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By T. P. Meloy

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,

Jan 1, 1963

By John V. Beall

One Sunday night last month the phone rang and it was George Schenck from Penn State. How would we like to see a big scrap operation, he wanted to know. A few days later we were on the Connecticut turnpike headed for New Haven to visit a large scrap operation, M. Schiavone and Sons. George had a large clam basket in the back which he explained was for collecting trophies. The car shredder, he said, turns out some fancy metal shapes. In fact, they have gained a certain acceptance as objets d’art among George's friends and relatives. He thinks there may be a small, but possibly lucrative secondary market for shredded cars in the art world if the idea is imaginatively promoted. On the way to New Haven we received a briefing on the scrap industry. The scrap business grew from humble beginnings. Mostly it was started by a few immigrant Jews who collected junk in hand- or horse-drawn carts. The fortunate one might even have had a truck. Before proceeding further, we hasten to point out that the word "junk" is strictly taboo among scrap people, who prefer to refer to their industry as the "secondary metals industry."

Jan 1, 1970

By D. Geiselman, A. G. Guy

Single cvystals were grown from high-purity magnesium containing known amounts of nitvogen in the range 0.0008 to 0.0048 wt pet. Crystals of known ovientation were tested in tension in an Instron ma chine to determine the yield strength and to obsevue wheather a yield point occurred. Slowly cooled crystals or those given a solution heat treatment did not show a yield point. However, crystals that were aged following a solution treatment showed a yield point for all of the nitrogen contents studied. It was concluded that nitrogen caused the yield point by the Cottrell mechanism. NITROGEN has been shown to produce sharp yield points in single crystals of cadmium, zinc,2'3 ß-brass,4 and iron,5,6 as well as in polycrystalline iron7 and molybdenum.8,9 Since magnesium has a structure similar to zinc and cadmium, it seemed reasonable that magnesium should also exhibit a sharp yield point provided it contained sufficient nitrogen. Bobalek and Shrader10 reported a total nitrogen content of 0.002 to 0.0065 wt pct in com- mercial magnesium alloys, an amount well in excess of that required by theory. However. magnesium differs from cadmium and zinc in that it forms a stable nitride, Mg3N2, which has a standard free energy of formation of -95,480 cal per mole at 25" c." If rather than being in solid solution, the nitrogen were predominantly combined as the nitride, it could not act to produce a yield point. This type of behavior is the basis for the elimination of strain aging and a yield point in steel by the addition of strong nitride formers such as titanium,12 columbium,13 aluminum,14 vanadium,15 and boron.16,17 Thus, there appeared to be factors both favorable and unfavorable to the production by nitrogen of a sharp yield point in magnesium, and the purpose of this investigation was to determine the actual behavior of magnesium crystals containing known amounts of nitrogen.

Jan 1, 1960

By Hermann Wedding

It is now fourteen years since we German ironmasters, in considerable number, visited the United States on the occasion of the Philadelphia Exposition, and found the iron metallurgy of this country, as must be frankly confessed, in an advanced stage of development not previously suspected by us. At that time the United States already occupied, as now, the second rank, with Germany in the third, the product of pig-iron for that year being, in Great Britain, 6550, in this country, 2093, and in Germany, 1850 kilotons.* This relative position has not been changed. The present annual product of the three countries is, in round numbers, Great Britain, 8380, the United States, 7790, and Germany, 4530 kilotons. But the proportion of the United States, which was, in 1876, but 15 per cent. of the world's product, has now advanced to 30 per cent. When we left America in 1876, it was not only with gratitude for cordial hospitality and for the liberality with which our professional colleagues here had opened to our inspection whatever was worthy of notice in our special field, but also with the conviction that we had collected a great treasure of new and interesting information which we could utilize for the benefit of our German Fatherland. Particularly the achievements of the never-to-be-forgotten Holley in the field of Bessemer practice, set us an inspiring example for imitation in our own country. As an expression of our thanks in more practical fashion, I attempt in this paper to sketch what we have done in Germany since

