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By B. H. Sage, W. N. Lacey

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By W. N. Lacey, B. H. Sage

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By F. Keller, R. H. Brown

BECAUSE of the extensive use of Alclad 24s alloy sheet in aircraft construction, there is much interest in the metallurgical changes caused by heat-treatment of this product.1,2 One of these changes is the result of the diffusion of soluble elements from the core into the coating during treatment. This paper deals with the thermal treatments that may influence diffusion and with the practical effects of diffusion on the serviceability of the product. As is well known, Alclad 24s-T sheet has a core of high-strength alloy combined with surface layers of relatively pure aluminum. The microstructure of a cross section of this product is shown by Fig. I. hot only does the relatively high-purity coating have a high resistance to corrosion, and hence serves as a mechanical barrier between the core metal and the corroding environment, but in addition this coating I exerts electrochemical protection over areas where the core may be exposed, such as cut edges. In addition, the coating affords electrochemical protection to projecting heads of *417S-T, 17S-T and 24S-T rivets, or attached members made from these alloys. Under some conditions of heat-treatment, however, diffusion of copper into the coating will alter the electrochemical relationship between the coating and the core to the extent that only partial protection will be obtained under some corrosive conditions. The reason for the electrochemical protection lies in the fact that the coating layers of pure aluminum are anodic to the alloy core. The addition of copper to aluminum produces alloys in which the potential is lower than that of the pure metal. Moreover, as the amount of copper in solid solution in z4S alloy is increased, the potential of the alloy becomes more cathodic. When heat-treated at 920°F. and quenched in cold water, 24s-T is about 0.16 volt cathodic to pure aluminum. However, copper will diffuse from the core into the coating, and if it reaches the surface the potential will be altered in a cathodic direction. Thus the potential dif-erence between the core and coating may be less than 0.16 volt, depending upon the thickness of the coating, and the time and temperature of heat-treatment. Of the methods available for determining the extent of diffusion of copper from the core into the coating of Alclad 24S-T, two are generally used; namely, the metallographic and the solution potential method.3 METALLOGRAPHIC METHODS Metallographic methods will reveal the progress of diffusion of copper into the coating. For instance, the diffusion zone in the coating intermediate between the coating surface and the core is shown in Fig. I. This photomicrograph is of a polished and etched cross section of 0.040-in. Alclad 24S-T sheet. Diffusion proceeds into the coating more rapidly along the grain boundaries than through the body of the grains. consequently, the diffusion zone is not of uniform width

Jan 1, 1944

By G. W. Healy, J. C. Schottmiller

Molten silicates were found to exist in the Cr-Si-0 system at temperatures above 1450°C. one atom of oxygen is readily removed from CrzOs in the presence of Si02 at 1700°C, forming a silicate melt. Steam-hydrogen ratio measurements made at this temperature indicate that the free energy of the reaction: Cr20s(c) + Hz = 2CrO (in Si02 -saturated melt) + H20 is approximately 5600 * 1500 cal. A deep-blue chromous silicate, probably Cr2Si04, forms from these melts at about 1400" to 1500°C, and is characterized by.its distinctive X-ray diffraction pattern and optical properties—distinct pleochroism and high refractive indices. THE question of the state of oxidation of chromium in slags has vexed metallurgists for many years The experiments of Koerber and Oelsenl suggested the probable presence of divalent chromium in silica-saturated slags equilibrated with high-chromium melts. Hilty and coworkers2 had also found chromium at lower valency, as Cr304, in inclusions formed from oxygen-saturated Fe-Cr melts with as little as 10 pct Cr. In both cases, disproportiona-tion of the lower oxide to CraO3 and chromium was found to occur to a greater or lesser extent, depending upon the rate of cooling from the high temperature. The work on Cr304 was sufficiently detailed for chipmans to derive its thermodynamic properties, but Oelsen's experiments in the silicate system were not extensive enough since most of his runs were made with slags containing large amounts of manganese oxide in addition to iron and chrome oxide and silica. The present study describes experiments carried out to map out an approximate liquidus diagram in the CrzOs, "CrO", SiOa portion of the Cr-Si-0 system, and to measure the partial free energy of solution of oxygen in the system. EXPERIMENTAL 1) Approximate Melting-Point Determinations. Preliminary trials showed that when an equimolar mixture of Cr20s and SiOa was treated with hydrogen in the temperature range 1500" to 1600°C, copious amounts of steam were evolved, and a low-melting liquid formed which could be quenched to a blue, crystalline, material having a distinctive X-ray diffraction pattern. It was found that the identical material could be produced by heating intimately mixed, finely divided Cra03, Cr, and SiOa, held in a tungsten crucible, under purified argon. Thus, it was possible to prepare mixtures containing any desired proportions of chromium, silicon, and oxygen, pel-letize them, heat to temperature in the furnace shown in Fig. 1, and observe, after cooling, whether the pellet remained unchanged or showed signs of incipient, partial, or complete melting. 2) Free Energy of Solution of Oxygen. This was studied by measurement of steam-hydrogen ratios for the reaction: H20 (gas) + O (dissolved in charge) + Ha (gas) The experimental method chosen was to prepare a

