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By Henry B. Fernald

THE Federal income tax treatment of expenditures for exploration and development for mines and other natural deposits (other than oil and gas) was materially changed by special provisions of the 1951 Act that are continued in the present 1954 Code." These present provisions for mines in stance they are the same as the 1951 amendments to the 1939 Code, Secs. 23 (cc) and (ff), respectively, except that for exploration the allowable annual deduction is increased to $100,000 (from $75,000) and minor changes in case of property transfers are made with respect to the four-year limitation. Before 1951 the statutes made no specific pro- visions regarding development and exploration for mines, but the rules were prescribed by Treasury regulations: 1) Before the mine entered the production stage, all development and exploration expenditures for mines, less net receipts, were to be capitalized recoverable through depletion or written off as losses when determined worthless. 2) After a mine entered the production stage, development expenditures were deductible as expenses-currently if ordinary expenses, but on a deferred basis if extraordinary in scope. This recognized the two separate periods, one before and the other after beginning of the production stage. There was no distinction between an exploration and a development period, but exploration was included as part of development.

Jan 1, 1958

By John Jermain Porter

(San Francisco Meeting, October, 1911.) THE value of any particular ore, coke, or limestone, for iron-making, depends upon its effect, first, upon the quality or value of the resultant product; and second, upon the cost of smelting. The factors under the first head are the percentages of phosphorus, manganese, and other elements, which remain in the pig-iron ; while those under the second head are the percentages of iron, carbon, or lime, the slag-forming constituents, which must be fluxed, and any other ingredients which give rise to variations in cost of fuel and flux. The first of these criteria of value is perhaps not capable of being reduced to a general formula embracing all cases, since it must vary to a great extent with market-fluctuations. For example, Bessemer pig is worth sometimes more and sometimes less than foundry-pig ; and the premium paid for high manganese varies within wide limits. The second, or smelting-value, however, can be expressed numerically with a fair degree of accuracy; and it is with this phase of valuation that the present paper is concerned. The utility of a means of comparing numerically the relative smelting-values of different ores, cokes, and limestones, is self-evident, although it may not have importance in Northern practice, where materials are largely standardized. On the other hand, there are, especially in the South, many furnace-managers who must use a great variety of materials of widely varying grade; and it is with special reference to this district, and in connection with the efficiency-methods which I have elsewhere proposed,1 that the methods herein described were devised.

Mar 1, 1912

By Scott Turner

MY YEAR OF SERVICE as president of the A.I.M.E. came at a time when the mineral industry had suffered severely because of disturbed economic conditions throughout the world. The Institute, an integral part of this industry, had been similarly affected. Its membership and revenues decreased; it was confronted by problems of retrenchment at a time when its vigorous operation was especially important to its members, of some moment to the mining industry, and of value to the nation. Throughout the last year, the recession of activity in our industry continued with slight abatement. Your Board accordingly exercised such economy within the Institute as was possible without impairment of essential functions. It endeavored to aid in sustaining the morale of members, their sense of professional unity, and their interest in maintaining research and the interchange of scientific and technologic data upon which the progress of our industry depends. Effort was made to assist in the difficult task of finding employment for needy members; our endeavors have met with some success.

Jan 1, 1933

By J. O. Whiteley

IT is difficult to give a refining outline that may be followed for any and all combinations of the platinum metals; different combinations require different methods of attack. This paper does not pretend to go into all of the reactions of the metals of the platinum group, but will outline the commercial refining of platinum scrap. TYPICAL PLATINUM SCRAP As a concrete case, let us take 100 oz. of miscellaneous scrap, made up of jewelry scrap, dental scrap and laboratory ware. This lot will contain some platinum, palladium, iridium, ruthenium, rhodium, gold, silver and copper. The first problem is to get all of the metals in solution. If the scrap is principally platinum, palladium and gold, a treatment with aqua regia is the course to pursue; but if the scrap contains alloys high in iridium or ruthenium, aqua regia will act too slowly. In the case in hand, we are going to presume that we have scrap high in iridium and ruthenium, and proceed accordingly.