Jan 1, 1891

A tentative plan for the Colorado Meeting has been formulated as follows: One day will be spent at Denver, one day at Colorado Springs, one day at Cripple Creek, a trip by automobile to the top of Pike's Peak, one day at Pueblo, one day at Leadville. All the principal mines and mills of the districts mentioned will be visited, including the gold mines in Cripple Creek, the lead, zinc, and steel works. of Pueblo, the production of ferro-molybdenum by electric furnace at Leadville, etc. Special arrangements are being made for the social entertainment of ladies at all points; one evening at Colorado Springs will be devoted to a reception and dance, and the usual dinner will he given on another evening. The following papers have already been accepted for the Colorado Meeting, and some have already been published: Fireproofing Mine Shafts by the Anaconda Copper Mining Co. By E. M. Norris. (March Bulletin.) Air Blasts in the Kolar Gold Field, India. By E. S. Moore. (March Bulletin.) The Use of Coal in Pulverized Form. By H. R. Collins. (April Bulletin.) Coal Mining in Washington. By F. A. Hill. (April Bulletin.) Carbocoal. By C. T. Malcolmson. (May Bulletin.) Gaging and Storage of Oil in the Mid-continent Field. By O. U. Bradley. (March Bulletin.) An Interpretation of the So-called Paraffin Dirt of the Gulf Coast Oil Fields. By A. D. Brokaw. (April Bulletin.) The Theory of Volcanic Origin of Salt Domes. By. E. DeGolyer. (May Bulletin.)

Jan 5, 1918

By George S. Rice

Ten years ago: October, 1914, the author had the privilege of giving an illustrated address on investigations of coal-dust explosions1 to this Institute at one session of its fall meeting in Pittsburgh, Pa,. On the following day, the members had the opportunity of seeing a large-scale explosion test at the Experimental Mine near Bruceton, in which the explosion was made to follow a predetermined path by means of rock-dust barriers of various types, which had prevented the explosive waves from reaching the outlets of the mine by the shortest paths.2 There was also shown a ((home-made" rock-dusting machine discharging the dust from a flexible nozzle, and a cement gun operated for the quick erection of a fire or ventilation stopping, such as might be put up after an explosion. Following that paper, there was presented a paper by J. Taffanel, Director of the Lìévin testing station in the Pas de Calais, which reviewed the French coal-dust investigations.3 A paper4 by Howard N. Eavenson contains lists of explosions that occurred in North America and Great Britain, from early in the 19th century to 1912; in France to 1903, and Belgium to 1909. Although explosions still occur, we are hopeful that we have entered a happier freedom from these visitations, as the result of increased knowledge of the causes and means of prevention. Looking back over coal-dust investigations, there appear to have been periods of advance and of stagnation. Coal-dust Investigations From the earliest times of coal mining, which chiefly affected Great Britain as the first nation to take up coal mining on a large scale, to the beginning of the 19th century, no one thought of coal dust as an explosive agency; firedamp was the cause dreaded. It was believed, when Sir Humphrey Davy invented his safety lamp in 1815, that a solution had been found for the prevention of mine explo-

Jan 1, 1925

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt' studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger' discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and

By John V. Beall

With some difficulty we framed the picture of the village on the mountain getting in the railroad bridge and tunnel at the base. It was a charming scene of red-tile roofs on a green mountain in the golden autumn sunshine with the black hole of the railroad tunnel looking like something out of the movie, "The Train." We clicked the shutter, advanced the film and started back to our rented Audi. At which point there was a hail from the other side of the railroad bridge. A man in uniform was brandishing an object in the air which looked suspiciously like a rifle. We peered around. We were the only other persons in view. He must be yelling at us. He was now closing the distance at a brisk, determined gait but was still 100 yards away. The car was handy but the road was straight, paralleling the railroad tracks for some distance. We dismissed the idea of running for it. Who knows, he might shoot. When he came up we didn't have much of a conversation because it had taken us a week to learn three words of Yugoslavian-zhiveli, long life, huhvalla, thank you, and schlivavitza, the national drink (plum brandy). None of these seemed appropriate. We got the Idea that photographs of railroad tunnels and bridges were prohibited. The guard, for such he seemed to be, took the Audi plate number, administered a last scowling reprimand and stalked off. This incident was the only one in a 15-day visit to Yugoslavia which we would have associated with "Iron Curtain restrictions."

