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By Bert Sandell

MUCH has been said and written about the various uses of die-castings, their applications in the various industries and their advantages and disadvantages. Examination of this literature, however, fails to disclose any data concerning the effect of temperature upon any of the physical properties of die-casting alloys. The uses and applications of die castings are so numerous, and of such a varied nature, that far too lengthy a manuscript would be required to list all of them. Brief mention of some specific cases will suffice to illustrate the temperature ranges in which certain die castings function. Automobile hardware, such as hub caps, door handles, radiator caps, etc., can be used as one example. Castings of this type are constantly exposed to varying climatic conditions, temperatures ranging from below zero to upwards of 100° F. Refrigerator parts, such as ice-cube trays, etc., form another example. Approaching the other temperature extreme, we encounter conditions such as are found in kitchens in which oven-heat indicator parts, cooking utensils, waffle grids, etc., embody use of die castings, where temperatures as high as 500° F. are often met with. Because of this variation in service temperatures, it was felt necessary to ascertain the effect of these temperatures upon the physical properties of die-casting alloys. The Charpy impact test was chosen first because of its simplicity, and because of the fact that brittleness is more likely to be objectionable in die castings than hardness or other physical properties.

Jan 1, 1932

By Frederick Crabtree, A. R. Powell

When Professor Stoek asked for a paper on the above subject, it was too late to prepare by June 1, or near that time, one that would invoive any appreciable amount of experimental work or original research; but the suggestion was made that a review of the literature bearing on the subject might be submitted in good time, and that later this could be supplemented by any experimental data obtained during the summer, if experiments were carried out. In accordance with this suggestion, there are submitted the following notes on references found in the literature of recent years bearing on sulfur in gas. It is to be understood that, in general, these notes express the opinions of the authors whose papers are abstracted, not necessarily the opinions of the abstractors. Very little published information was found bearing directly on producer-gas sulfur, so this has been supplemented, in certain phases of the subject, by references to illuminating gas. Methods of analysis and processes for the elimination of sulfur from the gas are, without much doubt, very closely related in these two products. As in illuminating gas, sulfur is found in producer gas mainly as hydrogen sulfide, mixed with a much smaller and variable quantity of carbon bisu1fide.l The presence of minute quantities of other organic-sulfur compounds has been intimated, but no definite statement is made concerning these. The amount of sulfur present in producer gas is variable and depends on several conditions. The primary factor is the quantity of sulfur in the fuel, but the form in which the sulfur exists, the temperature of the producer, the air-steam ratio, and the efficiency of the scrubbing process are all determining factors. When the coal used contains less than 0.5 per cent. of sulfur, the sulfur in the gas will not exceed the quantity found in the average illuminating gas.2 Sulfur in producer gas may safely run higher than that in coke-oven gas, due to the lower-flame temperature

Jan 1, 1920

By Yang Tsang Woo

I will endeavor to describe the methods of silver-mining and smelting employed by the natives in Mongolia. Modern methods have been applied there, but with little success; and, since they are familiar to most members of the Institute, I will simply mention that the failure was due to the high price of coke used in smelting the ore in modern furnaces, and to the unsuitable mill-machinery employed for concentrating the galena, which is finely distributed in the ore. The Jehol silver-mines are situated about 45 miles NE. of Jehol, the capital of Mongolia. They embrace two mines, 5 miles apart,—the Ku Shan Tze mine and the Yen Tung Shan mine. They were first worked by natives 50 years ago, about the time when mining was so flourishing in other parts of the world,—for instance, in California and Australia. The upper part of the vein is galena mixed with iron-stone, and is 2 to 4 ft. thick. At lower levels the vein is composed of silver-lead ore running between quartz-porphyry walls. Limestone, talc and black shale, colored by graphite, are found in other parts of the mine. Crystalline limestone is found 1 mile NE. of Ku Shan Tze. Granite is encountered in the Yen Tung Shan mine. Mining.—The native method of working the mines is most primitive. The same method may have been employed a thousand years ago. A small inclined shaft, 4 ft. by 4 ft., is sunk in the vein-stuff where the appearances are most favorable. Another shaft is sunk 20 or 30 yds. away, for ventilation. The shaft follows the vein in a zigzag fashion in whatever direction the vein appears to be richest. Timber is used only in soft ground. Where the ground is hard, the roof is cut into an arch-form. In some places, instead of using ladders, steps are cut in the rock, just wide enough to hold one foot. The deepest native workings are 400 ft. below the