Jan 1, 1928

By H. J. Modi, P. L. De Bruyn

In recent years interest has been aroused in flotation rate studies both from a technical and a more practical aspect. With increasing fineness of grind becoming a necessity in treatment of low grade ores, differences in flotation rates of various size ranges will assume importance in the evaluation of overall recovery results. Theoretical analysis of flotation kinetics was initiated by Schuhmann, who sought to define flotation rate of a given mineral and specified size range in terms of certain physical variables of the flotation system. Using as a basis for his analysis the bubble- particle encounter hypothesis previously advanced by Gaudin, Schuhmann writes for the rate of flotation (R,) of particles of average size x, [ ]

Apr 1, 1956

By H. W. Miller, V. H. Wilhem

Although the year 1933 was a period of uncertainty, considerable new development was initiated, with a high percentage of favorable results, for owing to financial conditions only projects of merit were proposed and developed. Unfavorable marketing conditions caused severe financial losses to refinery and sales departments of nearly all companies during the first half of the year. In anticipation of stabilized Government control, earnings were generally favorable during the third quarter but failure of the Government to take legal action against violators of the proration orders, and lack of agreement on a definite plan of curtailment, resulted in considerable overproduction and demoralization of the market structure during most of the final quarter. However, toward the close of the year Government action against violators of the Oil Code had a tendency to decrease overproduction materially and give the market a firmer tone. As a whole, the price structure of crude oil was maintained at a high level during the year; in fact, at a much higher level than the price of refinery products warranted. At no time during the year was production within 10,000 bbl. daily of the state allotment, overproduction of crude reaching a peak of 70,000 bbl. on Sept. 7, average daily average for the year being about 27,000 barrels. Numerous plans for equitable curtailment were prepared and tested during the year, none of which fully solved the many and intricate problems faced by operators who were in most cases willing to curtail if they could feel that cooperation was being practiced by their neighbors. Outstanding events in California oildom during the period under discussion may be classified under the following headings: 1. New discoveries. (a) New development in proven areas. (b) Deeper zones in settled pools. 2. Unproductive wildcat operations. 3. Whipstocking practice and procedure. 4. Progress of unit and orderly plans of development.

Jan 1, 1934

By Clyde E. Williams

MUCH has been said recently concerning the depletion of the Lake Superior iron ore re- serves. Estimates given indicate a total life of the present known reserves of twenty to thirty years. Some argue that there is no need to concern ourselves about the possible depletion of the Lake Superior iron ore supply because foreign ores can be brought in to this country at a lower price than rich agglomerated ore can be produced from the lean domestic ores. Some fear, as a result of this, a displacement of the steel business from present districts to the Atlantic seaboard. Others show that foreign ores will be brought to interior points via the projected Great Lakes-St. Lawrence waterway. Others believe that the South, given better freight rates, will extend its iron and steel market into northern territory.

Jan 1, 1931

By C. E. Corson

THE experiments of which the results and significance are set forth in this paper do not by any means cover the whole subject of the heat-treatment of the material referred to, yet they constitute a contribution to that general subject, rather than to the special department of annealing. The material here considered is acid open-hearth steel, containing from 0.50 to 0.80 per cent of carbon, with a nearly uniform percentage of other elements. This class of steel is rapidly increasing in commercial importance. It is even rumored that the rail-specifications of some railroads will hereafter require open-hearth steel. Yet this particular grade seems to have received less study and description from the standpoint of the metallographist than many others. The investigation here described was directed to the following points:-Steel containing about 0.50 per cent, of carbon : 1. The structure as related to the temperature, at the same rate of cooling; 3. The structure and physical properties as related to temperature at different rates of cooling; 3. The structure and physical properties as related to different finishing-temperatures and different rates of cooling; 4. The bearing of these observations upon the statement of Prof. Albert Sauveur.1