Jan 1, 1964

By Howard R. Keil

PRIOR to World War II, approximately 500 tons per day, or one-third of the ore being shipped to the Golden Cycle Mill at Colorado Springs, Colo., from the Cripple Creek district, was being treated in the flotation plant. The remaining 1000 tons, along with the flotation concentrates, received the usual roasting and cyanide treatment. Since it was not possible to make a disposable tailing on the general run of Cripple Creek ores by flotation alone, it was necessary to treat the flotation tailings by cyanidation, along with the roasted ore. By this treatment, an overall economical tailing could be made. The gold ores from the Cripple Creek district are the highly siliceous sulphotellurides with approximately 3 pct total sulphides. In the lower grade ores most of the values are found in very finely disseminated pyrite. In some of the higher grade ores the tellurides, calaverite and sylvanite, can be recognized. After several years of floating Cripple Creek gold ores, having a very low mineral content, it was concluded that this type of ore required a Type of flotation machine that would give a rather violent aeration and agitation. This action produced a fairly deep froth column which contained not only the free mineral, principally pyrite, but also most of the middling product; this was most essential in producing a low grade tailing by flotation alone that could be discarded to waste. After investigating most of the current types of flotation machines, it was decided to convert to the Fagergren type. During World War II, the flotation plant was modified to handle lead and zinc ores. The treatment of these ores was carried on until April 1946. At this time the flotation plant was again reconverted to handle the Cripple Creek ores. SELECTING ORES FOR FLOTATION During the period of reconversion a considerable amount of experimental work was carried on in the laboratory to determine if a disposable tailing could be made by flotation alone, on certain selected ores from the Cripple Creek district. It was found that most of the dump ores and a few of the low grade mine ores could be treated by this method with very satisfactory results. After the preliminary test work in the laboratory, it was decided to carry on further work on a plant-size scale to see if similar results could be obtained. On April 15, 1946, a part of the plant was put into operation as a pilot plant. The various ores that had been found suitable for treatment by this method in the laboratory, were run through the pilot plant at the rate of 200 tons per day for a period of several months. Results were so encouraging that it was decided to put the plant in full-scale operation. Since that time plant capacity has been increased from 500 to 1000 tons per day. This has been done not by the installation of more machinery but by (I) crush-

Jan 1, 1947

By James W. Halley

' FINE-GRAINED " steels have been standard products for many years. This paper describes an investigation of the effects of some of the more common grain-growth; inhibitors used to produce these steels. The properties, response to heat-treatment, and the deoxidation practice necessary to produce "fine-grained" steels have been the subjects of numerous papers. It has been shown that a substantial quantity of' aluminum is necessary to produce this type of steel, and it has been indicated that titanium and zirconium produce a similar result. For some time there was a lively argument between those who felt that aluminum refined the grain and those who felt that aluminum oxide was the effective agent. This argument subsided with an apparent victory for those promoting aluminum oxide. Most of the work on grain size has divided steels into two broad classifications based upon McQuaid and Ehn's original carburizing test at 1700°F. or some similar test at this temperature. If the steel coarsened at this temperature, it was coarse grained, while if it did not it was fine grained. Quantitative data concerning how much a certain amount of aluminum raised the coarsening temperature and affected the properties, all other factors being constant, are very meager. Similar information regarding titanium and zirconium is practically nonexistent. The published information on aluminum yields some quantitative information. Epstein, Nead and Washburn' gave the first quantitative information on the amount of aluminum necessary to prevent grain growth at 1700°F. They showed that the addition of a pound to a pound and a half of aluminum per ton (0.05 to 0.075 per cent) would assure steel that would not .coarsen during a McQuaid-Ehn test at 1700°F. Herty, McBride and Hough2 reported that a steel containing 0.020 per cent acid-soluble aluminum coarsened between 1742° and 1832°F., while steels containing 0.016 per cent and 0.017 per cent acid-soluble aluminum coarsened between 1652~ and 1742°F. compared with similar aluminum-free steels that started to coarsen at 1580°F. Herty3 also showed a marked improvement in low-temperature notched impact resistance with increasing acid-soluble aluminum up to 0.030 per cent. McQuaid4 compared the coarsening of steels containing 0.011 to 0.204 per cent total aluminum and found a maximum coarsening temperature at 0.098 per cent aluminum. He had no samples between 0.015 and 0.098 per cent aluminum. Houdrement5 found a marked decrease in coarsening temperature with aluminum contents above 0.50 per cent. Kinzel, Crafts and Egan6 found that aluminum and zirconium improved thy low-temperature impact resistance of a low-alloy steel, while titanium was detrimental. Sims7 shows that sulphur increases the coarsening temperature and that the maximum coarsening temperature is between 0.04and 0.06 Per cent added aluminum. The

