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and would also contribute to the post-war employment. -As far as the future is concerned, I doubt whether any of the present geophysical methods will ever be developed to directly indicate ore. However, the geochemical methods and certain combinations between chemical and geological methods now used might be the answer to our prayers for direct and more definite methods of determining the quality of the ore or its relative metal content. Geochemical and spectrochemical analysis of minute content in ground waters, in soil or in plants and trees, living or dead, will be extremely important and I would venture to predict that in the very near future each mining or exploration company and each assay oflice will have its own spectroscope equipped for accurate chemical analysis, not only to guide the daily work in the mine, but also for identifying ores as well as for guiding exploration, geological mapping and the evaluation of geophysical indications. These methods, although they are still in their infancy, promise very much for the future. Radioactivity methods could also be helpful when sufficient facilities for radioactivity determination can be made available. They have already been used to a great extent in oil exploration and experiments have shomn great promise for ore exploration also. As for future surveys of large areas, the exploration for physical contrasts will be made from the air, using aeroplanes, helicopters, etc. Already electrical and magnetic methods have been designed whereby the instruments are carried in the aircraft and by automatic recording the location of anomalies is made in a simple enough manner. It should be possible in this way to cover, say, a square mile in an hour. Later Discussion Replies to Dr Lundberg. J. B. Macelwane.*—Someone has said that if a person knows his subject well enough he can explain it in words of one syllable. The point is well taken and I think the converse is also true. If a person cannot explain a subject clearly in simple words, it is either because he has not sufficient command of the language, or he is not master of his subject. Now it is obvious, it seems to me, that the remedy for both of these unfortunate conditions lies not in less education, but in more. If Dr. Lundberg has met geophysicists who confused and discouraged prospective clients by their inability to talk the language of the mine owner or of the mining engineer or geologist, the fault most probably lay in the geophysicist's lack of sufficient training; but it may also have been the want of ordinary common sense, which no amount of education can supply. It is hard to understand the position taken by Dr. Lundberg. Does he regret his own extensive training? noes he wish to say that he would have had greater success in geophysics if he had been only a mine hand with an instrument and a rule of thumb? As a matter of fact, I find it rather difficult to account for his presentation before this Committee on Geophysics of an emotionally distorted picture of the Report of the Committee on Geophysical Education, after the lapse of an entire year since the Report was read and discussed in its proper place, unless he honestly thinks he is handicapped by his knowledge and training and wishes to warn the whole profession against a similar fate. I regret that I am obliged to disagree so emphatically with Dr. Lundberg's thesis— but I believe it would be dangerous if left unchallenged, both because of the inaccurate statements it contains concerning the recommendations made in the Report and because of the ultimate discredit that would be bound to fall upon genuine geophysics if Dr. Lundberg's recommendations were extensively followed out. S. F. Kelly.*-—The argument that a science and its practitioners can be improved by debasing the standard of educational preparation is indeed a strange argument to come from the pen of a man with the education of Dr. Hans Lundberg. In criticising the Committee report, moreover, he has to a certain extent set up a straw man to belabor. The statement that the Committee report recommends that

Jan 1, 1946

When the writer first began his search for the early history of coal he was amazed at the paucity of information in literature about it, and while after six years many of the reasons for such a scarcity are understood, there are still many cases, even within the last two centuries, when one who can appreciate the tremendous part coal has played in the development of modern times, finds it hard to realize how little attention was paid to this material in those early clays. Occasionally a traveller or observer is found who foresaw how valuable coal was to be when industries were developed, but these were few and to most of those recording its occurrence it was just another mineral. George Washington was farsighted in his view of the development of this country and the need for means of transportation across the mountain barrier, but it was at least sixteen years after he must first have known of coal before he made any reference to it in his journals. He did, however, knowingly or not, select some valuable coal properties in the lands lie obtained in the West. This was then almost entirely an agricultural country, and what industries there were found a great abundance of wood fuel within easy access, there were no steam plants, and all iron was made with charcoal; in fact, the "captive mines" of the iron industry then were large timber "plantations," and when these were exhausted the furnace usually was abandoned and another one built elsewhere, as transportation of charcoal was quite expensive. Along the seaboard the cities and industries began to import coal from England and Nova Scotia early in the eighteenth century, but until the war of the Revolution began the total quantity of coal used yearly in this continent did not exceed nine thousand tons. In 1800 only two places, Pittsburgh and Richmond, Virginia, were using coal to any extent for domestic purposes and it was much later. than this that the amount of coal used in Philadelphia, New fork, and Boston exceeded that of wood. Practically all of the early travellers and writers mentioning coal are noted in the following pages. Several Englishmen who were evidently familiar with its use and value at home, mention its presence as being of great future promise to the young nation, but to nearly all it was more or less of a curiosity and the smoke caused by its use an abomination, and it

