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By Charles Barron McIntosh

BECAUSE of the well known relationship between a low atmospheric pressure and increased amounts of methane in coal mines, attempts have been made to find associations between low pressures and coal mine explosions. An early study by F. Able disclaimed this relationship. He found that half the explosions took place during a rising barometer when methane content in a ventilated mine would be decreasing. A more recent study by C. L. Hosler revealed a close relationship between anthracite mine explosions and low atmospheric pressure. Bituminous coal mine explosions, where coal dust as well as methane can be exploded, were found to be more closely associated with a rising pressure following a low barometer than with the falling or low pressure period. Emphasis on rising pressure periods led the present writer to investigate the effect of the post-frontal or post-cyclonic weather on coal dust. Dust samples of uniform mesh were exposed in an Illinois mine. Analyses of the dust taken before and after the passage of cold fronts and their accompanying low pressure troughs indicated an increase in coal dust moisture prior to a frontal passage and loss of moisture from coal dust following the time of lowest pressure. Thus the warm, moist air (Tropical Maritime)found over the mine during the falling pressure period was cooled in the mine and moisture added to the dust. Cold, dry air (Polar Continental) accompanies' the rising barometer following a frontal passage and the air, being heated in the mine, subtracted moisture from the coal dust. A similar but seasonal phenomenon occurs from summer to winter, the dry dust period in winter being recognized as the more dangerous period. The question arose as to how the short period or daily changes in moisture content of coal dust compared with the seasonal changes. Temperature and humidity statistics were obtained from the surface and mine entry for the months of July andJanuary. The gain and Ioss of mdisture. to the hine were calculated for these two morths as were the gain and loss associated with mT (Tropical Maritime) and cP (Polar Continental),air masses as observed in the investigatiynsl. Temperature and humidity statistics tigatiynsl.taken from [the two air masses represent atimp span of only 34 hr. The redultant changes as presented in the accompanying table verify the supposition that short period changes in coal mine moisture may attain the magnitude of recognized dangerous seasonal changes. Statistics for the mT air and the July air have been placed next each other and those for cP and January air together for easier comparison of the two warm and two cold air units. The last column readily reveals that there is little difference in the amount of moisture being deposited in the mine from the mT air and the July average air. A similar conclusion is reached regarding the loss of moisture from the mine when it is affected by the cP air mass or the average January air. This comparison would be particularly true from late fall through early spring when strongly contrasting air mass changes are a common occurrence. The invasion of cold, dry air following a cold front thus produces a drying period that could well receive more attention as a danger period for coal dust explosions. This drying period would compare with Able's explosion period during a rising barometer. The drying period is also perltinent in Hosler's findings, where it was noted that the average explosion day (for bituminous coal mines) followed the day of lowest atmospheric pressure. Moreover, the author's investigation of some 365 coal mine explosions also indicates that this post-frontal period should receive special attention in connection with mine safety measures. Two comparatively recent major explosions in Illinois (Centralia and West Frapkfort) occurred after the mines had been under the influence of cold-dry air for 25 to 30 hr-following a deep low pressure passage. Dust was the important explosive element in both these explosions.