Jan 1, 1903

By W. P. Dyrenforth, W. E. Horst

Although, separating or concentrating minerals, based on differences in. their magnetic properties has been practiced for years1 the early industrial applications of magnetic separators were involved with the most highly magnetic materials. These early separators were used to concentrate magnetite, separate metallic iron from furnace products, and separate iron and brass turnings. Next, the addition of a pretreatment operation, such as roasting or calcining, to transform certain iron-bearing minerals into a highly magnetic compound that could readily be separated from the altered mineral mixture using existing magnetic separation machines was added to the flowscheme. As the number of magnetic-separator installations grew, steady development of better equipment evolved including the design and implementation of induced magnets having high-intensity fields, These developments of course greatly expanded the field of magnetic separation and made it possible to commercially separate or concentrate very weakly magnetic minerals which previously had been considered as nonmagnetic minerals. A number of different designs of magnetic separators were well developed and the unit operation of magnetic separation was gaining wide acceptance in mineral processing operations when two events occurred that dampened these developments. First, the Mesabi iron range with its direct-shipping iron ore was discovered and placed into operation. This of course significantly reduced the need for magnetic separation to meet the raw material requirements of the iron and steel industry. Second, the advent of selective froth flotation, was so successful in solving many mineral process problems that electrical concentration techniques being developed at that time, including magnetic-separation methods, were either terminated or received low priority ratings. During the past two decades interest has been renewed in the use of electrical concentration methods to solve mineral separation problems. As the direct-shipping iron ore reserves are depleted more emphasis has been placed on magnetic upgrading of lower value iron ore available throughout the world. In addition, magnetic separation techniques have found numerous applications in the non-metallic and industrial minerals industry to supplement froth flotation and thus add to the variety of beneficiation methods available.

Jan 1, 1971

A three day international mining convention was held At the city hall of Nelson, B. C., June 19-21. It was held under the auspices of the Nelson-Slocan and British Columbia Mining Men's Club, the Northwest Mining Association of Spokane, the Kootenay Mine Owners' Association, assisted by the Spokane Chamber of Commerce, the Vancouver, Chamber of Mines, the City of Nelson, the Associated Boards of Trade of Eastern British Columbia and the Nelson Board of Trade. The technical program was in charge of Columbia Section, American Institute of Mining and Metallurgical Engineers and Western Branch and Kootenay-Boundary Branch, The Canadian Mining Institute. The first day was given over to the judging of mining exhibits and manufacturer's displays; the organization of a branch of the Canadian Mining Institute, and the reception of visitors from Spokane. On Friday afternoon a joint session of the Canadian Mining Institute and the American Institute of Mining and Metallurgical Engineers was held.

Jan 8, 1919

By T. S. Lundy

Anand and Agarwala recently determined diffusion coefficients by the residual activity (Gruzin) method for several tracers in large-grained, high-purity aluminum. D values at any particular temperature in the range of 400" to 630°C were about four orders of magnitude lower for cd115, 1n114, sn113, and pdlm than for Ag. Corresponding values for Do and Q in the Arrhenius equation were also quite small. It was pointed out previously that unusually low diffusion coefficients within the region of a specimen near a free surface may be the major cause of such anomalous results for impurity diffusion in silver and in aluminum.44 Anand and Agarwala considered this possibility but rejected it because their penetration profiles were "homogeneous" and "yielded diffusion coefficients obeying the Arrhenius plot". Neither of these two criteria satisfactorily prove or disprove the presence of a near-surface effect. Such can be accomplished only by direct serial sectioning in which the chips ground from the specimen are assayed for tracer content. In fact, such experiments always should be done prior to use of the somewhat indirect Gruzin method where the finer details of the transport process cannot be determined. There have been several other reports of unusually low D, Do, and Q values for impurity diffusion in silver and aluminum.1"4 It is interesting to note that all of these studies made use of the Gruzin method. Also, in all cases where the same systems were examined by use of a direct serial sectioning technique, large near-surface effects were observed. One must conclude therefore that the reported anomalous diffusion parameters for cd, In114, sn113, and pd in aluminum are due to some near-surface effect, while the results for Agl10 indicate that no such effect was encountered for this system.