Sep 1, 1906

R. W. Guard (General Electric Co., Schenectady)— The method of fractional replication discussed by the author has proven very valuable to us in applied research connected with alloy and process development where many of the same experimental difficulties exist. Several of our experiences may be of assistance to those who want to apply the method in these fields. Contrary to the author's observation that interactions are rarely significant, we have found in a number of cases that first order interactions exist which are significant and metallurgically important. Because of this difference there are two further precautions which should be taken in order to minimize the difficulties from this point. First, in evaluating the importance of

Jan 1, 1957

By A. B. Hildebrandt

P. B. Baxendell is to be complimented for an exccllent piece of work. To our knowledge there has been no previous publication of field data on the flow of oil and gas through the annulus of a well. It is certainly gratifying to see this work on annular flow confirm the previous published correlation procedure on tubing flow. It extends considerably the range under which reliable gas-lift calculations can be made. Baxendell discussed this work with us about a year ago and was kind enough to send a large scale plot of his correlation. We had been designing gas-lift installations on flow through the annulus, assuming that the original correlation of the f factor based on tubing flow' was valid as long as we stayed within the same mass velocity range on which the correlation was based. Doing this work necessitated the use of an equivalent diameter for the annular flow. The equivalent diameter is defined as area' of stream cross section wetted perimeter and for the case of an annulus is D, — D,. Substituting this in the basic equation correlating energy loss along with the area to flow required to convert the velocity, to volumetric flow rate, D (Baxendell's Eq. 7) becomes dell's expression, D,). Similarly, the D in 1.4737 X 10 (M&/D) becomes (D, + D;) for annular flow. On receipt of Baxendell's data, we. of course, recalculated it to put it into the form we were using, and to see how well it agreed with the correlation based on tubing flow. Fig. 1 shows the results, which were certainly gratifying. For low values of (D, - D,) pv, the data coincide with the data on flow through tubing, whereas at high values the data on flow through the annuli appear to be leveling off to a constant value. For very high rates of flow where the turbulence is very high, one might expect the value f to level out and become constant. A bulletin published in 1914 by the U. of Wisconsin presented results of a large number of laboratory teats in air lifting water through short lengths of 1.25-in. tubing. It was possible to correlate a random sampling of

By Robert L. Braun, Arthur E. Lewis

A contained nuclear explosion is proposed to produce a chimney of broken ore well below the water table. After the chimney is filled with water and reaches hydrostatic equilibrium, oxygen, under pressure, is introduced near the bottom of the mass of broken rock. The increase in solubility of oxygen at high hydrostatic pressure is sufficient to initiate the oxidation of the primary sulfides, chalcopyrite and pyrite. The oxidation and dissolution of these sulfides produces enough heat to increase the temperature of the ore and water in the chimney as much as 100° to 150°C. The rate of dissolution of chalcopyrite exposed to oxygen-saturated solutions becomes so rapid under these conditions that the rate of copper extraction becomes limited by the accessibility of chalcopyrite to the solutions. Means of solution control and distribution of oxygen in the chimney have been examined in some detail. A calculational model utilizing experimentally determined solubility rates is utilized to estimate the temperature rise in the chimney and the rate of copper recovery as a function of initial temperature, sulfide content of ore, and size of ore particles. It is concluded that the high pressure and high temperature obtainable in a large ore mass broken by nuclear explosives promise the rapid and economic recovery of minerals not considered soluble by conventional in-situ leaching methods. The method should be broadly applicable to the kinds of deep deposits that must be depended on for future production and with minimum disruption of the environment.

Jan 1, 1974

By George Newton

When Mr. Bailey asked us to present a paper describing our new BOF shop, he requested that we avoid a presentation heavily laden with detail and statistics. Not only have we attempted to do this, but also we have prepared a number of colour slides which, hopefully, will provide you with a graphic conception of the facility. The installation of the BOF facility at the Steel Co. of Canada's Hilton Works was delayed many years because of the remarkable production growth of the oxygen open hearth furnaces in No. 3 shop. However, in mid-1960 it became strongly evident that not only would increased ingot capacity be required, but also that N0.2 shop - with vintage non-oxygen open hearth furnaces - would have to clean its stacks in the near future, or be closed down. A decision to embark on the BOF facility was made in 1967 after an extended period of in-depth planning and assessment of industry trends.