Jan 1, 1942

By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By P. R. Hines

Diphenyl guanidine is used as an accelerator in vulcanizing rubber. Other rubber accelerators are also flotation collectors, e.g., dithiocarbamate, thiazole, and the xanthates. Urea and its derivatives are good flotation collectors,' and guanidine is the nitrogen analog of urea. These two characteristics suggested testing diphenyl guanidine as a flotation collector. Diphenyl guanidine has been tried in flotation work previously, but references give no details.'.' Bunker Hill Co. of Kellogg, Idaho, supplied the ore sample used in these tests. The sample was typical of the ore milled in 1949 and contained 4.52 pct Pb and 1.08 pct Zn. A flotation test made by the author with potassium ethyl xanthate as a collector, the same flotation reagents, and the same grind employed in regular Bunker Hill mill practice was the standard for comparing results with the compounds and derivatives of guanidine. The compounds and derivatives of guanidine are only fair collectors of galena. However, if potassium ethyl xanthate were used in the galena float, its presence later in the sphalerite float would make it impossible to introduce another type of collector and be certain which collector contributed the result, so the compound or derivative of guanidine under test was used in both the galena and sphalerite floats in Table I. On both the galena and the sphalerite in the Bunker Hill ore, the depressing action of sodium cyanide and zinc sulfate is much greater with collectors of the guanidine type than with the xanthates. If the depressing agents are left out when a guanidine type of collector is used, but a pH of 8.6 is maintained with either lime or sodium carbonate, the depressing action is approximately the same as in the standard xanthate test. Consequently the depressing agents, sodium cyanide and zinc, were not used in the galena floats of tests 1226, 1228, and 1286, Table I, so the galena floats would be on a comparable basis with the standard xanthate test. As shown by the tests in Table I, the loss in the tail when diphenyl guanidine is used is 8.3 to 9.3 pct, as compared to 17.6 pct with potassium ethyl xanthate, or a recovery of 2.3 to 2.0 lb more zinc. Concentrate grade is 13.7 pct with potassium ethyl xanthate and increases to 22.9 and 31.8 pct with diphenyl guanidine, showing a much higher selectivity. Unless the Barrett's No. 4 coal tar creosote is considered to be a collector, no collector other than diphenyl guanidine is present in the tests, Nos. 1226, 1228, and 1286. Tests 1218, 1253, and 1263 in Table I1 were run to check the effect of the depressing agents used in flotation of the galena (sodium cyanide and zinc sulfate) upon subsequent flotation of sphalerite by diphenyl guanidine. Urea was substituted for potassium ethyl xanthate in tests 1253 and 1263 because it is a good collector for galena and a poor one for sphalerite, and the effect of the depressing agents is more marked with urea than with potassium ethyl xanthate. Test 1205 checks the effect of urea alone without any depressing agents when used for the flotation of galena. Table I1 shows that diphenyl guanidine as a collector for sphalerite is compatible with other flotation reagents used in floating galena. When the depressing agents sodium cyanide and zinc sulfate are used in the galena flotation step, the amount of lime in the sphalerite flotation must be increased (compare 1253 and 1263). Table I11 gives some of the compounds of guanidine which were tested and compared. Some of the compounds and derivatives of guanidine* are solu- * Diphenyl guanidine is in commercial production and is available on the market. ble in water and others are not. Those tested were fed dry. When an organic collector is promising, its compounds and derivatives should be tested and their comparative collecting power recorded. Eventually, in this way, it may be possible to discover some of the essential chemical characteristics of a good collector. For example, it is interesting to compare the diphenyl and dibutyl derivatives in Table IV with those of urea in Table 111, Example 3, U. S. Patent 2,664,198. All are good collectors. Table I shows some of the effects of lime on recovery of sphalerite by diphenyl guanidine. Table V

Jan 1, 1960

[Paragraph No. PREFACE ON ASSAYING I BALANCES AND WEIGHTS 2 Balances required for Assaying 13 How assay Weights are made 3 Assay Weights based on the Centner 18]