Jan 1, 1969

A FEW nights ago while working in the small hours of the morning on a clarion message intended for this page, we repaired to the kitchen for coffee, as is our wont when the solitude of the late hour and the stillness of the night seduce thoughts from the job at hand to reminiscences. The thought occurred, as we slowly dissolved the instant coffee in boiling water, that this modern world of canned, frozen, and dried foods deprives us of some of the subtler and therefore more delightful pleasures of life. We recall the aroma of boiling coffee which greeted us on getting up in the morning before the ease of instant coffee deprived us of the aroma from the old coffees. This line of thinking led us to place the blame on our wife for taking the easy way of making coffee and thereby depriving us of some of our enjoyment. From thinking about our spouse, it is only a short step to thinking about "the boss" or bosses in general.

Jan 9, 1951

STANDING COMMITTEES Executive CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership BENJAMIN B. THAYER, Chairman. KARL EILERS, JOHN H. JANEWAY, Jr., JOHN D. IRVING, HERMAN A. PROSSER. Finance EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library JAMES F. KEMP, Chairman.1 JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALEX. C. HUMPHREYS,4 BRADLEY STOUGHTON.

Jan 1, 1914

By L. G. Laureau

This paper is presented to call the attention of steel-manufacturers to the need of further reform in the manner of casting and handling ingots. The problem of making the work usually performed in and around the casting-pit less dangerous to the men and less costly to the management is one which has occupied the minds

Jan 1, 1885

By G. P. Tiwari

Recrystallization and grain growth in thoria dispersed nickel and nichrome were recently studied by Webster as a function of temperature and deformation. The unexpected part of these results was that specimens which had received heavier deformation developed greater resistance to recrystallization. Retardation of recrystallization was accompanied by the formation of voids around thoria dispersion. To explain these results, Webster suggested that the formation of void around the particles increased the effective size of thoria particles. This resulted in greater impediment to the grain-boundary migration and as a consequence the recrystallization of the matrix is retarded. In the present note an alternative and more probable explanation for the effect of voids on recrystallization is presented. The exact mechanism of void formation in thoria dispersed nickel or nichrome is not known. However, it is reasonably certain that it must be preceded by the stress concentration in the matrix around thoria dispersion during the deformation.'' The resulting stress concentration must be sufficient enough to supply the surface energy for the new surfaces created. Further, the decrease in the strain energy of the matrix surrounding the potential void nucleus must be larger than the surface energy of the newly created surface. The release of strain energy due to formation of crack results in a strain free cylinder of the material around the voids.13 If the void formation is not localized, at few points only (as is the case here), this process may lead to considerable amount of release of strain energy of the matrix. The pattern of recrystallization behavior of single phase homogeneous matrix as well as the matrix having a second phase dispersion is same except for the fact recovery and recrystallization are more clearly delineated.14 In general, the recrystallization temperature is lowered (i.e., recrystallization is easier) with increase in the amount of cold work. This is due to the increase in stored energy in the matrix with increasing amount of deformation. If somehow there is a relaxation of strain energy in the matrix, the recrystallization should become difficult because of the decrease in the amount of stored energy available for recrystallization. Since the formation of voids leads to a decrease in the strain energy of matrix, the recrystallization of the matrix would be inhibited due to the formation of voids during deformation prior to recrystallization. It has been observed by earlier workers15'16 that the presence of preexisting voids in a matrix retards the recrystallization. The essential issue here is how do the voids act to produce this effect. If the voids influence recrystallization only by blocking the grain boundary migration, then the effect should be maximum when they are present almost exclusively along grain boundary. These conditions are obtained during high temperature deformation. However, the voids produced due to creep along grain boundary are not able to prevent recrystallization17 suggesting that they are not effective in blocking grain boundary movement. Recently it was shown by Davies and Williams that the voids can act as sinks for vacancies." As a result the processes dependent on vacancy diffusion like recovery, recrystallization, dislocation climb, and so forth, will be hindered. This fact may be responsible for inhibition of recrystallization during subsequent deformation and annealing cycles. It is to be noted here that there is a large difference between the density of voids in creep experiments and the other experiments where retarding effect of voids on recrystallization is seen. The voids in former may number up to l04 to l05 per sq cm whereas in latter cases the voids density is typically around 1010 to 1013 per sq cm. It appears that the decrease in supply of vacancies in creep is insufficient to adversely affect the recrystallization due to low void population. The author is grateful to P. Das Gupta and S. P. Ray for helpful discussions. Author's Reply D. Webster Tiwari appears to have misunderstood the nature of grain boundary-particle interactions. Tiwari (quoting Cahn) states that second phase particles become more effective as they become smaller, therefore as the voids in TDNiC make the thoria particles effectively bigger their ability to resist grain boundary movement is impaired. This particle size argument was originally proposed in the form of an equation by Zener 20 years agol9 and is not necessarily valid as is discussed below. However, assuming it is valid, it predicts a greater boundary restraining effect by smaller particles simply because their combined cross sectional area is greater at a constant volume. If the number of particles remains the same and their effective size increases, as in the present case, Zener's equation predicts a greatly reduced grain size. This is because the effect