Jan 1, 1946

By Howard R. Keil

Prior to World War 11, approximately 500 tons per day, or one-third of the ore being shipped to the Golden Cycle Mill at Colorado Springs, Colo., from the Cripple Creek district, was being treated in the flotation plant. The remaining 1000 tons, along with the flotation concentrates, received the usual roasting and cyanide treatment. Since it was not possible to make a disposable tailing on the general run of Cripple Creek ores by flotation alone, it was necessary to treat the flotation tailings by cyanidation, along with the roasted ore. By this treatment, an overall economical tailing could be made. The gold ores from the cripple creek district are the highly siliceous sulphotel-lurides with approximately 3 pet total sulphides. In the lower grade ores most of the values are found in very finely disseminated pyrite. In some of the higher grade ores the tellurides, calaverite and sylvanite, can be recognized. After several years of floating cripple Creek gold ores, having a very low mineral content, it was concluded that this type of ore required a type of flotation machine that would give a rather violent aeration and agitation. This action produced a fairly deep froth column which contained not only the free mineral, principally pyrite, but also most of the middling product; this was most essential in producing a low grade tailing by flotation alone that could be discarded to waste. After investigating most of the current types of flotation machines, it was decided to convert to the Fagergren type. During World War 11, the flotation plant was modified to handle lead and zinc ores. The treatment of these ores was carried on until April 1946. At this time the flotation plant was again reconverted to handle the Cripple Creek ores. Selecting Ores for Flotation During the period of reconversion a considerable amount of experimental work was carried on in the laboratory to determine if a disposable tailing could be made by flotation alone, on certain selected Ores from the Cripple Creek district. It was found that most of the dump Ores and a few of the low grade mine ores could be treated by this method with very satisfactory results. After the preliminary test work in the laboratory, it was decided to carry on further work On a plant-size scale to see if similar results could be obtained. On April 15, 1946, a part of the plant was put into operation as a pilot plant. The various ores that had been found suitable for treatment by this method in the laboratory, were run through the pilot plant at the rate of 200 tons per day for a period of several months. Results were so encouraging that it was decided to put the plant in full-scale operation. Since that time plant capacity has been the from 500 to 1000 tons per day. This has been done not by the installation of more machinery but by (I) crush-

Jan 1, 1949

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG's ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid' have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey' presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,

By William R. Patterson

ACCORDING to the phase diagram for the Mn-Ni system,' the high-temperature, fcc y-manganese solid solution is stabilized to below room temperature, in the range approximately 22 to 28 wt pct Ni. However, pearson2 cites evidence in the literature showing that for manganese contents greater than about 75 wt pct the quenched phase in Mn-Ni alloys is fct. This is in keeping with zener's3 suggestion that in manganese-rich alloys the fcc high-temperature phase undergoes a diffusionless or martensitic transformation to a fct structure upon quenching. Work by Basinski and christian4 on manganese-rich compositions in the similar alloy system Mn-Cu established that in alloys of greater than about 82 wt pct Mn the y-manganese phase underwent a fee fct martensitic transformation upon quenching to room temperature. Striking evidence for this martensitic transformation was the highly twinned or banded microstructure, an example of which is shown in Fig. 1. Similar microstructures have also been found in quenched Mn-Cr5 and Mn-Au6 alloys. In the present investigation, we attempted to obtain similar evidence of a fcc — fct martensitic transformation in manganese-rich Mn-Ni alloys. Manganese alloys in the range 10 to 30 wt pct Ni were prepared by arc-melting, under argon, at atmospheric pressure. The alloys all were 50 g in size, and negligible weight loss occurred during melting. The starting materials were electrolytic manganese and nickel, both of 99.9+ pct purity. The alloys were subsequently homogenized 48 hr at 1750°F, hot-rolled 50 pct at 1700°F, annealed 2 hr at 1700°F, and water-quenched to room temperature. All heat treatment was done in purified argon. Both X-ray and metallographic techniques were used to examine the structures of the quenched alloys. X-ray diffractometer studies were conducted on powder specimens obtained from filings rean-nealed 2 hr at 1700°F in argon and water-quenched. Identification of the intensity peaks from the diffractometer counter traces showed that below about 10 to 12 pct Ni the y phase decomposed partially upon quenching to give an a- + ?-manganese structure. In the range approximately 12 to 25 pct Ni, the structure was found to be fct ? manganese with a c/a ratio approaching 1.0 at 25 pct Ni. Beyond approximately 25 pct Ni, the structure remained fcc. These results, including lattice-parameter determinations, are given in Table I. Metallographic examination. was carried out on specimens polished and etched after quenching, and also on polished specimens reannealed and quenched. In the first case, the distinctive twinning or banding so prevalent in Mn-Cu alloys was sought, while in the second, the surface relief effect generally regarded as being truly characteristic of a martensitic transformation was sought. The microstructure of representative alloys in the range 12 to 25 pct Ni is shown in Fig. 2. The structure of the Mn-15 pct Ni