Jan 1, 1949

By J. A. Herbst, K. Rajamani, Y. C. Lo

In spite of potential theoretical and economic advantages of large-diameter ball mills, many manufacturers elect not to build them owing to what is perceived as an excessively large design risk. This is because traditional predictions for mill scaleup to large diameters are not always accurate. Alternative methods of analysis and scale-up are required. Recent studies have shown that detailed population balance models which account for important grinding subprocesses (grinding kinetics, material transport, and classification) are capable of predicting the performance of small- and intermediate-diameter mills (up to 4.3 m, or 14 ft) from small-scale batch tests. These same models are used in the current study to predict the performance of a "borderline "large ball mill (4.7 x 5.5 m, or 15 x 18 ft) at Asarco's Sacaton operation, a ball mill (5 x 5.8 m, or 16.4 x 19 ft) at Kennecott's Chino operation, and one of the world's largest ball mills (5.5 x 6.4 m, or 18 x 21 ft) at Cities Service Pinto Valley operation. Model parameters required for scale-up have been estimated in a 380-mm-diam (15-in.-diam) batch mill. Predictions are compared with the results of detailed plant sampling in the three plants. For the Sacaton and Chino operations, the error of the predictions was found to be less than 2.5%, while the corresponding error for the Pinto Valley operation was less than 2.7%. It is concluded that proper representation of the major subprocesses of grinding in the model equations is the key to achieving accurate scale-up. Of special importance is the need to account for the size distribution of the grinding media and the influence of the size distribution environment in the mill on grinding kinetics.

Jan 1, 1986

By J. E. Hanlon, J. D. Wolf

The relaxation peaks observed in plastically deformed materials at low temperatures have been reviewed by sack1 and Niblett and wilks. 2 In particular, the dislocation-relaxation in columbium has received considerable study.3-6 The present work deals with the lower-temperature dislocation-relaxation peak (referred to by Chambers and Schultz as the a peak) in columbium and Cb-5 pct Zr. The columbium and Cb-5 pct Zr specimens were machined to 3/8-in.-diam by 7-in.-long rods from bars hot-extruded at 1200°C. The internal friction and resonant frequency of the samples were measured in torsion at kilocycle frequencies at a maximum strain amplitude of -10-6. The interstitial content of both materials was approximately 70 ppm N and 200 ppm 0. The dislocation-re laxation peaks were measured in the hot-extruded state and after successive anneals. Fig. 1 is a compilation of the data. The resonant frequencies for the columbium and Cb-5 pct Zr samples were, respectively, 5.5 and 6.5 kc. Other workers have noted that the dislocation-relaxation peaks in columbium are not characteristic of a single relaxation time. As can be seen in Fig. 1, the zirconium addition further broadens the spectrum of relaxation times. The magnitude of the modulus defect as computed from resonant-frequency data also reflects this extension. The occurrence of the low-temperature a peak at a position 20°K higher in Cb-5 pct Zr as compared to pure columbium, in the hot-swaged state, suggests a decrease in the average dislocation mobility for the alloy. The authors do not feel that these data are sufficient to permit an interpretation in terms of any detailed models.

Jan 1, 1967

By F. E. Bachman

Although it has been apparent to me for a long time that too great weight was currently given to the silicon-contents of foundry-iron, and that the theory of the control by silicon of the carbon-contents of cast-iron is unsound, or that, at best, the influence of silicon is too small to be of much practical value as a guide in foundry-work, it never seemed to me desirable to enter the lists against either the " silicon-fad " or the theory, for the reason that I had neither the time nor the facilities to prove my position, nor any better theory to offer. But since Mr. Summers has taken the step, it seems but right that I should give such facts as are at hand in support of his contention. At the same time I do not think these are enough to prove the case if the contrary proposition were not itself, as it seems to me, based on insufficient evidence. Both Keep's and Turner's conclusions seem to be drawn from irons carrying less than the normal amount of carbon; Turner's " base " being, moreover, a steel rather than a pig-iron, and both the white base and the ferro-silicon of Keep being so low in carbon that compounds of them would not give a material approaching the carbon-contents of a normal casting, and having, therefore, little value as showing the effects of silicon on foundry-irons, even if his samples were treated under the same conditions as those to which pig-metal is subjected in making castings.