Jan 1, 1970

By T. M. Morris, W. E. Horst

W. E. Horst—In regard to the flotation rate being described as "first orcler" for flotation of quartz particles below 65 p in size (or any size studied in this work) in this paper, it appears that the authors' conception of rate equations is not in agreement with cited references. A first order rate equation has as one of its forms the following: a In.=a/a-x=kt where a = initial concentration, a—x = concentration at time t, t = time, and k = constant. The constant, k, has the dimension of reciprocal time which is similar to the specific flotation rate, Q. described by Eq. 2 in the authors' article, as has been previously discussed by Schumann (Ref. 1 of original article). The plotted data presented in Fig. 4 of the article utilizes the specific flotation rate, Q (min.'); however, there is not adequate data given to indicate the order of the rate equation which describes the flotation behavior of the quartz system studied. Results from the experimental work indicate that the relationship between rate of flotation (grams per minute) and cell concentration (provided the percent solids in the flotation cell is less than 5.2 pct and the particle size is less than 65 p) is described by an equation of the first order (R, = k c+", n being equal to 1 in this size range) and the use of the first order rate equation does not apply. Similarly the relationship for other particle size ranges studied is expressed by equations of the second or third order depending on the magnitude of n. T. M. Morris—The authors are to be commended for the experiments which they performed. As they state in their discussion the concentration of collector ion In solution did change with change in concentration of solids in the flotation cell. Since for a given slze of particle, flotation rate increases with concentration of collector until a maximum is reached, the effect of concentration of particles in their experiments was to vary the concentration of collector ions. A collector concentration which insures maximum supporting angle for all particles eliminates the unequal effect of collector concentration on various sized particles and the effect of size of particles and concentration of particles upon flotation rate could be more clearly assessed. I believe that if the authors had increased the concentration of collector to an amount sufficient to attain a maximum supporting angle for all particles they would find that the specific flotation rate of particles coarser than 65 p would be constant with change in the concentration of solids in the flotation cell, and that a first order rate would apply to the + 65 as well as to the —65 p sizes. It might also be discovered when this change in collector concentration was made that the maximum specific rate constant would be shifted toward a coarser fraction than when starvation quantities of collector are used since this practice favors the fine particles and penalizes the coarse particles. P. L. de Bruyn and H. J. Modi (authors' reply)—The authors wish to thank Professor Morris for his kind remarks and for mentioning the influence of equilibrium collector concentration on flotation rate. With a collector concentration sufficient to insure maximum supporting angle for all particles, a first order rate equation may indeed be found to be generally applicable irrespective of size. Such a concentration would, however, lead to 100 pct recovery of the fine particles and consequently defeat the essential objective of the investigation to derive the maximum information on flotation kinetics. To establish absolutely the validity of any single rate equation for a given size range, the ideal method would be to work with a feed consisting solely of particles of that size range. Use of such a closely sized feed would also eliminate the possibility of the interfering effect of different sizes upon one another. The authors do not believe that increasing the collector concentration would shift the maximum specific flotation rate (Q) towards a coarser fraction. Experimentation showed Q to be independent of solids concentration for all particles up to 65 µ in size, whereas the maximum value of Q was obtained in the range 37 to 10 p. Professor Morris contends that the addition of starvation quantities of collector favors fine particles at the expense of coarse particles, but the reason for this is not entirely clear to the authors. The comments by Mr. W. E. Horst are concerned only with the concept of the term "first order rate equation." According to the usage of this term in chemical kinetics, time is an important variable, as is shown in the equation quoted by Mr. Horst. All the experimental results reported by the authors were obtained under steady state continuous operations when the rate of flotation is independent of time. To be consistent with the common usage of the "first order rate equation," it would be more satisfactory to state that under certain conditions the experimental results show that the relation between flotation rate and pulp density is an equation of the first order.