Jan 1, 1965

By Wallace W. Key

Chalk is a natural calcium carbonate occurring as the remains of soft, friable, minute marine organisms. Whiting can be either finely ground calcium carbonate prepared from chalk, marble, or limestone or the product obtained by chemical precipitation from a solution or suspension containing lime. Until relatively recently, whiting made from limestone was termed "whiting substitute," but it is now usually designated as limestone whiting. Precipitated calcium carbonate, sometimes called "precipitated whiting" or "precipitated chalk," is a finely divided calcium carbonate product obtained by chemical precipitation from a solution or suspension containing lime. Considerable quantities of precipitated calcium carbonates are produced from many chemical processes. Naturally occurring calcium carbonate in a variety of crystalline forms and in all degrees of chemical purity forms a substantial part of the earth's crust. Exactly where a chalk grades into a marl or calcareous shale through increase of clay or silt or into a hard limestone through consolidation and crystallization is difficult to determine because no rigid specifications have been promulgated for classifying them. Composition and Properties Once considered to be amorphous, chalk was later found to be cryptocrystalline. In the pure state it consists entirely of CaCO3, but many deposits are impure. When impurities are removed and the material is reduced to a finely divided state, it is known as chalk whiting. Much confusion attends the use of the term "chalk" as well as the classification of whiting materials. For instance, blackboard chalk is not necessarily chalk but is sometimes plaster of paris or a form of talc. Colored "chalks" may be true chalk colored and compressed with a binder but are probably such materials as hematite, clays, or carbonaceous matter. The term whiting was applied exclusively to the product derived from true chalk before World War I. Chalk imports were difficult to acquire during World War I, and whiting substitutes, a term applied to the products derived from natural rock deposits and precipitated calcium carbonate, were introduced. Substitute whitings were not acceptable at first, but it was found that blending true chalk with substitutes often created an improved product; eventually by selection of limestone and finer grinding, products not only acceptable, but for some uses superior to chalk whiting, were developed. Gradually the term "substitute" was dropped because chalk whiting had lost its importance, being largely supplanted in the United States by other whiting materials. Whiting is now made in ever-increasing quantities from limestone, marble, dolomite, marls, vein calcite, oyster-shell, as well as primary and byproduct precipitated calcium carbonates. Distribution of Chalk Europe-In England, France, Belgium, Denmark, and other European countries highpurity chalk occurs in extensive beds. The Cretaceous period, or the "age of chalk," in geologic history receives its name from the great deposits of chalk exposed on either side of the English Channel. It has been estimated that oceans in which chalk and allied deposits were formed covered more than 500,000 square

Jan 1, 1960

INTRODUCTION The meaning of cash flow has already been defined as after-tax earnings available for use by the corporation or business. It is therefore apparent that a significant part of mineral economic evaluation is concerned with correct and accurate computation of taxable income under existing tax laws, and the proper treatment of tax allowances and deductions. The various methods of depreciation, depletion, and amortization are all means whereby the investor can earn back or recover, before taxes are imposed, the investments made for purposes of doing business or for the production of income. Each of these three types of tax deduction are applied to different investment items such as property, equipment, buildings, research, etc. The cost of buildings, equipment, machinery, and transportation equipment are representative of capitalized business costs that must be recovered by depreciation over the life of the asset. The property investment costs of acquiring natural resources such as minerals, oil and gas, and standing timber are examples of investment costs that may be recovered by depletion. Several other capitalized business costs, such as research expenses and trademark expenses, may be recovered by amortization. The term "capitalized" means that the in- vestment cost is not deducted as an operating expense in the year that it is incurred, but is spread out over a period of years through depreciation, depletion, or amortization deductions according to lawful schedules. Of course, any capitalized cost can only be deducted once. The other costs of doing business which are not capitalized, such as labor and operating costs, are said to be "expensed," i.e., they are written off for tax purposes in the year they occur. DEPRECIATION Depreciation, according to US tax law, is a deduction from taxable income permitted as a "reasonable allowance for the exhaustion, wear and tear of property out of its use or employment in a business." The original cost of the property is the usual basis for determining depreciation. Since depreciation write-off is applied over the useful life of the asset, the first step is to determine the estimated useful life or its allowable depreciable life. These two lives may or may not be the same. No average life is applicable to all types of depreciable assets under different conditions or in different types of business. It is the taxpayer's responsibility to determine the useful life of the asset according to his own operating conditions and experience, within the guidelines set by the US Internal Revenue Service (IRS). The Class Life Depreciation Range (ADR) System permits the taxpayer to choose from a range of depreciable lives at 20% below or above the present guideline life. The second step required in calculating depreciation is to determine an estimated salvage value for the asset. The salvage value is an estimate, made at the time of acquisition, of the amount of money which can be realized by the sale of the asset at the end of its useful life. The four depreciation methods most widely used in the US are: (1) the straight-line method, (2) the declining balance method (double declining balance), (3) sum of the years - digits method, and (4) units of production method. Straight-Line Depreciation Method The straight-line depreciation method is the simplest for calculating depreciation. The depreciation for each year is determined by subtracting the estimated salvage value from the first cost of the asset and dividing the result by the years of life. The method gives equal annual deduction over the depreciable life. Salvage value equal to or less than 10% of the first cost may be ignored. [first cost - salvage Straight line = years of life ] Declining Balance Depreciation Method Declining balance depreciation, or double declining balance (DDB) as most frequently applied, is used for accelerating depreciation in the early years of the asset and is the fastest depreciation method allowed by the US Internal Revenue Service. The declining balance

