These phenomena give rise to two general principles which provide the basis for analyzing the effects of making any underground excavation. The first of these is that the total force resulting from the stresses across any plane in the rock, including any plane through the excavation, must be the same before and after the excavation is made. The second of these is that energy must necessarily be released as a result of making an underground excavation.

Jan 1, 1969

E. Windsor Richards, London, England:—In reading this paper the most interesting point to me mas the question of the maximum percentage of phosphorus allowable in the steel rail. Mr. Colby said, and we will all agree with him, that the engineer knew, and even a steel-rail maker grants that phosphorus is the most undesirable constituent of steel. We in England have been for a long time considering a specification for the supply of steel rails. This matter has been taken up by the Institution of Civil Engineers, the Mechanical Engineers, the Iron and Steel Institute, the Institute of Naval Architects, and the Electrical Engineers. Committees have been formed,and the whole matter has received most careful attention. They arrived at last at an analysis which I will read: " The carbon is to be from 0.35 to 0.5 per cent.; the manganese from 0.7 to 1.0 per cent.; the silicon, not to exceed 0.10 per cent.; phosphorus, 0.07; and sulphur, 0.07 per cent." As to the phosphorus, which is the most important point of all in the analysis, we have for many years, and indeed until very lately, always agreed to supply steel which would not contain above 0.06 per cent. of phosphorus. Iron-ores are not quite as good now as they were formerly, and the manufacturers at the meetings of the committees referred to, tried to obtain an increase in the allowance of phosphorus. They asked the Sub-committee to agree to 0.08 per cent. of phosphorus. They tried all they possibly could to obtain that; but they failed. English engineers in Great George Street and all over England, representing the important Associa tions I have mentioned, would only agree to 0.07 per cent. and that is the maximum allowance of phosphorus. Mr. Colby is an able advocate, but with all his ability he would not have been able to persuade the English engineers to agree to 0.08 per cent.

Jan 1, 1907

By Baxter C. Madden

Stress corrosion is defined and certain examples are illustrated. A number of test methods, to determine the resistance of materials to stress corrosion, are being developed at Wright Field. The criterion as to the validity of a method is stated. Three types of specimens and the method of stressing each type are described. Five different corrosive conditions are set forth. The results of tests to date, although too few for any general conclusions to be arrived at, are presented. The program for the continuation of the investigation is indicated. A bibliography is included. The development of the method of loading a cantilever-type specimen, so that a nearly constant stress at a large deflection may be realized, is presented as Appendix I.

Jan 1, 1945

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

By J. M. Mutmansky, T. K. Greer

This paper takes a look at the optimal velocity to be used in coal mine entries and determines a statistical relationship for optimal velocity that can be applied under current mining conditions. This relationship provides the optimal velocity for coal mine airways under variations in power cost, mining cost differential, airway friction factor, time value of money, airway lifespan, and quantity of air carried. This enables the ventilation engineer to make an easy, rapid determination of the optimal velocity for planning purposes.