Jan 1, 1957

Jan 1, 1909

By B. E. Thompson, H. B. Fuqua

For a very brief description of the North Texas area, and the general geological features with which it is associated, the reader is referred to the opening paragraph of last year's summary1. A more complete discussion of the structure of the area, together with other interesting data concerning it, has been published recently by the Bureau of Economic Geology at the University of Texas2. It has been impossible for the authors to isolate the statistics for production for each of the many small pools of this district, as such statistics are not kept by operators except by counties or arbitrary divisions of counties. The total number of wells drilled in Archer, Wichita and Clay counties also has been subject to some estimate, as many of the shallower holes are not reported. While both routine development in proven or semiproven areas and exploratory drilling during 1935 showed an increase over the year 1934, the discovery of new producing areas of importance did not show improvement over that period. Several extremely local productive spots within semiproven areas were found in Archer, Cooke and Wilbarger counties; and extensions to older producing areas were developed in Archer, Baylor, Cooke, Montague, Wichita and Wilbarger counties. In Archer County, the Grace and Woods No. 1 Archer County (Fee), 4 miles northwest of Archer City, in the Thomas Glass survey, encountered a sand from 2836 to 2845 ft. of Pennsylvanian (lower Canyon) age, which showed an initial yield of 75 bbl. daily. While its production is of negligible importance, it is given special mention in this review because of the fact that it is producing from a new and deeper horizon than has been previously exploited in the county. Little deep development occurred in the district during the year. The Walter Gant No. 2 C. M. Worsham in J. M. Swisher survey, about 14 miles east of Henrietta, in Clay County, was abandoned at 5127 ft. in

Jan 1, 1936

T. T. READ, Secretary of the Committee on Industrial Organization, presents the following very interesting monthly ad interim report: Reports from London are to the effect that 750 housing schemes for workers, involving the erection of 128,000 new dwellings, have been submitted to the Local Government Board. Birmingham alone needs 14,000 new houses, and the Housing and Town Planning Committee of the City Council considers that 5000 new houses must be built each year for the next 20 years. Nine hundred acres of land has been acquired, on which to build 10 to 12 houses per acre for the next two years. The town of Dudley, which built 300 modern dwellings in 1915-1916, submitted schemes for another 500 houses. There is a shortage of building materials required, specially brick. Financial assistance has been received for reopening brick yards that were closed during the war. W. E. Dickson, vice president of the Midvale Steel & Ordnance Co., is reported in the daily press as stating that his corporation is planning to spend $8,000,000 in improving its plant and assisting its employees in building their own homes. The company will advance 90 per cent. of the cost of the house and extend payments over a period of 12 years. Methods of work employed in building 256 houses at Quincy, Mass., for the workers of the Fore River shipyards are described, by Joseph Meltzer, in the Engineering News Record for May 29, 1919. The approximate cost was about $3500 per house, not including water supply, sewers, streets, and sidewalks. "Comparative Costs of Tenantry and Home-Owning;" "A Plain Talk on Helping Home-builders;" and "More Plain Talk on Home Building" are the titles of three publications of the Information and Education Service of the Department of Labor. These publications should be' of a good deal of service in convincing employees that it is to their interest to own their homes rather than to live in rented houses. The same Service has issued pamphlets discussing the cost of materials.