Jan 1, 1958

By J. B. Newkirk

IN 1939 Bitter and Kaufmann1 suggested that iron, precipitating from a copper-rich, Cu-Fe solid solution, appears initially as coherent particles of r-Fe which transform to the body-centered-cubic form of iron when the alloy is cold worked. Since then there has been considerable discussion, supported only by indirect evidence, regarding the validity of the concept. For example, Reekie, Hutchison, and Hether-ington2 interpreted the changes in electrical resistance accompanying the aging of Cu-Fe specimens in terms of a coherent 7-Fe precipitate which transformed to the incoherent a-phase during long aging or cold working. Greninger- ound that Cu-Fe alloys which had been water quenched from 1050" and then held at 650°C for 3 hr changed from weakly to strongly ferromagnetic as the aged wire was subsequently cold worked. He also found diffraction lines corresponding to body-centered-cubic iron in Debye-Scherrer patterns given by aged and worked specimens but lines corresponding to only one face-centered-cubic phase in specimens which had been aged but not worked. Knoppwost,' and later Cech and Turnbull,5 found that aged Cu-Fe specimens showed a slight increase in ferromagnet-ism after they had be? cooled in liquid nitrogen. Very recently Denney6 followed the kinetics of the precipitation reaction as indicated by the saturation magnetization, hardness, and diffuse X-ray effects. The experimental results reported by all of the authors mentioned above are readily explained in terms of the Bitter and Kaufmann concept. However, most of the evidence is indirect when used to define the structural changes involved. It was the aim of the present investigation to determine the mechanism of precipitation of iron from a Cu-Fe solid solution in the light of available published information and with additional new and more direct experimental data. Experimental Method At 1060°C copper will contain up to 3 atomic pct Fe in equilibrium solid solution.7 The solvus slopes rapidly toward lower iron concentration, so that at 600°C only about 0.5 pct Fe remains in solution at equilibrium. Below the eutectoid temperature (850°C), the iron-rich phase in equilibrium with the copper-rich solid solution consists of body-centered-cubic a-Fe. Above 850 °C the equilibrium iron-rich phase is face-centered-cubic r-Fe. The alloy to be studied was made by melting electrolytic iron and OFHC copper by induction under vacuum in an Alundum-lined crucible. The metal was held molten for about 5 min, after which time the power was turned off and the crucible was tipped about 70" to promote directional solidification. The resulting ingot, containing 2.5 wt pct Fe by analysis, was clean, large grained, and free of gross segregation. Slices % in. thick were cut from the ingot, rolled to 1/8 in. in thickness, homogenized in hydrogen at 1060°C for 24 hr and, finally, quenched in cold water. Specimens for all subsequent tests were made from these slices. Squares measuring about 1 cm on a side were cut from the slices to make specimens for studying hardness and microstructure. Wires (0.020 in.) for the Debye-Scherrer survey were drawn from 1/8 in. sq rods which had been cut from the homogenized slices. Large crystals for observing diffuse X-ray diffraction effects were prepared by mechanically

Jan 1, 1958

By J. W. Pugh

VANADIUM has only recently received consideration with respect to structural applications. It would appear likely to find service where its high electrical resistance and constact temperature

Jan 1, 1958

Jan 1, 1958

By R. L. Ziegfeld

It has often seemed to me that people are too prone to turn to new and untried materials in an effort to solve their problems, without giving sufficient consideration to the old stand-bys, except as a last resort, It?s a little like middle-aged men who are swept off their feet by the fresh beauty of a young girl without first considering the many advantages that a more mature woman has to offer. Maybe it?s because, like the older woman, the older materials have to make a determined effort to keep themselves looking young and attractive. T at?s just about the situation with which the lead industry is laced. We have to make a determined effort to keep lead looking young and attractive to industry. However, there is one difference and it is important, Lead can not only be kept looking young, but it can, in fact, actually be kept young, This results from two things. First, industry and technology are constantly changing. For example, we have known for years that the density of lead makes it ideal to stop gamma rays, but it is only recently that atomic fission as a source of gamma radiation has become an important tool of industry, That makes old knowledge about lead useful in developing a new market for it.

Jan 1, 1958

By W. C. Hittinger, J. McGlassan, J. W. Peterson

THIS paper describes the result of an investigation of the production of thin alloyed layers on a thicker substrate of pure germanium as one step in the manufacture of transistors.' The technique of alloying materials with semiconductors is a means of introducing small amounts of impurity elements in the alloyed regions of the crystal lattice of the semiconductor, the presence of which make possible the junction type transistor.2 Impurity elements are added which will produce regions having differing electrical resistivities and means of carrying current. Impurities are of two types: those which produce an excess of electrons (negative or n-type), and those which produce a deficiency of electrons (positive or p-type) in comparison to the pure semiconductor. The boundary between two such regions is designated a p-n junction. Elements in Group V of the periodic table, having five valence electrons, give rise to an excess of electrons when present substitutionally in the semiconductor lattice (usually germanium or silicon from Group IV). Similarly, elements in Group III create a deficiency of electrons. Germanium and silicon which are substantially free of impurities of either p or n-type are designated intrinsic (i-type) semiconductors. The usual junction ----trarnsistor has