Jan 1, 1972

By H. S. Chiang, D. F. Lu, S. S. Peng

INTRODUCTION The most important element in a successful lingual mining is a good roof control. The modern longwall mining employs hydraulic powered supports for roof control at the face area. The application of hydrau¬lic powered support requires the knowledge of over¬burden strata behavior for proper selection of sup¬port type and capacity. Failure to do so could lead so serious loss. There are several methods available for determining the required support capacity (1-3). While these methods are simple for application, they do not include the complicated roof behavior observed in longwall mining. As research progresses and operational experience accumulates (4,5), the concept about the designing and selection of powered support improves. The design of a longwall powered support consists of three major phases: 1. structural integrity and stability of the powered support, 2. external loadings induced by the movements of the overburden strata, and 3. interaction between the support, roof and floor. Phase 1 involves structural analysis (5) and full-sized testing (6) of the supports. Its validity is limited by the accuracy of the assumed external loading because of the uncertainty about the actual loading underground. The third phase includes the reaction of the support and the floor to the movements of the overburden strata and vice versa. Among the three phases, the second phase concer¬ning the external loading seems to be the least known because of the complicated behavior of the roof strata. There are many unresolved problems. For example, does the main roof break periodically and cause periodic roof weighting in the face area? If so, are there any rules governing its behavior? How does the roof load on the support canopy! Finally, how can one determine the required support capacity and select a proper type of support to meet a certain roof behavior? In order to answer those questions, underground instrumentation and observations were performed at 4 longwall panels in 3 separate mines for the past two years. This paper summarizes the current findings. PANEL LAYOUTS AND EQUIPMENT EMPLOYED The three mines selected are all located in West Virginia; two in northern and one in southern West Virginia. As shown in Table 1, seam conditions (i.e. seam, depth and thickness) and panel layouts are different among the three mines. The most significant difference in equipment is the face powered supports. Three mines used three different types of shield; 2-leg caliper, 2-leg lemniscate, and 4-leg lemniscate chock-shield. (Fig. 1) UNDERGROUND INSTRUMENTATION AND OBSERVATION PROGRAM Two events were instrumented in each observed longwall face: one was the hydraulic pressure (resistance) of the powered supports and the other was the canopy load distributions. In addition, the gob caving conditions were visually observed and recorded. Leg and Support Resistances One or two automatic Weksler Pressure Recorders were installed at the designated shield support,. In most cases, the daily charts were used to record the pressure variations in both the front or the rear legs (for the 4-leg shield), or in both the leg and the fore-pole ram (for the 2-leg shield). The recorded pressure w a s then converted to load or resistance by multiplying it by the cross-sectional area of the hydraulic leg or canopy ram piston. Fig. 2 shows the typical pressure-recorded charts for the 4-leg and 2-leg shields in a 23-24 hour period. The support resistance is the summation of the resistance in each of all the legs for that support. Generally, the resistance of the fore-pole ram will not be considered in determining the capacity of the support because of its rather small vertical compo¬nent force at the tip of the fore-pole. Canopy Load Distribution External load distribution on the canopy as exer¬ted by the roof was monitored. The measurements employed 12-14 pieces of pressure cells (6-inch square) that were uniformly arranged in two rows on the canopy. After support setting, the pressure changes in the cells were monitored at various stages of the mining (supporting) cycle while the support leg pressures were recorded continuously by the pressure recorders. Based on the calibration chara¬cteristics of each pressure cell as performed in the laboratory before and after each underground test, the cell pressures were converted to actual loadings. From these load measurements the canopy load distri¬butions and the relations between measured canopy loadings and support leg resistances were determined. Accordingly, the supporting efficiency of the shield support can be determined.

Jan 1, 1982

By William C. Overstreet, Paul K. Theobald, Jesse W. Whitlow

Monazite placers in a region of the Carolinas explored in 1951-1954 by the USGS are estimated to contain at least 53,000 short tons of thorium and 4600 short tons of uranium. None of these deposits is being mined. The 5200-sq mile area investigated extends northeast along the western Piedmont from the Savannah River in South Carolina to the Catawba River in North Carolina. Much of the region is 700 to 1100 ft above sea level. Gentle hills and broad interfluves give a local relief of 100 to 200 ft. This increases to 1700 ft at the west margin of the area where the east flank of the Blue Ridge is approached in South Carolina and the South Mts. are entered in North Carolina.