Jan 7, 1919

By H. B. Fuqua, B. E. Thompson

For a very brief description of the North Texas area, and the general geological features with which it is associated, the reader is referred to the opening paragraph of last year's summary1. A more complete discussion of the structure of the area, together with other interesting data concerning it, has been published recently by the Bureau of Economic Geology at the University of Texas2. It has been impossible for the authors to isolate the statistics for production for each of the many small pools of this district, as such statistics are not kept by operators except by counties or arbitrary divisions of counties. The total number of wells drilled in Archer, Wichita and Clay counties also has been subject to some estimate, as many of the shallower holes are not reported. While both routine development in proven or semiproven areas and exploratory drilling during 1935 showed an increase over the year 1934, the discovery of new producing areas of importance did not show improvement over that period. Several extremely local productive spots within semiproven areas were found in Archer, Cooke and Wilbarger counties; and extensions to older producing areas were developed in Archer, Baylor, Cooke, Montague, Wichita and Wilbarger counties. In Archer County, the Grace and Woods No. 1 Archer County (Fee), 4 miles northwest of Archer City, in the Thomas Glass survey, encountered a sand from 2836 to 2845 ft. of Pennsylvanian (lower Canyon) age, which showed an initial yield of 75 bbl. daily. While its production is of negligible importance, it is given special mention in this review because of the fact that it is producing from a new and deeper horizon than has been previously exploited in the county. Little deep development occurred in the district during the year. The Walter Gant No. 2 C. M. Worsham in J. M. Swisher survey, about 14 miles east of Henrietta, in Clay County, was abandoned at 5127 ft. in

Jan 1, 1936

By Knut Conradsen

In the study 208 heavy mineral concentrates (pan samples) from Jameson Land, East Greenland, are considered. Each concentrate has been analysed (by spectroscopy) for the content of (approx.) 25 elements. Furthermore the exact sampling position and the geological characteristics of the environment have been registered. In the study is shown how different multivariate methods combined with geological knowledge of the area can be used in the interpretation and classification of the data. Special emphasis is put on the problem of finding reliable expressions for the background level of the element concentrations in the area. This is done by means of severel discrimination procedures. The other main subject is a demonstration of the applicability of isoscore maps - originating from factor analyses - in the evaluation of the co-variability of the data, and thus give another way of classifying the individual samples according to the content of different elements.

Jan 1, 1977

By J. P. Hammond, C. J. McHargue, J. R. Holland

IT has been reported that both berylliumL and zirconium&apos; developed the same basic textures during rolling at temperatures up to 1475 °F as at room temperature, differing only by an increase in the spread of basal planes toward the transverse direction as the temperature of deformation was increased. Iodide titanium&apos;&apos; rolled at 1050°F has a texture similar to the cold-rolled texture, {000l}, 25° to 30" from the rolling plane toward the transverse direction, <1010>, Rolling iodide titanium at 1450°F produced a more random condition with the basal planes parallel to the rolling plane and no direction strongly aligned with the rolling direction.

Jan 1, 1957

By A. W. Ashbrook

The constraints which are being imposed on metallurgical operations in respect to the environment and worker hygiene are having a substantial influence on the various processes which are being studied and developed for future use. The unit process of solvent extraction can be no exception. It is therefore vital that sufficient be known about the effects of a solvent extraction process in terms of its environmental and hygiene impacts before the process gets to the construct- ion stage. The purpose of this section is to bring these matters to the readers&apos; attention, and to indicate, albeit briefly, some of the problems, and what we know about the effects, of SX processes from an ecological point of view. Hydrocarbons Petroleum hydrocarbons are bio-degraded to form C02; several factors may limit the rate of bio-degradation, which are as follows:

Jan 1, 1978

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,&apos; and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,&apos; and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946