Jan 1, 1958

By E. S. Fisher

GRAIN coarsening implies a discontinuous type of grain growth during which a few grains in a fine grained recrystallized matrix grow to large grain sizes at the expense of the matrix. Studies of this phenomenon in various metals1,2 indicate that grain coarsening may result when continuous grain growth in a fine grained matrix is inhibited by either a dispersion of very fine inclusions or by a strong texture. In the former case a period of annealing time exists prior to grain coarsening during which grain growth inhibition is gradually de- creased by dissolution or coalescence of the dispersed inclusions. This mechanism can be made to occur in uranium during anneals at high a phase temperatures. ' A study of some of the factors influencing the kinetics of grain coarsening and the coarse grain sizes in a uranium has led to a method for preparing a uranium single crystals. Previously such single crystals containing considerable substructure were prepared at this laboratory by a phase change method, similar to that described by Cahn.3 Attempts to prepare more perfect single crystals by strain-anneal techniques were unsuccessful. Cahn3- as reported his attempts to apply such techniques to uranium. He proposed that the failure of strain-anneal techniques is basically due to the many twins which

Jan 1, 1958

By Peter Haasen

INDIUM antimonide has the zincblende structure. A possible defect that does not disturb the indium tetrahedron surrounding any antimony atom in this lattice (or vice versa) is obtained when neighboring

Jan 1, 1958

By E. S. Machlin, C. W. Chen

THIS investigation is concerned with the origin of the intercrystalline voids and cracks formed in metals and alloys subjected to stress at elevated temperature. There have been many suggestions in the recent literature relating to this problem. Greenwood' suggested that the voids may be produced by vacancy condensation. Zener has stated that shear-stress relaxation across grain boundaries could initiate high tensile stresses at the regions blocking grain boundary slip and thereby cause the formation of cracks. Chang and Grant3 have described the formation of cracks at grain boundary triple points and have experimentally verified Zener's mechanism for the grain boundary regions in the vicinity of a triple point. Subsequent to the completion of this investigation, Gifkins4 developed a model which made use of Stroh's5 mechanism of fracturing to produce sub-microscopic fractures that subsequently grow by grain boundary slip. Chen and Machlin,6 in answer to Gifkins, described a model deduced from the present investigation, in which grain boundary slip provides both the stress to fracture at grain boundary jogs and the deformation required to separate fractured jog surfaces. The possibility of gas condensation to form intercrystalline voids and cracks is eliminated as a basic mechanism because such voids and cracks are developed in vacuum melted material containing minute amounts, if any, of gaseous impurities. In a theoretical evaluation of this problem, Machlin7 concluded that void nucleation by vacancy condensation during creep-rupture is improbable but that vacancy condensation on supercritical sized voids to produce growth is probable. This investigation was begun to evaluate the suggested mechanisms for intercrystalline fracture. In particular, in order to correlate vacancy supersaturation ratios produced in creep with those determined by Bal-luffi and Seigle8 as critical for , the nucleation of voids, specimens were obtained from the same heat of brass as used by the latter authors, through the courtesy of Dr. Seigle. The experiments conducted in this investigation fall into the following categories: 1) Brass—observation of voids produced under a variety of conditions, including creep under compression, to evaluate the mechanisms of void nucleation and growth. 2) Bicrystal experiments to check the mechanism of void nucleation deduced in this investigation. 3) Morphology of intercrystalline voids produced in a variety of metals. Each set of experiments will be described and discussed separately. Experimental Techniques A special creep-rupture test rack was constructed which made it possible to apply the stress to the specimen in a controlled atmosphere of inert gas, reducing gas, or vacuum. All the creep-rupture tests on a-brass (30 pct Zn) were conducted in nitrogen under a pressure slightly above atmospheric. Either dead weight loading or constant elongation rate loading could be applied with the load measured by means of a strain gage dynamometer. In order to obtain a coarse-grained crystal structure stable at