Jan 1, 1970

By AIME

AS with Phil Kraft, referred to on this page last month, travel has always held a great fascination for Raymond Frank Baker and for that reason he determined to become a geologist. He had heard that geologists travel and that was what he wanted to do. Now as chief geologist for The Texas Co. his early wish has been fulfilled-he spends almost one third of his time journeying' from one oil field to another. Mr. Baker was born in New Haven, Conn., on Jan. 11, 1892, and went through the public schools in New Britain. A stalwart New Englander, he attended Yale and in 1912 received a degree in civil engineering. For a year following this he worked as a civil engineer for the New York Central Railroad, but his early urge to travel widely could not be satisfied here. So in 1913 he re-entered Yale and until 1916 studied mining and economic geology. He had a little taste of field work, which later became so enjoyable to him, in the summer of 1915 when he worked with the U. S. Geological Survey as a geologic aid. In 1916 he made his first contact with The Texas Co. when he entered their Tulsa office as a geologist. This early career was interrupted by service in the

Jan 1, 1947

By George B. Langford

ON THE QUESTION of postwar controls there are today three schools of though ; some advocate state control of everything the socialists ; second are those who advocate the removal of all governmental control over industry - the freedom of enterprise ideal ; and third are those who advocate a middle course - sufficient control to stabilize economic and industrial life, and to prevent violent fluctuations such as we saw in the interwar years. I advocate this third course. I firmly believe un free enterprise, but not in freedom of enterprise, or laissez faire, and there is a great and significant difference between these two.

Jan 1, 1944

By William E. Ford, Edward Salisbury Dana

URANINITE. Cleveite. Broggerite. Nivenite. Pitchblende. Isometric. In octahedrons (o), also with dodecahedra1 faces (d) ; less often in cubes with o and d. Crystals rare. Usually massive and botryoidal; also in grains; structure sometimes columnar, or curved lamellar. Fracture conchoidal to uneven. Brittle. H. = 5'5. G. = 9'0 to 9'7 of crystals; of massive altered forms from 6'4 upwards. Luster submetallic, to greasy or pitch-like, and dull. Color grayish, greenish, brownish, velvet- black. Streak brownish black, grayish, olive-green, a little shining. Opaque. Comp. -A uranate of uranyl, lead, usually thorium (or zirconium), often the metals of the lanthanum and yttrium groups; also containing the gases nitrogen, helium and argon, in varying amounts up to 2'6 p. c. Calcium and water (essential?) are present in small quantities; iron also, but only as an impurity. The relation between the bases varies widely and no definite for- mula can be given. Radium was first discovered in this mineral and it has been shown that it and the helium present are products of the breaking down of the uranium.

Jan 1, 1922

By AIME AIME

THE petroleum engineers have the conference habit. They drop in, thresh things over, and drop out. No time is wasted. So it was at the Fort Worth meeting of the Petroleum Division, Thursday and Friday, Oct. 8 and 9; headquarters, Blackstone Hotel. Associate Chairman Albertson arrived the morning of the 7th, to tie in any loose ends of the technical program. S. M. Greenidge, chairman of the local committee, checked the arrangements with his committeemen at a luncheon that noon. By mid-afternoon the next day's attendance was anybody's guess-there were no noses to count. But when the gavel sounded Thursday morning 175 members and guests were present, also the official A.I.M.E. party consisting of President Lovejoy, Secretary Parsons, and George Otis Smith. Shortly after adjournment Friday afternoon all but a handful had vamoosed, lit out, disap¬peared. But, in the meantime, it was a grand conference, attendance maximum every session, and the discussion fast and furious. The discussion came from all over the floor, sometimes as good-natured sniping, sometimes in long volleys that were almost fatal to the reporter. Everyone knew his subject and few there were who had nothing to say.