Jan 1, 1985

By R. A. Wagstaff

SINCE the time of the early Egyptians, the use of copper has been a boon to the life of most of the civilized world. Its use has been varied; in many connections, the art by which it attained its greatest usefulness has been lost. In this paper an endeavor will be made to take into consideration some of the many changes that have occurred during the last 40 years of copper-smelting operations. During that period the copper blast furnace has been almost forced out of existence by new methods of ore concentration-first, gravity concentration, and then flotation. These new methods of concentration introduced many new factors into the metallurgy of copper. The product was wet, it was fine and it was high grade. To overcome all these factors many changes have been necessary throughout the smelting agenda. New equipment has been necessary for transportation, unloading, sampling, bedding and moisturing in all smelting plants, especially the custom smelter. During the early days of "flotation," little was known about filtering or the use of an alkaline circuit; often the concentrate going to the smelter contained 20 to 25 per cent moisture. It is easy to imagine the difficulty arising with a product of this nature when it had to be shoveled by hand labor. To meet these conditions, mechanical unloading and sampling devices were soon developed. In many instances such good progress was made that actual costs for handling this unfavorable product were lower than those formerly incurred on the old product. Today most sampling of copper ores and concentrates is being done by mechanical sampling, pipe or augur sampling, or shovel sampling. Where concentrates are uniform in metal content, a great many of the plants now use pipe or augur sampling. For spotty ores, the old shovel sample with cone and quartering during the final stages is still in use. Where big tonnages are handled, mechanical sampling of concentrates is being done, with satisfactory results. To curtail slow and tedious cutting and mixing procedure, mechanical mixing boxes, splitters and cutters are used to cut down labor costs. MILLING As crude ores become scarcer, the use of milling operations increases. The few crude ores that are still smelted are used as fluxing types. To use these ores finer grinding has been found advantageous. This has made for better bedding and fluxing conditions, which in turn makes for faster smelting, lower fuel consumption and better metal recovery. The degree of fineness is more or less determined by the nature of the product. Most plants have set a standard of through ¾ -in. mesh screen for roaster- reverberatory smelting and through ¾ in. mesh screen for converter fluxes. For some refractory ores; even finer grinding has been found to be advantageous for good reverberatory smelting.

Jan 1, 1944

By W. H. Yarroll

This paper presents a general discussion of the utility of the statistical technique known as multiple correlation, and gives three specific examples of its application. The first demonstrates the most simple form, or straight-line, multiple correlation. The other two demonstrate multiple correlation analysis in best-fitting third-degree parabolas. With the increasing availability of digital computers, the method becomes entirely feasible where heretofore its use was impractical. The advantages of the method are discussed, and curves are presented which were developed by computerizing the regression equations developed in the examples. The method described in this paper is for use with complex systems, and the examples given are complex metallurgical systems. This subject falls under the general classification of cybernetics, which is defined' as "the science of control and communication, in the animal and the machine." Machine, in this case, can include chemical and physical processes which take place within machines and processing equipment of all kinds. The classical approach to scientific investigation has been the construction of simple models and the changing of variables one at a time. This method is wholly inadequate for obtaining useful information from the complex systems of modern technology including many of our flotation and hydrometallurgical processes. Cybernetics offers the method by which complex systems which have been implemented as an art in the past can now be analyzed with all the discipline of a science. Mathematical techniques for achieving multiple correlation analysis have decided advantages over some of the other statistical methods.2-4 Multiple correlation does not require a series of experiments that have been rigidly planned as do many of the other statistical methods. For this reason, it can be used effectively for interpretation of information from op- erating plants, where planned experiments are impractical, as well as for laboratory experiments. First-degree multiple correlation has been used for many years, and was useful, but limited to linear or nearly linear relationships. The technique described in this paper provides a method for analyzing systems which may be non-linear. This particular technique is multiple correlation analysis in best-fitting third-degree parabolas. It is quite possible that lack of reference to the technique has been due to the overwhelming mass of computations it requires even for relatively simple problems. With the advent of computers, however, its use has become entirely feasible. For the benefit of those who may not be familiar with the subject, it might be well to pause at this point to discuss multiple correlation analysis — what it is and what it achieves. To go back to the old familiar fitting of a set of points with a best-fitting straight line by the least squares procedure, it is conceded that this a good method where there is only one independent variable influencing the dependent variable under consideration, and providing that the relationship is linear. In most fields of investigation, however, there are usually a number of factors exerting important influence, and they frequently bear relationships with the dependent variable other than straight line. Under these conditions, it is easy to see how misleading a simple correlation study might be. Multiple correlation can be used for any number of variables. Within the experience of the writer, this technique has been used to establish regression equations for determination of carbon rate, burden permeability, and production rate on iron blast furnaces, production rate on open hearth steel furnaces, life of molds for steel ingots, rolled steel tensile strength and various defects in rolled products, the performance of ore dressing equipment, and optimization of extractive metallurgical process variables. The discovery of mathematical correlation does not prove, per se, true cause-and-effect relationship, but simply establishes a hypothesis. If the regression equation can be used to make successful predictions of what will happen with future arrays of independent variables, then one can feel reasonably assured that true cause-and-effect relationships have been discovered.

Jan 1, 1968