Jan 1, 1958

P. Herasymenko (New York University, New York) —The authors' experiments on equilibria between water vapor and liquid synthetic slags represent a valuable contribution to our knowledge of the nature of liquid slags. They can be regarded as a proof of ionic splitting of water molecules dissolved in slags. The assumption that water dissolved in slag was com- pletely ionized was made in my report on hydrogen equilibria in steelmaking as early as 194010. In that paper, the first systematic data were given on the content of ionized hydrogen in acid and basic open-hearth slags. The paper probably escaped the notice of the authors, although they mention the articles published later by other investigators who reported erratic and

Jan 1, 1958

By W. C. Hagel, H. J. Beattle

DURING an earlier examination of high-temperature alloy, A-286, the presence of an unknown intermetallic compound was verified by X-ray diffraction. Owing to its prominent appearance at grain boundaries, the arbitrary name of G phase was assigned.' Low-silicon, vacuum-melted heats were found to contain no G phase, and this investigation was initiated to determine the influence of silicon on G-phase formation; additional work was undertaken to extend existing data on other intermetallic compounds and the aging reactions in this group of alloys. Taylor and Floyd2-4 observed that the Ni3Al phase (y') and the Ni8Ti phase (7)) are the only equilibrium intermetailic compounds in nickel ternary alloys containing up to 25 pct Cr and 10 pct Ti or Al. They found that y' can dissolve considerable nickel, chromium, and titanium, although the stoichio-metric composition of 7 remains fixed. Nordheim and Grant5 confirmed that age hardening of 80 pct Ni-20 pct Cr alloys of the Nimonic-80 type is due to precipitation of y', where aluminum is partially replaced by titanium. They suggest that optimum hardness and ductility result from increasing the titanium to aluminum ratio toward the end of the y' solubility range and from increasing total titanium and aluminum content to the maximum limit permitted by processing. Such information is necessary for those seeking to improve the service-temperature range and long-time structural stability of high-temperature components. Experimental Methods Compositions of materiais studied. are listed in Table I. Alloys D, E, and F possess representative A-286 analyses; silicon increases from less than 0.02 to 1.75 pct in alloys A to H; in alloys I to K, titanium decreases from 2.24 to 0.39 pct, and aluminum increases from 0.1 6 to 240 pct. Alloys A and D were solution heat treated for 4 hr at 1700°F, oil quenched and aged for 0.5, 2, 6, 12, 30, 70, 200, and 1000 hr at 1200°, 1300°, 1400°, and 1500°F. Therefore, a total of 33 specimens was required for each

Jan 1, 1958

Jan 1, 1958

By Y. C. Liu

IN the study of the rolling recrystallization of face-centered-cubic metals, a most unusual observation is the frequent occurrence of a sharp re-crystallization texture of cube orientation. Although the general conditions under which this texture occurs are known,2,3 its origin is still not well understood. Based on the observed relationship between the {110}<112> deformation texture and the (113}<211> recrystallization texture, regardless of the effect of alloying elements2,4,5 or the symmetry of the deformation texture,&apos; there is a strong indication that a specific component of the deformation texture is related to a specific component of the recrystallization texture. Using the rotational reorien-tation relationship as a means of correlating the deformation and recrystallization textures, it was proposed that the deformation component which related the cube texture has {358)<523> indices."&apos; The investigation reported here was undertaken to seek experimental evidence for the validity of this proposition. Experimental Procedure Two copper single crystals having an initial orientation within 2" of (358) [523] indices were prepared in the manner described in Ref. 5. The purity of the copper was between 99.94 and 99.97 pct. The original dimensions of the crystals were as follows: specimen A, 0.465 in. thickness, 0.844 in. width, and 0.955 in. length; specimen B, 0.535 in. thickness, 1.120 in. width, and 1.36 in. length: Rolling was done on a laboratory rolling mill according to the following schedule: 0.010 in. per pass to 50 pct reduction in thickness, 0.005 in. per pass to 70 pct reduction inthickness, 0.002 in. per pass to 85 pct reduction in