Jan 1, 1936

By A. M. E. Eilers

No one who has visited our Western mining districts, and studied the economical part of the beneficiation of the ores occurring all over that vast extent of country, can underrate the high importance of the above subject. By far the larger number of the districts which contain smelting ores, i.e., argentiferous and auriferous lead, or copper ores, are situated in the Great Basin, that great plateau between the Rocky Mountains on the east, and the Sierra Nevada on the west, almost the whole of which is comprised at present in the boundaries of Nevada, Utah, and part of Arizona. This region is essentially a barren country. The extreme dryness of the atmosphere permits but a scanty vegetation in the plains ; and even in the detached mountain-chains running through it-generally from N. to S., or from N. W. to S. E.-there are no trees found except dwarfed pines and mahogany, at the head of sheltered ravines, and a few cottonwoods and willows, which fringe the insignificant streams, before the water sinks in the arid plains. Nearly all the mountain-chains in this region are rich in silver ores. That class of these ores which is adapted to amalgamation, and rich in silver, has been worked with profit for more than ten years. But before the advent of the transcontinental railways, mining was restricted to these ores alone, and the consumption of fuel could be met with the scanty supply of forest trees in the immediate vicinity of the mining districts. Since, however, the Union and Central Pacific Railroads have brought the Great Basin nearer to the commercial centres of the East and the Pacific coast, thus reducing the expenses of freight and labor materially, other silver deposits, containing poorer ores in greater abundance, have been rapidly taken

Jan 1, 1873

By David T. Day

In the summer of 1898, a demand suddenly arose for commercial quantities of the element osmium. At least half a ton was wanted for the manufacture of a new incandescent light. This led the writer to examine localities where platinum had been reported, in order to determine whether osmiridium mas contained in the crude platinum. With the co-operation of the concern most interested, the Welsbach Light Company, and in company with its President, Col. William E. Barrows, I visited most of the leading American localities where platinum has been obtained. I also wrote to every available placer-mine in the West for samples of the heaviest sands, in order to test them for platinum. The results of this inquiry are given in the present paper. Distribution. The notices of the occurrence of platinum in this country given in scientific journals include two interesting observa tions in the East. One concerns a nugget described by Peter Collier of Washington, D. C.,* and said to have been found on land adjacent to the village of Plattsburgh, N. Y., which weighed 104.4 grammes, and contained sufficient chromite to reduce the specific gravity from 17.35 for the heaviest portion to

Jan 1, 1901

G. M. TAYLOR,* Colorado Springs, Colo.-The ore treated at the United Eastern is primarily a gold one and is cyanided-the counter-current decantation method being employed. One of our employees visited this plant a few months ago and, on his return, reported that the moisture in the tailing was carrying 20 c. per ton, which would appear to be somewhat high. As this type of plant has been advocated by one of the recognized cyaniding engineering firms in the country, and a number of these plants are in successful operation, it does not seem to me that the dissolved loss could be so high, and I would like to know if any one can give any definite information on this point? J. V. N. DORR, New York, N. Y.-I am very glad that Mr. Taylor has raised this question. When I first read Mr. North's paper and saw his statement, that they had an actual dissolved loss of 21.5 c. per ton, I was very much puzzled at this high loss which appeared avoidable by another decantation or the addition of a rotary filter. Reading it again, however, I noted that the actual dissolved loss of 21.5 c. given was evi-dently obtained by multiplying the assay of solution discharged from Z. thickener by the tonnage. On the basis of 283 tons milled per clay, this means $56.54 going to the clam. He states, however, that he returns from. the dam into the system, 70 tons daily assaying 40 c. per ton or $28 per day, so it would seem reasonable, unless I have overlooked something to regard the actual dissolved loss as $56.54 less $28 or $28.54, equaling 10.8 c. per ton. Even this loss, however, is much higher than good practice elsewhere, and can be accounted for largely by the tonnage being handled, which I believe is 30 per cent. above the capacity planned.