Jan 1, 1980

By E. P. Valby

A method is presented in which the hydrocarbon weight fractional analyses of the well effluents from a true gas-tip-portion well and a true dark-oil-ring well furnish the basic data for determining the properties of any mixture of production from the two sources. The effect of injected gas on these properties can be computed. Comparison of similar properties of a given well effluent to the properties of mixtures of the basic well effluents will give the relative amounts of production from the two sources and injected gas. Presentation of Problem Oil fields having an area of gas-cap, or light-oil production, over the dark-oil area present a problem of increasing gas-oil ratios during the production of an oil well. The use of pressure maintenance in a field such as above, or a cycling project, wherein residue gas from an absorption plant is injected into the reservoir, adds to the problem, because a part of the increased gas-oil ratio may be due to the production of injected gas. The usefulness of a means to determine the amount of injected gas in a well effluent led to the development of a method in which well-effluent analyses of a true gas-cap-portion well and a true dark-oil-ring well furnish the basic data needed to determine whether injected gas of a known composition is present in a given well effluent. Development op Method The method presented herein is based upon the principle that if two fluids, or well effluents, having different properties are mixed in known proportions by weight, • the properties of their mixtures can be computed. Conversely, if these basic data are known, the properties of a mixed well effauent can be used to compute the relative amounts of each type of well effluent in the mixture. A convenient way of making these computations is to have the fractional analyses of the base well effluents and mixtures expressed in weight fractions The mathematical equations expressing the properties of mixtures will be developed for a two-component system consisting of the well effluents from the dark-oil ring and the gas-cap area. The added effect of injected gas, a third component, will also be developed. The following assumptions have been made in developing the method: 1. The gas-cap and dark-oil fluids exist initially in separate portions of the reservoir. 2. The fluids in each portion exist in a single phase at pressures above the saturation pressure for the dark-oil fluid. 3. The composition of each fluid is substantially constant throughout its respective portion of the reservoir. 4. Changes in reservoir pressure and temperature will not change the composition of the fluid entering the well bore. 5. The injected gas displaces original gas-cap fluid 100 per cent. •• 6. AS the injected gas travels through a

Jan 1, 1945

By C. E. Birchenall, G. Derge

IN studying the kinetics of slag-metal reactions, it has become increasingly apparent that a complete knowledge of all aspects of interface phenomena will be required to clarify these processes adequately. A part of the data required for all oxidizing slags used in the refining of impure iron to steel is the rate of exchange of iron between the slag and metal phases. The simplest equilibrium of this type is that between liquid iron and iron silicate slag when both phases are equilibrated with the silica crucible containing them. In this study, the exchange of iron between the two liquid phases has been measured by using radioactive Fe as tracer. The observed high exchange rate indicates the ease with which such interfaces may be crossed in refining processes. The experiments required for this study involved relatively minor and normal modifications of well established techniques. Melting was accomplished by induction heating in heavy walled, fused silica, rotating crucibles." Rotation was used to minimize dilution of the slag by crucible erosion. The melting stock was ingot iron. Slags were prefused in iron crucibles using chemically pure grade oxide reagents. The special conditions applying to the active iron additions will be described for individual experiments. Suitable precautions were observed with regard to protection against radiation hazards.' Identification of Activity This particular study was initiated several years ago, but held in abeyance because the radioactive iron available at that time contained a foreign activity which concentrated in the slag so as to mask the iron activity and render the results unin-terpretable. With the benefit of experiences from other studies, radioiron of suitable purity can now be prepared. As received from the Isotope Div. of A.E.C., the unit appears to contain Fe + Fe50 and a high activity cobalt. The cobalt and iron are separated by repeated ether extractions, and the purified iron stored for sufficient time for the Fe'7 44 day half-life) to decay to negligible activity, leaving only Fe as the active isotope. This was confirmed by the absorption curves for slag and metal samples from heat No. 1. In Fig. 1 the experimentally measured points for the absorption curves of slag and metal are fitted by the calculated slope of 5.8 mg per sq cm in aluminum, which corresponds to the Mn K doublet emission resulting from the capture of an orbital electron of Fe" by the nucleus. This shows that the radioactive species are the same in both slag and metal and identifies it as Fe55 Description of Individual Heats For the first heat, the radioactive iron was contained in the prefused slag. The active Fe55 had been precipitated with carrier and was added as Fe2O3 during fusion in the iron crucible. The charge of 500 grams of ingot iron was melted, the protective iron sleeve added, rotation started, and a prefused, inactive slag was added to allow the system to approach equilibrium. After about 5 min at temperature, the wash slag was skimmed and the active slag added. Initial slag and metal samples were taken as soon as the slag was molten. Additional samples were taken at indicated intervals thereafter. Slag samples were dipped with a small iron spoon and metal samples were sucked into 1/4 in. ID silica tubes. The slag and metal samples were pulverized and mounted for radioactive counting. The slag samples were analyzed chemically for FeO. Temperature was read after the last slag sample by immersion of a Pt-Pt-Rh thermocouple protected by a fused silica sheath. Since no significant variation of rate with temperature was observed