Jan 1, 1899

By George A. Roberts, Arthur H. Grobe

H. H. Hausner (Sylvania Electric Products Inc., Bayside, N. Y.)—I tested the 18-8 stainless steel powder described by Grobe and Roberts and the results were excellent. The powder was compacted and sintered in purified hydrogen to a very low density (approximately 20 pct and more porosity). Where the other powders show very little ductility when sintered to such a low density, the described stainless steel was surprisingly high in ductility. I would appreciate it if the authors could give us some data on a similar powder but without silicon and also data on 430 stainless steel powder. H. S. Kalish (Sylvania Electric Products lnc., Bay-side, N. Y.)—I should like to verify the excellent results obtained by Grobe and Roberts with their pre-alloyed stainless steel powder. It seems to me, however, that their data are conservative and that even better densities and higher tensile strength can be obtained with these powders by the selection of proper particle size fractions. The accompanying data were obtained by sintering compacts pressed from the powder made by Vanadium-Alloys Steel Co. to 0.8 in. in diam about % in. high in a cylindrical double action die without the use of lubricant. The compacts were sintered for 1 hr at 2370°F in hydrogen purified by passing it through a Deoxo unit (palladium catalyst) and a Lectrodryer. Even the density obtained using the as-received (—100 mesh) compacted at 40 tsi was quite high as was the hardness. This indicates that by increasing the sintering temperature slightly above 2350°F the coining and subsequent secondary sintering operation can be avoided. With the — 325 mesh fraction, however, very much higher density can be obtained and a high hardness. I have no tensile data to present, but I feel that it is not too optimistic to expect. that unusually high tensile strengths and good ductility can be obtained in this sintered material on the basis of the density and hardness data. The sintered stainless steel made by the above-described methods came out of the furnace very bright and clean. The purified hydrogen atmosphere is important in sintering stainless steel to reduce the oxide present in the powder. The result of such a sintering is good densification and good ductility of the sintered product. G. A. Roberts (authors' reply)—We are greatly indebted to Messrs. Hausner and Kalish for their discussions of our paper. Their encouraging remarks are greatly appreciated and their confirmatory data will do much to add to the value of the paper. At the present time it is impossible to provide complete data on a similar stainless steel powder without silicon, but we do know that, in general, the properties are slightly inferior. Data on such a powder and on other stainless steel types are to be published in the near future.

Jan 1, 1952

By E. H. Rose

From the more distant members and some not so distant, the plaint is often heard that they cannot justify the expense and time required to attend the AIME Annual Meeting. Almost invariably, the reason given takes this form: "I just don't see that I would get enough out of it." Often the would-be clincher is added: "Besides, the meat of it all comes out in print anyway." Not long ago, a group of us who have seldom missed a meeting in recent years fell to discussing this phenomenon, and found ourselves in emphatic agreement that anyone holding such a belief indicates by his first remark that he does not know how to attend a convention, and by his second, proves it. He is, by and large, the man who has never been there, and of him, there are many.

Jan 1, 1949

By Raphael G. Kazmann

Is electricity from nuclear-fueled power plants a partial solution to the energy shortage? According to various public and private institutions, the answer is an emphatic "yes." According to various other groups, the answer is an equally emphatic "no." I believe that a true and scientifically valid "yes" or "no" answer at this stage is premature because of conflicting claims and inadequate data regarding these two fundamental aspects: (a) the duty of uranium, i.e., the actual number of kilowatt-hours that can be generated from a ton of natural uranium through the use of light water reactors; and (b) the availability of uranium in the US to meet the lifetime requirements of the reactors scheduled for construction in the 1975-1985 period, as well as to supply the requirements of those reactors now in operation.

Jan 8, 1975

By Pierre de P. Ricketts

Having had occasion while in Europe during the past summer to visit some of the foreign mints and assay offices connected with the same, I thought a brief description of the general process of coining employed, and such items connected with assaying as were new, might prove interesting to the Institute. The principal foreign mints are: the Royal Mint, London; and the mints in Paris, Brussels, Utrecht, Berlin, Vienna, Copenhagen, St. Petersburg, Stockholm, Madrid, Milan, Rome, and Constantinople. My time only permitted my visiting a few of the principal and largest given in the list, and for a description of the remainder I am indebted to the kindness of Mr. James M. Napier, who in company with the deputy master, and chemist of the Royal Mint, made a complete inspection of all the European Mints in 1870.

By R. A. Conkling

DORSET HAGER, Tulsa, Okla. Recently we have, been doing a little work along the same lines Mr. Conkling has outlined iii his paper. I am not prepared to say that Mr. Conkling is not correct but our results do not agree with his. I think it is a question of difference in correlation and interpretation of the well records. Our cross-section of the Cushing pool does not agree with that of Mr. Conkling and we find instead of the beds thickening in the syncline, there is a tendency to thicken on top of the anticline. We took the north dome of the Cushing field, and are now trying to get all the records. It will probably be another month before we have all the data complete but our results at present do o not agree with those of Mr. Conkling at all.