Jan 1, 1958

By A. G. Guy

IN the course of a research on steady-state diffusion it became necessary to make diffusion calculations for a finite solid. This problem was found to be sufficiently different from the corresponding problem for the semi-infinite solid for an entirely new approach to be necessary in obtaining a useful solution. The assumption of an exponential variation of the diffusion coefficient with concentration&apos; was no longer a practical necessity, so that the new solution offered the possibility of handling diffusion in semi-infinite solids for arbitrary variations of the diffusion coefficient with concentration. In discussing the principle on which this method of calculation is based, it is convenient to consider the relatively simple problem of one dimensional diffusion into a matrix that initially contains none of the diffusing substance. The solution of the set- ond Fick Law,?C/?t=D0?2C/?x2, for diffusion into a semi-infinite solid is3 C/C=1-F(x/2vD0t [1] where C is the concentration of the diffusing substance at a depth x cm below the surface after dif- A. G. GUY, Member AIME, and M. GOLOMB are Professor of Metollurgicol Engineering and Professor of Mathematics, respectively, Purdue University, Lafayette, Ind., A. S. YUE, formerly with Purdue University, is now with the Research Laboratory, Dow Chemical Co., Midland, Mich. TP 4505E. Manuscript, July 18,1956. fusion has occurred for t seconds; C, is the concentration of the diffusing substance at the surface of the matrix; Do is the diffusion constant, expressed in sq cm per sec; and + represents the Gauss error function. The corresponding solution for diffusion into a finite solid of thickness, 1, is conveniently written for the change in concentration, C+, at a point midway through the matrix and for times, t, great enough for the following equation to be used4 c1/2/C1=(1/2-2/?e-?2D0t/l2) [2] In Eqs. 1 and 2 the diffusion coefficient is represented by the symbol Do (rather than by D) to emphasize that these equations are valid only for constant values of D. To understand how these equations can be modified to take account of actual variations of D, such as that shown in Fig. 1, first consider the fact that for a given time of diffusion theconcentration at a given point is determined, not by the D value alone, but by the ratio x/vD0 in Eq. 1 and by a similar ratio, l2/D0 in Eq. 2. Even though in fact D varies, it is possible to keep this ratio constant by using a special coordinate system, x,, that varies with D in the appropriate manner. The necessary character of this special coordinate system can be easily visualized by imagining that

Jan 1, 1958

H. G. Haemers (Ghent University, Belgium)—The authors claimed "the results of their work indicate that the metals can be arranged in a sulfation series similar in its application for selective sulfation tot the electromotive series for displacement of metals from solution". The series as stated in decreasing order for tendency of SO3 give up, is the same as that stated by free energy diagrams. Indeed, the degree of stability of a sulfate is measured by the free energy of sulfate formation out of the corresponding metal oxide and SO3. The more negative the value of the free energy (-DG) the greater the stability of the sulfate. As a second consequence this statement results in a relative aptitude for capture of SO3 by each metal oxide when brought in contact with the sulfate of other metals. Let M1 and M1 be the two metals, and — DG1 and — DG2 their free energy values at temperature T. Both sulfates are stable at temperature T if - DG1 < O and — DG2 < O. In case where — DG1 < — DG2 the stability of M1SO4 is greater than that of M2SO4, and when M1O (oxide of

Jan 1, 1958

By A. J. Kesterton

MORE than 90 pct of the total tonnage of ingots made at Abbey Melting Shop is for steel sheet to specifications ranging between 0.055 and 0.07 pct maximum carbon. Since the rate of carbon elimination in the open hearth declines considerably as the carbon approaches these low levels, the use of oxygen for this purpose constituted a profitable field for development, particularly to increase ingot output. Development Several experiments were carried out initially in which water-cooled guns, originally of all-steel construction and later with fabricated copper heads, were introduced manually through a hole in the back wall of one of the 225 net ton furnaces, the oxygen being delivered about 4 to 6 in. above the slag. Successful blows were obtained, but manipulation of the gun was cumbersome. Application through the charging doors by means of bare steel lances was considered but rejected, because much of the scrap was light, necessitating a large number of buggies per charge, and consequent long occupation of the track in front of the furnaces by buggies. To construct an efficient mechanism it was decided to experiment with the introduction of the gun through a hole in the roof. This was eventually successfully achieved, with the following advantages. 1) The actual mechanism required is simplified, and can easily be remotely controlled. 2) No large steel framework projects out over the back platform, possibly interfering with tapping, and there is no danger of damage by casting cranes. 3) The railway track in front of the furnaces is left entirely clear for the passage of scrap buggies, eliminating interference with adjacent furnaces charging. 4) As compared with the use of bare steel lances, a water-cooled jet eliminates the manpower required to handle, control and change the bare pipes. 5) A jet through the roof can be situated over the center of the bath so that, whatever the direc-