Jan 1, 1954

By J. G. Tilton

While most of the Pittsburgh coal horizon is dependably regular, there are areas where it is dis-turbed by sandstone cutouts which can seriously hamper mining operations. Because these channel sandstones often cut out the coal abruptly, they are difficult to detect by core drilling; and mine operators, for want of a better way to discover them, have largely trusted to luck to avoid them. This paper, based on a study the author is presently conducting, is an attempt to point out some sources of information and signposts which might aid the operator in determining the presence of a cutout before he begins to mine. The presence of sandstone cutouts in the Pittsburgh coal has been known for many years. Some of these irregularities were observed at outcrops and others were discovered by drilling, but the majority were and are found during mining operations. These sandstone cutouts are commonly called "faults" and have been a bane to mining companies wherever they have been encountered. Profiles of some typical deposits appear in Fig. 1. The cutouts disrupt the normal system of mining, replace valuable coal reserves, create ventilation problems by emitting large quantities of gas and sometimes oil, limit the number of entries that can be economically driven, affect the quality of the coal, disrupt the normal structure of the coal, and create roof control problems. It might be expected that such severe disturbances in the structural regularity of the coal would instigate determined and extensive searches for possible cutouts prior to mining operations, but this apparently has not been so except in isolated cases. Two reasons may be cited to explain this lack of exploratory work. The first and probably the strongest reason is the over-all regularity of the Pittsburgh coal. No coal seam in the country exhibits the horizontal continuity and relative regularity of the Pittsburgh coal. It lies in an almost unbroken sheet across southwestern Pennsylvania, eastern Ohio and northern West Virginia, and has been recognized as far east as the Potomac Basin of western Maryland. Over 5729 square miles are underlain by this coal, of which 2077 square miles are in Pennsylvania, 2214 square miles in West Virginia, 1410 square miles in Ohio, and 28 square miles in Maryland. The area covered by this study is outlined by the map in Fig. 2. Over most of this territory the coal has the following characteristic structure as illustrated in Fig. 3: roof coal, draw slate, breast coal, parting, bearing in coal, parting, brick coal, parting, and bottom coal. With such regularity of thickness and structure, mines were opened and laid out with confidence that the coal would be present. Extensive drill testing was considered unwarranted and it was also quite expensive because the coal dipped to the west away from the Monongahela River. Consequently, drill holes were widely spaced and rarely encountered ad-

Jan 1, 1968

By L. S. Darken

It has long been recognized that the driving force in an isothermal diffusion process may be regarded as the negative gradient of the chemical potential (partial molal free energy) of the diffusing substance. This equivalence is exactly analogous to the fact that a mechanical force is the negative gradient of the potential energy. Nernstl in 1888 expressed these driving forces in terms of osmotic pressure, which is directly related to the chemical potential and free energy. The relationship between the diffusivity, mobility and activity coefficient of electrolytes in aqueous solution has been developed in great detail by Onsager and FuossZ with results which have recently been confirmed experimentally by Harned and Nuttall. This interpretation of the driving force in isothermal diffusion has been discussed earlier by the author,4,5 who pointed out4 that "for a system of more than two components it.is no longer necessarily true that a given element tends to diffuse toward a region of lower concentration even within a single phase region"; departure from the behavior of an ideal solution may be so great that the concentration gradient and the chemical potential gradient, or activity gradient, may be of different sign, thus giving rise to "up hill" diffusion. Since, in the discussion of that paper,4 some skepti- cism as to the validity of this conclusion was expressed, it seemed desirable to adduce experimental evidence to support it. Evidence of such diffusion in nonmetallic systems has already been reported. For example, it was observed by Hartley" in a series of experiments in which sodium chloride diffused from a saturated solution in about 5 pct acetone in water into a solution virtually free of salt but with essentially the same acetone concentration. Specifically, a wine glass containing crystalline salt and saturated solution was totally immersed in a large glass cylinder containing the acetone-water solution without salt; the difference in specific gravity was such as to prevent convection. Diffusion of salt was accompanied by a marked depletion of acetone in the wine glass; after 3 days the acetone concentration decreased from 5.37 pct at the top of the glass, where the salt concentration was low (0.93 pct), to 1.84 pct at the bottom where the salt concentration was high (21.64 pct). This "uphill" diffusion was found to be such that the partial pressure (activity) of acetone was essentially equalized throughout the system when a steady state gradient of sodium chloride was maintained. In order to demonstrate the existence of such diffusion in metals, a series of four weld-diffusion experiments was made. In these measurements pairs of steel of virtually the same carbon content, but differing markedly in alloy content, were welded at the end and held at 10500 C for about two weeks. Subsequent analysis showed that carbon had diffused so as to produce an inequality