Jan 12, 1919

By Bunting S. Crocker

Bunting S. Crocker (Executive Vice President, Kilborn Engineering Ltd., Toronto, Ont., Canada)-This is an interesting report on laboratory-scale testing with pebble charges in 12-in.-diam mills, and the author correctly concludes that useful laboratory testing can be done. In the opening paragraphs he states, "laboratory pebble-milling tests have been considered too difficult to perform and not relevant enough to the actual grinding situation"!! This is definitely not so! The writer published detailed tests done in a 12-in.-diam mill comparing pebble and steel balls in 1952 6 and again in 1954 7. We note that our review paper in 1963 was the only one mentioned in the References. The author states that "a smooth lining is more frequently used in commercial-scale pebble grinding." The writer has designed some 22 plants treating 134,000 tpd in North America and Australia. He has also visited pebble installations in Norway, Sweden, Finland, and South Africa. All these plants correctly use heavier lifters than would be considered standard for ball mills of a similar size. Smooth liners are not recommended in wet ore treating plants. In the 1952 paper6 it was clearly demonstrated in the test work that the individual ore pebbles had to be the same weight-not the same diameter or size-as the steel balls if comparable grinding results were to be obtained. In the tests performed in this study most of the pebbles "passed 50-mm round hole screen openings and remained on a 40-mm round hole sieve. Correspondingly most of the ball mill experiments were performed with 50 or 40-mm steel balls". Thus, the balls and pebbles were essentially the same size or diameter. This means we are comparing apples and oranges. When the feed being ground is fine enough the pebbles will be superior. When the feed is coarse the steel balls will be the better. This is similar to grinding tests in which two sizes of steel balls are compared. In the middle of the article, "Crocker5 has reported that equal weights of pebbles and steel balls achieve the same grinding capacities under similar conditions …", then he proceeds to question this postulate. In the eight reports that I have published, I have never made this statement. What I have said is "for comparable grinding, the individual pebbles in the mill charge should be the same weight as the individual steel balls." This is not the first time that I have been misquoted on this point! It is most unfortunate that this test work has been done with a ball and pebble of the same diameter and not the same weight. It is impossible to properly evaluate the results. I also regret the fact that the screen analyses of the tests were not shown. Many of us who have been 40 years or less in the grinding game can easily read screen analyses at a glance. We can tell whether the top meshes are being ground by the ball charge, etc., etc. The graphs are fine for the summary or to illustrate conclusions but are often misleading in the report itself. However, we do agree that useful pebble grinding tests can be done in a 12-in. mill.

Jan 1, 1973

By A. N. Holden, W. E. Seymour

DURING the last several years, the U-Zr system has been studied at many laboratories as one of the research programs sponsored by the Atomic Energy Commission. The equilibria in part of this system have been difficult to determine, although the phase diagram from 0 to 60 atomic pct Zr has been established with reasonable certainty. Existing diagrams of the system vary appreciably beyond 60 atomic pct Zr, particularly with regard to the existence of an intermediate phase. Most existing diagrams show a transformation or reaction horizontal near 600°C. In 1955, a collection of uranium phase diagrams' was prepared at the Battelle Memorial Institute and the U-Zr diagram in that collection contained a questionable region in the vicinity of 60 to 80 atomic pct Zr. Summer-Smith" has published a phase diagram of the system that shows no intermediate phase. Summer-Smith did his work with powders and found only the uranium and zirconium eutectoid mixture from X-ray patterns of material annealed below 600°C. Mueller3 at Argonne National Laboratory did similar work with filings, and he found that initially there was a pattern of an intermediate phase, but on long-time annealing

Jan 1, 1957

By I. Iwasaki, P. L. De Bruyn

Electrical double-layer properties of the silver sulfide-solution interface in different electrolytes and the influence the properties exert on the adsorption of dodecylammonium acetate (DAA) were studied using an electrochemical titration technique. The flotation behavior of silver sulfide was observed using DAA as collector and the results were correlated with adsorption measurements. Silver and sulfide ions were identified as the potential determining ions and their adsorption densities were measured as functions of the pAg and of the ionic strength at two different pH values. The point-of-zero-charge (PZC) was observed to be at pAg 10.2, the value being independent of pH and of the nature and concentration of the electrolyte used. The surface charge of silver sulfide in these electrolytes was positive for pAg values less than 10.2 and was negative for pAg values greater than 10.2. The adsorption of amine on silver sulfide surfaces at pH 4.7 was found to be strongly dependent on the pAg. A shift in the PZC towards a lower pAg due to the adsorption of amine indicated a specific affinity of dodecylammonium ion towards silver sulfide surfaces. At pH 9.2 a strong adsorption of the undissociated amine molecule was indicated. The PZC shift towards a higher pAg and the adsorption of the amine was virtually independent of the interfacial electrical conditions.