Jan 1, 1958

By Richard S. Smith

THAT management and purchasing have developed a more closely-knit working relationship is evidenced by the fact that more and more companies are appointing the heads of their purchasing departments to the position of vice president. This is concrete and dramatic indication that management is utilizing the knowledge and experience gained in this department and working with it at the policy-making level. When the engineering department is at the planning stage of a project, the purchasing department is being asked to sit in on the preliminary discussions . . .today. One result of this cooperation is that drawings and plans will reflect the current situation on material availability and another is that standardization will be incorporated in new construction and equipment.

Jan 1, 1958

By M. R. Tek, F. H. Poettmann, M. L. Grove

The general problem of single-phase natural gas flow through porous media has been considered both by mathematical analysis and field experiments. Theoretical studies on the fluid dynamics of natural gas wells resulted in derivations of expressions which permit a ber-ter understanding of the flow mechanism for conditions under which Darcy&apos;s law is no longer valid. In applying these results to natural gas production and testing technology, special emphasis war placed on the study of low permeability, slowly stabilizing formations. These applications resulted in a method of predicting the performance coefficients of tight natural gas wells. The calculation of the performance coefficient requires the determination of the "test-index", pkh/µ, the drain- age radius, R, and the effective wellbore radius, rw. Methods for estimating these parameters from field data were also developed. Field data from 15 wells were collected and analyzed. The measured values of the performance coefficients were compared with the predicted values. This statistical evaluation gave a bias of 7.14 per cent and a standard deviation of 11.6 per cent. INTRODUCTION The performance of a natural gas well is determined by the physical properties of the reservoir rock, the extent and the geometry of the drainage area, the properties of the flowing fluid, and the conditions of pressure distribution within the drainage matrix. The relation between the quantity of gas delivered and the pressure drop within the reservoir is characteristic of the behavior of each well and is often referred to as the back-pressure behavior of the well. It is well established that for normal, single-phase gas wells the relationship between the gas delivery rates and the bottom-hole pressure take, in general, the form, Q = c(P3 8 -P2 1)n. ,.......(1) where C is the performance coefficient, and n is the exponent corresponding to the slope of the straight-line relationship between Q and (P2 s, — P2 l) plotted on logarithmic coordinates. The determination of a well&apos;s performance by the back-pressure behavior not only permits the production engineers to analyze many operating problems, but also provides necessary information useful and essential to predict the future development of the field.&apos; Important engineering and production problems such as calculation of gas deliverability into a pipeline at a predetermined line pressure, design and analysis of gas-gathering lines, determinations of spacing and number of wells to be drilled during field development to meet future market or contract obligations, etc., all depend, at least in part, on the availability and use of reliable back-pressure curves.&apos; In the past the behavior of gas wells was evaluated

Jan 1, 1958

By C. G. Dunn, P. K. Koh

TWO recent review papers have considered the origin of primary and secondary recrystalliza-tion textures from the point of view of oriented nucleation and oriented growth theories."&apos; Both theories require nuclei for primary recrystallization but provide no unequivocal answer to the question of what nuclei are. The answer to the same question regarding secondary recrystallization, however, often is that nuclei are certain primary recrystallization grains or primaries. The two theories differ, however, in specifying what the certain primaries are. In support of the oriented growth theory Beck and Hua originally stated "It may be assumed that in a re-crystallized material, even with a strong texture, there always are present some grains of practically any orientation. These may serve as nuclei for the coarse grains, provided that conditions are favorable for their growth." In commenting on this statement one would say that there are two restricting conditions: namely, that 1) the certain primaries (nuclei) are large enough to grow, and 2) their boundaries have high mobility. More recently Beck2 has con-

Jan 1, 1958

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958