Jan 1, 1949

By F. F. Poland

The purpose of this paper is to describe the recent applications and improvements made in the process and equipment for the recovery of metallic zinc from secondary metals by means of high temperature electric resistor furnace distillation. The process and high temperature furnace, as developed by Revere Copper and Brass Incorporated, Research and Development Department, was described in a previous paper. † Since the publication of that paper the process and equipment have been licensed to others. Consequently its field of application has been expanded, particularly for the treatment of scrap brass, galvanizers dross and scrap zinc. Other applications are being considered, particularly the melting of metallic titanium and special alloys requiring a controlled atmosphere. Consideration is also being given to modification in design that would allow the melting of copper cathodes for the production of oxygen-free and electrolytic tough pitch copper shapes without the necessity of blowing and poling. In the design of a furnace for melting copper cathodes it is intended that the fundamental principle of charging the solid material into a large pool of molten metal through a double door charging vestibule as shown in Fig 3 of the previous paper, † would be adhered to and, in addition, either dehydrated and desulphurized producer gas or commercial nitrogen, that is, approximately 96 pct nitrogen, 2 pct hydrogen 2 pct CO, also dehydrated, would be used to provide a protective atmosphere for the resistors and to flush out more soluble gases from the molten copper. The operation of a small unit producing approximately 1000 lb of copper per hr has shown that the commercial nitrogen will allow the production of tough pitch electrolytic copper when the metal is transferred from the meltdown unit contemplated to a special type induction unit where the oxygen absorption and temperature can be controlled. Standard practice in treating low grade scrap brass has been to oxidize the zinc by blowing air through the molten metal. This operation results in the recovery of approximately two-thirds or less of the zinc content of the brass in the form of an impure zinc oxide having only a fraction of the value of the zinc in metallic form. The balance of the zinc is lost to slag, fume and drosses. Fig 1 shows the revised flow sheet of the process for the treatment of scrap brass. For this application and as shown on the flow sheet a low frequency induction furnace has been substituted for the Wilkins-Poland type as a melting unit. This type of furnace has been found the most suitable for the purpose as will be shown by the following discussion. Serap Brass The melting of refinery scrap brass preparatory to distillation presents a melting problem quite different from the usual melting of brass mill scrap for recasting because refinery scrap is a heterogeneous mixture of alloys each having different melting and boiling points, and coated with a variety of corrosion products and foreign materials. In addition, brass and copper plated pieces of sheet iron, stainless steel, ceramic materials, and others are present that do not melt except at temperatures above the boiling point of the liquid bath. In the previous paper it is noted that difficulty was encountered in the melting of refinery grade scrap brass without excessive loss of zinc by volatilization and that 5 to 10 pct razorite flux was used to alleviate this condition. While this flux was successful in preventing the excessive loss of zinc by volatilization it interposed a low heat conductivity layer between the source of heat and liquid charge and resulted in lowering the melting rate of the furnace. This same problem presents itself in all types of furnaces in which the metal is heated by radiation and conduction from above the charge. It has been found in melting this type material that the melting rate per hour or per square foot of hearth area

Jan 1, 1950

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970

By John F. Elliott, John R. Rawling

The rate of reduction of silica to silicon by carbon at 1550° to 1700°C in iron blast-furnace type slag-metal systems has been investigated. In the tower portion of the temperature range oxygen transport in the metal boundary layer at the slag-tal interface is probably rate limiting. A second step, which apparently involves a chemical process in the slag at the slag-metal interface, appears to be rate limiting when the oxygen-transport limitation is avoided. Above 1650°C rate control of the reduction by carbon probably is mixed between the two steps. INVESTIGATIONS1.2 into the equilibrium distribution of silicon between graphite-saturated slags and metals typical of iron blast-furnace practice show that, under the experimental conditions specified, the reduction of silica to silicon is relatively slow compared with the rates of other slag-metal reactions under similar conditions. For this reason, the reduction of silica in blast-furnace slag-metal systems was considered to be an interesting subject for further study. Investigations of the kinetics of the reaction3-5 suggest that several possible steps may be rate controlling, and that the rate-controlling step depends not only on the physical state of the systems but also on the configuration of the apparatus. The main objects of the investigation reported here were to sug- gest plausible reaction paths for the reduction of silica under the experimental conditions chosen and to determine the step or steps which control the rate of reduction of silica. EXPERIMENTAL Two types of experiments involving the reduction of silica from the slag were carried out. In the first, the only reducing agent present was carbon (graphite), for which the over-all reaction is (SiO2) +2C(gr) —Si + 2Co(g) [l] The second type was a graphite-saturated ferro-silicon-iron concentration cell. In it silica in the slag could be reduced either by carbon according to Eq. [I], or by a reaction of electrochemical nature in which silicon was oxidized at the ferrosilicon-slag interface and silica was reduced at the slag-iron interface without the formation of CO. The two types of experiment are described below. Reduction of Silica with Carbon as the Only Available Reducing Agent. The reduction of silica was accomplished by allowing a liquid lime-alumina-silica slag and graphite-saturated iron to react in an induction-heated graphite crucible. The crucible was 2.25 in. diameter and 5 in. deep; it was fitted with a graphite stirrer which penetrated through the slag and into the metal, Fig. 1. The slag and metal charges weighed 350 g each. Pure carbon monoxide at a pressure of 1 atm was maintained above the melt by passing the purified gas through the crucible at a rate of 0.5 liter per min. The gas did not stir either the slag or metal. Temperature measurements were made by sighting an optical pyrometer down the hollow stirrer rod into a 1/4-in. hole drilled in the stirrer blade. The crucible temperature was maintained within *15"C of the required value by manual control of the power supply to the