Jan 4, 1917

By Byron W. Cheever

At the meeting of the Institute held in St. Louis, in October, 1886 (Transactions, xv., 448), I presented a paper upon the above subject. From the well-known action of certain solvents on phosphide and phosphate of iron, the conclusion was then reached, founded on analyses, that phosphide and phosphate of iron must be present in all iron. But this conclusion was based upon the reactions obtained in the analyses of iron phosphide and phosphate, in which the phosphorus existed in conditions different from those found in commercial iron. In the former, the phosphorus is concentrated ; in the latter, diffused. This fact left a reasonable ground for doubting the existence of phosphoric acid in commercial irons. Some direct method was therefore sought which would prove its presence. After investigating the subject for some time, I came to

Jan 1, 1888

By Pierre de P. E. M. Ricketts

HAVING had occasion while in Europe during the past summer to visit some of the foreign mints and assay offices connected with the same, I thought a brief description of the general process of coining employed, and such items connected with assaying as were new, might prove interesting to the Institute. The principal foreign mints are: the Royal Mint, London; and the mints in Paris, Brussels, Utrecht, Berlin, Vienna, Copenhagen, St. Petersburg, Stockholm, Madrid, Milan, Rome, and Constantinople. My time only permitted my visiting a few of the principal and largest given in the list, and for a description of the remainder I am indebted to the kindness of Mr. James M. Napier, who in company with the deputy master, and chemist of the Royal Mint, made a complete inspection of all the European Mints in 1870.

Jan 1, 1876

By F. B. Eiseman

IT is desired -to determine the effect of the extent of bank repairs on the final slag volume in acid electric steel-melting practice. It is understood that the repairs stud- TABLE I-Summary of Effect of Bank Repairs on Slag Volume [ ] ied here are necessary and the amount of sand added is that needed to maintain hearth and banks in a satisfactory condition. In this way the effect of repair materials on the amount of slag tapped would be found with a reasonable degree of accuracy. Ten heats were made for this study with careful attention to a uniform charge. The steel was the usual grade B and melting was carried out in a 3 1/2-ton top-charge Lectromelt furnace. Melting practice in all cases was the same-complete oxidation, with recarbonization by means of low-silicon pig iron.

Jan 1, 1947

OCHRE is a semimineral composed by Nature of earth and a tincture of yellow caused by a fumosity of lead ore. By itself it is a material without any [38] metal, although when it is used in smelting it helps to melt the harsh and sour ores of metals. I do not know that it has any other use, except to painters. Bole is also a red viscous earth which has a very astringent and drying nature. It has no very apparent smell or taste, and I think that the cause of its redness lies in the fumosities of iron ore, for it is a companion to this and is found in its mines. It is an efficacious medicine against any poison and in this capacity has an action like terra sigillata* or perhaps better. In

Jan 1, 1942

By R. W. Raymond

GEHEIMER BERGRATH Prof. Dr. HIERONYMUS THEODOR RICHTER, ex-Director of the Freiberg Mining Academy and Honorary Member of this Institute (to give him the full title, which nobody ever thought of using in his genial and unceremonious presence, and the whole of which I have omitted at the head of this notice, as adding nothing to the virtue and value of the man I knew), died on Sunday, September 25,1898. He was born in 1825 at Dresden, and in 1843, after some practical training in pharmacy, entered the Freiberg Mining Academy, where he devoted himself chiefly to metallurgy and metallurgical chemistry, under the guidance of the celebrated Plattner, whose masterly instruction in those arts, and also, especially, in assaying and the use of the blow-pipe, has been classic authority to the present day. In 1853, Richter was ap-