Jan 7, 1959

By Lyle L. Marsh, David L. Douglas

CORRELATION was made between the heat treatment and hardness of three U-Ti alloys ranging in composition from 8.5 to 50 atomic pct Ti. The following important observations were made: 1) A direct quench of y U-Ti solid solution resulted in the formation of a hard martensitic phase in low-titanium alloys. 2) Subsequent tempering initially increased the hardness by the precipitation of a fine dispersion of U2Ti; further precipitation of U2Ti with tempering time eventually resulted in softening. 3) High-hardness levels were obtained also by isothermal transformation of an 8.5 atomic pct Ti alloy at 400º and 500°C. 4) The crystal structure of the phases present at the solution-treating temperature (one region in the phase diagram excepted) and the temperature within a given phase region affected the hardness of both quenched and isothermally transformed alloys. Introduction It has been known since 1887 that the mechanical properties of metals were dependent upon their microstructure. Sorby pointed out in that year that annealed gray iron castings were softer than chilled iron castings by virtue of the graphite which had replaced hard cementite in the microstructure. Over the years, interest has increased in the effect of microstructure on the mechanical properties of metals, and now high-strength levels may be achieved by bringing about the dispersion of a second phase or by other microstructural adjustments. The nature of a second phase in an alloy strongly influences the properties. For example, the size, shape, amount, and distribution of a second phase plays a very important role in the ultimate properties of an alloy. Microstructural control is achieved by heat treatments. Hence, any alloy system of potential use should be understood in terms of its response to heat treatment and the resultant effects upon the properties.

Jan 1, 1958

Jan 1, 1902

By William Wraith

1. INTRODUCTION. AT the Washoe smelter,. Anaconda, Mont., the blister-copper from the converters is transferred, by means of a crane, to a refining-furnace,, in which it is brought to proper pitch by means of air and poles. From this furnace the refined copper, containing gold and silver, is poured into cast-iron molds placed on a platform-conveyor, giving an anode 36.75 in. long, 28 in. wide, and 21 in. thick. By reason of a disagreement between the smelter and the refinery, in reference to the silver-content of the anodes, it became necessary to investigate the methods of sampling used. II. SMELTER METHOD OF SAMPLING. At the smelter the sampling is done by " spotting " into water a small portion of the molten stream of copper as it flows from the furnace, by batting" the stream with a wooden paddle. The first sample is taken 30, min. after the pouring is started, three. other samples being taken at 1-hr. intervals, each sample weighing from 4 to 6 oz. The samples are dried, examined for particle's of burnt wood, screened on a 10-mesh screen of No. 8 wire to remove the fines, the oversize then screened on a 4-mesh screen of No. 20 wire to remove the coarse, the undersize of this screen being taken as the sample. Teh four portions thus obtained are thoroughly mixed and spli in half by passing over a 16-slot splitting-device, slots being 0.5 in. wide. One-half of the sample is sent to the laboratory for analysis and one-half kept as a duplicate. III. REFINERY METHOD OF SAMPLING. The method used at the refinery and also used in this investigation is the one developed by Dr. Edward Seller, of