Jan 1, 1965

By F. H. Wilson, E. W. Palmer

The solid solubility of iron in 2 to 10 pct cupro-nickels increases with temperature and nickel content. Property changes accompanying various heat treatments indicate typical precipitation hardening behavior. Iron content also affects softening temperature and sub-scale formation. These factors, as well as impingement corrosion resistance, influence the optimum iron content of commercial alloys. FOR many years Cu-Ni alloys have been used extensively in the form of tubes, pipes, and plates for the construction of salt-water lines and surface condensers on shipboard and in tidewater power stations. The 30 pct Ni alloy has been considered more resistant to rapidly flowing sea water than alloys of lower nickel content, and has been standard on ships of the U. S. Navy. Some ten years ago, the still better corrosion resistance obtained by modifying the 30 pct Ni alloy with approximately 0.5 pct Fe was recognized, and the iron-bearing alloy rapidly superseded the plain alloy as the standard material for severe service. In 1945, Tracy and Hungerford1 published a study of the effect of iron on the corrosion of various cupro-nickels in sea-salt solutions, and their data indicated that the 10 pct Ni alloy containing about 0.75 pct Fe was equivalent to the 30 pct Ni alloy containing 0.5 pct Fe. This was confirmed by LaQue in discussion of the above paper, and by results in an experimental condenser set up at the Kure Beach marine test station of The International Nickel Co., reported by Freeman and Tracy.' The 10 pct Ni iron-bearing alloy is now being very widely used in applications where the 30 pct Ni iron-bearing alloy was formerly considered standard. While this "substitution" has undoubtedly been stimulated by the present extreme shortage of nickel, it must be emphasized that it involves no loss of service performance, and would have occurred anyway in the course of time, for economic reasons. In view of the increasing use of the 10 pct alloy, it seems desirable to make generally available the results of several investigations of Cu-Ni-Fe alloys carried out in the Metallurgical Research Laboratory of The American Brass Co. in recent years. The present paper, deals with the constitution of these alloys in the copper-rich corner of the system, and with the variations in hardness and tensile properties resulting from the heat treatment of alloys containing various amounts of iron. Most of this work is concerned with alloys containing 10 pct Ni. With over about 0.75 pct fe, the 10 pct Ni alloy is suscep- Alloys Several series of cupro-nickel alloys containing iron were used in these investigations. Most of them were prepared in the laboratory, but two samples of commercially fabricated alloys were included. Series A—Nominally 2 and 5 pct Ni, each with 0 to 1.5 pct Fe. Series B—Nominally 10 pct Ni with 0.1 to 0.4 pct Fe. Series C—Nominally 1.0 pct Ni with 0 to 2 pct Fe. Series D—Nominally 10 pct Ni with 3 to 5 pct Fe. Series E—Nominally 10 pct Ni with 1 and 1.5 pct Fe.

Jan 1, 1953

By B. M. Larsen, K. Heindlhofer

THIS paper describes a relatively simple electrical apparatus that, through the close analogy between the flow of heat and of electricity, enables one to solve quickly and with satisfactory accuracy many complex problems in heat flow. This device, developed in 1935, has proved especially useful in the solution of certain practical problems relating to the design and efficiency of regenerators for an open-hearth furnace or coke oven, yielding within a few hours information that would take weeks or even months to acquire by mathematical1.2 or experimental3 methods of comparable accuracy. Its description now is prompted by growing interest in such analogues, as shown by several recent papers.4.5 The analogy between flow of heat and of electricity appears to have been recognized first by Maxwell who, in his famous Treatise on Electricity and Magnetism (1881) says: The analogy between the theory of the conduction of electricity and that of the conduction of heat is at first sight almost complete. If we can take two systems geometrically similar, and such that the conductivity. for heat at any part of the first is proportional to the conductivity for electricity at-the corresponding part of the second, and if we also make the temperature of any part of the first proportional to the electric potential at the corresponding point of the second, then the flow of heat across any area of the first will be proportional to the flow of electricity across the corresponding area of the second. .. Thus, in the illustration we have given, in which flow of electricity corresponds to flow of heat, the electric potential to temperature, electricity tends to flow from places of high to places of low potential, exactly as heat tends to flow from places of high to places of low. temperature He noted, however, that this analogy is restricted: ... there is, however, one remarkable difference between the phenomena of electricity and those of heat. Suspend a conducting body within a closed conducting vessel by a silk thread, and charge the vessel with electricity. The potential of the vessel and of all within it will be instantly raised, but however long and however powerfully the vessel be electrified, and whether the body within be allowed to come in contact with the vessel, or not, no signs of electrification will appear within the vessel, nor will the body within show any electrical effect when taken out. But if the vessel is raised to a high temperature, the body within will rise to the same temperature, but only after a considerable time, and if it is then taken out it will be found hot, and will remain so till it has continued to emit heat for some time. The difference between the phenomena consists in the fact that bodies are capable of absorbing and emitting heat, whereas they have no corresponding property with respect to electricity. According to this statement the application of the analogy would be limited to problems of steady flow that do not involve heat-capacity effects. In spite of this

Jan 1, 1945