Jan 1, 1972

The visitors to the October meeting will be given opportunity to visit the coal fields in Illinois, adjacent to St. Louis, the steam-shovel operations near Pittsburgh, Kan., and the Oklahoma oil fields. The coal mines of Illinois, Missouri, Kansas, Oklahoma and Arkansas furnish fuel over all of the central region of the country. Especially at this time, this district is of importance because of the necessity of producing enormous quantities to meet the country's demand. Some of the mines produce as much as 5,500 tons in 8 hr., and. the total output of Illinois, alone, in 1916, was 63,000,000 tons. Visitors may see elaborate underground electric tram systems, large underground machine repair shops, surface plants equipped for rapid loading, and some of the most modern coal-washing installations. The conditions for mining here are somewhat simpler than in the east.

Jan 8, 1917

By L. G. Austin

My first contact with industrial milling was during the time I worked in the electricity generating industry in the United Kingdom. In visits to power stations to investigate either deposits in the boiler furnaces or polluting deposits settling around the stacks. I had to check the performance of the vertical coal pulverizers, since poor pulverization aggravated both problems. Naturally, then, when I came to the USA in 1957 to take a PhD in fuel technology at Penn State, I was put to work to review the science of coal pulverization. After this reviewing, I was completely confused. On one hand, there was a well-developed understanding of stress-strain equations, and a rapidly developing knowledge of how stressed, brittle solids fractured, based on the Grifith crack theory. On the other hand, reading in the grinding literature gave me: -Kick's Law, which was clearly not correct in the light of modem fracture theory; -Rittinger's Law, which was also clearly not correct; -Bond's Third Law of Comminution, which was claimed to have something to do with the Grifith crack theory, but where the connection between the two was made by intuitive pseudo-scientific reasoning I could not accept; -the choice of mill motor power for the most common type of coal mill, the Raymond pulverizer, was calculated from the fan power required to move air through the mill. Although I could accept the empirical connection between the two, it made no sense from the point of view of fracture energy. Even today, most books or review chapters on size reduction start from these laws. Incorrect statements abound in the literature, such as "the Hardgrove Index is based on Rittinger's Law," which it is not, "The Bond theory states that work input is proportional to new crack tip length produced in particle breakage," which is not true, etc. My own test work showed that these "laws" did not fit the data for grinding of coal. At about this time, Epstein (1948) and Broadbent and Callcott (1956), following the original work by R.L. Brown (1941) at the British Coal Utilization Research Association, proposed describing breakage as a series of fracture stages. I took their concepts and developed the basic differential equation for a batch grinding process continuous in time, analogous to a batch chemical reactor. Robin Gardner then joined the project and did his PhD on treating batch grinding in the same way as a batch chemical reactor. He found that the basic equation had already been partially derived by Sedlatschek and Bass (1953) in Ger- many. We confirmed experimentally the validity of the equations for describing batch grinding (1962) and formulated the equation describing steady-state continuous grinding in a fully-mixed mill. At about the time this work was published, Gaudin and Meloy (1962) and Filippov (1961) independently published essentially the same equations, but without experimental proof of the validity of the concepts. I will give a brief overview of what these beginnings had led to in the design of mills for size and power, and show some of the results of this more detailed understanding of grinding processes. Concepts of Fracture Mills such as tumbling ball, rod, pebble and autogenous mills and vertical mills such as the Raymond, and E-type, apply compressive stress to lumps or particles relatively slowly. Compressive stress applied to a particle of an elastic brittle solid imparts overall strain energy to the solid and produces local regions of tensile stress, [(Fig. 1)] (Berenbaum and Brodie, 1959).

Jan 1, 1985