Mar 1, 1910

By G. Donald Emigh

Nothing is more important to life-plant and animal-than phosphate. Its compounds are essential to the energy functions of all living systems and for the formation of bones and teeth. Animals get their phosphate from eating plants and other animals, or domestically from feed supplements. Plants get their phosphates from the soil. Man's most important use of phosphate is for fertilizer; approximately 95% of the world's phosphate rock production is consumed by fertilizers. Most of the balance is processed in electric furnaces into elemental phosphorus, the important raw material for making industrial phosphates. Recovery of uranium from phosphates has been possible but not widely used. However, recent significant developments have generated interest in such recovery in the US and elsewhere. Phosphate occurs in all igneous and sedimentary rocks, and in all fresh and salt water. However, economical recovery is limited to deposits where natural concentration of the phosphate mineral has occurred. Occasionally natural concentration is great enough that the material can be used as mined; generally, however, the ore is low grade_ and must be concentrated. Phosphate rock is produced in 31 countries. Fig. 1 shows the location of major phosphate rock producers as well as some of the known phosphate deposits not yet in production. In the last decade the world phosphate industry has experienced steady growth. World production rose from 98 Mt of phosphate rock in 1973 to 140 Mt in 1982. Fig. 2 shows the growth curve of rock production and graphically illustrates the almost straight-line rise since 1945 in both US and world production. Table 1 gives the breakdown, by countries, of world rock production, 1974 through 1979. Table 2 shows US rock production by producing areas. Definitions of Terms Used in the Phosphate Industry Phosphate Rock: Commonly called rock in sedimentary deposits and apatite in igneous deposits. Those expressions generally include any mined, or mined and beneficiated, fluorine-containing calcium phosphate used as the raw material for the next stage of manufacturing. The average phosphate content in rocks is 0.1 to 0.2% P2O5, as documented by McKelvey (1973). About 200 minerals contain more than 1 % P2O5. However, the important mineral in igneous rocks is fluorapatite, [Ca5 (PO4),3 F], containing about 42% P205 and 3.8% F2; in sedimentary rocks the important mineral is francolite, a carbonate fluorapatite containing up to 2% molecular CO2. Both are in the apatite family of minerals. Most phosphate rock, whether beneficiated or not, is a fine-grained material. The expression phosphate rock has no relation to its phosphate content. For example, phosphate rock from Idaho used in the production of phosphorus may contain about 24% P205, whereas rock from Morocco may contain 36.6% P2O5. Phosphorite: A deposit of phosphate directly or indirectly of sedimentary origin, which is of economic interest. Grade of Phosphate Rock: The calcium phosphate content of phosphate rock is expressed in different world areas by one of the following terms: BPL (bone phosphate of lime) TPL (triphosphate of lime) P2O5 (phosphorus pentoxide) P (phosphorus-not commonly used) An illustration of relationship is: 80% BPL = 80% TPL = 36.6% P5O2 = 16% P

Jan 1, 1983

By C. W. Clark, J. H. Schloen

Two papers have been written previously concerning operations at the Montreal East plant of Canadian Copper Refiners Limited. The first one,1 written in 1932, described silver-refinery operations at the time for producing silver and gold bullion from tankhouse anode slimes; the second,2 published in 1933, consisted of a description of the entire plant. Since publication of these papers the refinery has become the world's largest producer of refined selenium. The first selenium was produced in August 1934. Tellurium production on a commercial scale followed in October 1935. This paper will deal with selenium and tellurium production and also with present operations in the silver refinery. Blister cakes from Hudson Bay Mining and Smelting Co., Flin Flon, Manitoba, and commercial anodes from Noranda Mines Limited, Noranda, Quebec, are refined at Montreal East. Both these bullions have unusually high gold, selenium and tellurium content. The average assay of raw slimes produced from domestic and Noranda anodes is about 40 per cent Cu, 3600 oz. per ton Ag, 800 oz. per ton Au, 22 per cent Se and 3.7 per cent Te. EARLY SILVER-REFINERY OPERATIONS From the start of operations in 1931 until July 1934, the raw slimes were oxidize-roasted at 700° F. in a Nichols-Herreshoff furnace, acid¬leached with tankhouse discarded foul electrolyte (20 per cent H2SO4), filtered and charged directly to the doré furnace for refining to doré metal. This is the customary method for treating tankhouse anode slimes but was not suitable at the Montreal East plant because of the high selenium and tellurium content of our slimes. In the acid-leaching process about 50 per cent of the selenium and tellurium in the roasted slimes was dissolved in the electrolyte. These elements were recovered with the copper as a sludge in a small electrolytic

Jan 1, 1938

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman's arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman's paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman's work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"'. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963