Jan 1, 1899

By K. A. Jackson, G. A. Chadwick, A. Klugert

The diffusion field ahead of a lamellar interfnce is analyzed using an electrical analog. A self-consistent solution is obtained for the shape of the interfnce and the diffusion field by an iterative process. The solutions presented here are for a 50-50 eutectoid or eutectic, The shape of the interface is found to he independent of growth velocity and lamellar spacing, and to depend on the relative values of interfacial free energies at the phase houndaries . The mode of growth of lamellar eutectics and eutectoids has been a subject of much interest for many years.1-4 Mehl and Hagel 1 have shown photomicrographs taken by Tardif when he attempted to determine experimentally the shape of an advancing pearlite interface; the results are completely ambiguous. Brandt' and schei13 have made approximate calculations of the composition ahead of a lamellar growth front. The shape of the advancing front and the composition distribution ahead of the front are difficult to calculate because one depends on the other. It is the purpose of the present paper to describe a method by which this calculation has been done. Lamellar-eutectic growth usually occurs under conditions where the growth is fairly rapid, and the interface temperature is close to the eutectic temperature. The growth rate is usually determined by heat flow. Eutectoid growth, on the other hand, can best be studied by quenching to some temperature, and allowing growth to proceed isother-mally. In both cases the growth is believed to be controlled by diffusion* rather than by the atomic kinetics of the transformation. This being the case, a single treatment of the diffusion equation will apply to both cases, provided the region of the interface in a eutectic may be considered to be isothermal. If a part of the interface could appreciably change its thermodynamic driving force by advancing ahead of or lagging behind the mean interface, then the two cases would not be similar. Eutectics normally grow in temperature gradients of the or-der of a few degrees per centimeter. The normal eutectic spacing is the order of a few microns. Part of the interface would have to extend many lamellar spacings ahead of the mean interface before it experienced sensibly different conditions. The interface temperature is usually a few tenths of a degree below the eutectic temperature so that temperature differences of the order of one-thousandths of a degree (a displacement of one lamellar spacing) would be unimportant. Protrusions large compared to the mean spacing do occur when one phase only grows into a eutectic liquid. This is usually a dendritic type of growth, and easily distinguishable from the lamellar mode of growth. A single treatment of lamellar growth will apply equally well to both eutectic and eutectoid decomposition. At the interface, which as shown above is essentially isothermal, the difference between the equilibrium eutectic temperature Teu and the actual interface temperature Ti, can be divided into two parts: 1) the composition varies across the interface, so that the local equilibrium temperature is not Teu; and 2) the interface is curved, so that the local equilibrium temperature is depressed according to the Gibbs-Thompson relationship. This undercooling can be written as Teu-Ti =?T = mAC(x) + a/r(x) [1] where ?C(X) is the departure of the composition at a point x on the interface from the eutectic composition, see Fig. 1, r(x) is the local radius of curvature at a point x on the interface, m is the slope of the liquidus line on the phase diagram, and a is a constant given by where s is the interfacial free energy, TE is the equilibrium temperature, and L is the latent heat of fusion. The calculations in this paper will be made only for the case where the phase diagram is symmetric, that is, the eutectic occurs at 50 pct, the liquidi have the same magnitude slope m at the eutectic temperature, and C,, the amount of B rejected when unit volume of a freezes, see Fig. 2(a), is the same for both phases. As shown in Fig. 2(b), the composition ahead of the a phase will be rich in B, the composition ahead of the ß phase will be rich in A. The composition at the phase boundary is the eutectic composition. The difference between the local liquidus temperature and the actual tempera-

Jan 1, 1964

By C. W. Gibbs, E. K. Parks

In 1929 the Standard Oil Company of California commenced the development of a device for obtaining temperatures and pressures in flowing and shut-in wells and of suitable running equipment for such a recorder. Although simple in principle, the recorder has required much experimental work in its development. The various problems have now been solved to such an extent that it is believed that the apparatus affords a sturdy and reliable means for obtaining information regarding depth pressures,—apparatus that may be turned over to a well gang for routine operation. As an example of the rough usage the device will withstand a recent incident may be cited. Owing to failure of the lowering line at the conclusion of a run a recorder was dropped some 6300 ft. through 2 1/2-in. tubing filled with gassy oil. The device was fished out undamaged and with the pressure record intact, although the instrument had been subjected to a pressure greater than 2300 lb. per sq. in. for some 24 hr. after impact at bottom. Description of Recorder The instrument is of the continuous recording loaded spring type (Fig. I). Temperature is not recorded continuously but is obtained by maximum recording thermometers in an auxiliary thermometer well. The entire instrument assembly, from bottom of the recorder to top of the socket, is 6 1/2 ft. long and weighs less than 25 lb. The maximum outside diameter of the recorder shell is 1 1/4in., and all attachments need be no larger. This permits lowering the device inside 2-in. tubing. The operating principle is simple. The well pressure acts upon a piston A resisted by the extension of spring B. The spring deflection is recorded by a stylus C upon paper within the recording drum D. Springs.—To improve accuracy at lower maximum well pressures five interchangeable spring assemblies are used. These have maximum pressure ranges of from 250 to 5000 lb. per sq. in. Piston diameter is the same in all cases, and each spring is designed for a deflection of about 5 in. for maximum pressure loading. A complete spring assembly there-

Jan 1, 1934