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By C. G. Dunn

Identification of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereo-graphic projection with one pole per orientation.' However, accurate data based on calculations of the positions of all {1001 planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. Method of Computing Orientation OF a Twin It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given in terms of two angle variables, two sets of which appear in the following equations: Polar Net Wulff Net x = , sin ?p cos Fbp x = r COS ?w y = r sin ?p sin Fp y = r sin ?w cos Fw % = r cos ?p z = r sin ?w, sin +, The three numbers z, y and z determine a length r as well as a direction (0, 4) in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 + L2)1/2, where h, k and I are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {Ioo} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3,4' Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A' being one of the four {112} or {III} type* first-order twills of S. The orientation of S—i.e., the positions of poles of (I00)

Jan 1, 1945

By H. J. Maguire

(Presented by invitation at a meeting of the Spokane Local Section, Feb. 17, 1912.) THOSE familiar with mill-practice understand the work required of an average bucket-elevator, but I wish to call special attention to the wear on the buckets. I have been studying in what manner the life and service of the bucket might be improved, and I feel that an adjustable lip, attachable to each bucket without the aid of rivets, will be of material advantage. For illustration, consider the feed-elevator of a typical mill in the Cur d'Alène district. The ore is carried by water in a launder from the feed-rolls and dumped in the "boot" of the elevator, directly in front of the ascending bucket. Middlings from the return-rolls are similarly handled. Under this condition the bucket not only carries the ore, but also picks it up, and this latter requirement determines the life and service of the bucket. It might be said that it would be better practice to convey the feed to the elevator and dump it directly into the bucket, but at one mill at which this plan was tried the results were disappointing and the rubber belt was badly worn. The wear of the bucket is confined to the lip and the corners which have to pick up the material. When the lip on a corner of a 7- by 12-in. malleable cast-iron bucket is worn down about 3 in., the bucket is of no further value as a carrier and has to be replaced. The worn bucket, containing about three¬quarters by weight of the metal of the original bucket, has a scrap value of about 10 per cent. of that of a new bucket. To the cost of the bucket, however, should be added the time-cost of replacing the old bucket by a new one. This time-cost is considerable when the loss per hour, to cease operating the mill, is about $200. It is out of the question to put lips on a bucket unless the latter was originally fitted with this device. For if it is attempted to fit lips upon buckets not originally provided with

Sep 1, 1912

ROBERT PEELE, * New York, N. Y.-I should like to ask Mr. Neale how the members of the production committees at the individual mines, who came from the mine workers themselves, were chosen or appointed; also from what classes of employees they usually came? J. B. NEALE.-In the union fields, they were chosen by a local. In the non-union fields, they were chosen either by the men in mass meeting or by the company officials. The last way was very unsatisfactory because it gave the men an opportunity to say that they were going to be passed upon as to whether they were slackers or not, by men chosen by the company. When they were chosen by the locals or at mass meetings of the workers, the appointments have been very much more satisfactory. R. D. HALL, ? New York, N. Y.-The matter of inefficiency on the part of the operator is one that I think we may well take into account, because there is a very large inefficiency on the part of the coal operator; it has arisen from reasons almost beyond his control and will continue for these same reasons. It is no use arguing a moral responsibility on the part of the operator, when you make efficiency very largely a loss to the operator who puts it in force. If you ask a man working on a clay wage to work with more efficiency. he says, "Well, I may do it or I may not," it all depends how he feels, but he does not lose anything financially by not working hard. If you ask the man who is working by the ton to put out more tons, he makes a profit by putting out more tons. How is it with the operator? If he gives a man all the cars he needs and all the power he needs, if he runs after his working men and waits on them, he does not get his coal out any cheaper than before.. He gives the man a better chance and there is more efficiency, but at the same time he has increased his expenses all along the line. At the end of the year he finds that his profits have been less than if he had had less efficiency. The efficiency is really against him in many ways. Because he gets a larger tonnage, he reduces the overhead to a certain extent; but hiss tonnage may not be any greater because he may work fewer days. As Mr. Taylor remarked some tine ago, supposing he puts in a machine that is very much more effective than any he had before, he has the same scale; the miner gets out more coal, but he himself does not get any benefit out of it because he has a scale fixed, so much per ton.

Jan 4, 1919

By AIME AIME

APOCRYPHAL, no doubt, but widely entertained is the proposition that top-flight mining geologists never agree with each other on anything. Being rugged individualists, they frequently seem intolerant of opinions that conflict with their own. However, one may suspect that controversy is often more apparent than real. For example, at last summer's meeting of the American Mining Congress, Ira B. Joralemon and Reno H. Sales, discussing "Mining Geology, Today and Tomorrow," seemed to be in serious disagreement over various phases of the subject; but much of this arises from the different angles of approach of the two distinguished and successful ore finders.

Jan 1, 1941

By John D. Weibmer

A strong step towards acknowledgement of mining as a skilled trade has been taken by the Tintic Division of Kennecott Copper Corp. In May 2 ceremonies, a pilot program was signed into force which, possibly for the first time in US history, recognizes mining as an apprentice trade and grants journeyman status to those who complete the prescribed training sequence. The apprenticeship standards, hammered out after months of consultation between management, labor, and government, are presently limited only to underground hard-rock mining and only within Kennecott's Tintic Division, but the architects of the program are confident that the concept will spread-first to other underground operations where miners desire documented evidence of their special skills, then to open-pit and soft-rock operations.

Jan 6, 1977

By Charles Becker

THE practice of drying phosphate in Florida is as old as the industry, which began a little more than half a century ago. The methods, however, have changed considerably. At first, the natural process of exposure to the sun and air was used, later supplemented by wood fires beneath open-air stationary dry kilns and drying towers of various designs. It was not until the early nineties that rotary driers came into use, and at first they were of very small design and fired with wood. As the industry grew and tonnage increased, so likewise grew the number and size of rotary driers, until today the largest installations are 6 ft. up to 7 ft. 6 in. in diameter, and 55 to 60 ft. long, fired with crude oil. The reasons for drying phosphate rock are: (1) to eliminate freight on water in the shipment and (2) to facilitate the good grinding qualities required by the buyers in their acidulation. Phosphate pebbles vary materially in natural characteristics and each property has a direct bearing on the processing. In making comparisons of cost and operating conditions, the following are usually taken into consideration: 1. The hard dense pebbles, which contain very little interior moisture and 6 to 8 per cent total moisture, usually produced from the low-grade deposits. 2. The lighter, porous pebbles, which contain 4 to 5 per cent interior moisture and a total moisture ranging from 9 to 15 per cent. 3. The product of recovery operations using oily reagents, containing from 15 to 25 per cent moisture. 4. The size of the pebbles. Usually the plus 5-mesh material is considered as "coarse rock"; the minus 5-mesh plus 24-mesh is "fine rock," and the minute particles below 24 mesh are called "concentrate." 5. The amount of moisture allowed in the dried product. The practice is generally to dry down to 1.5 to 2 per cent moisture. There is, however, an actual range in guarantee of from 1 per cent maximum to 3 per cent maximum.

Jan 1, 1936

By W. J. Sharwood

The assay or estimation of the total gold content of an ore presents little difficulty, when circumstances permit of securing a thoroughly representative sample. The general practice has been fairly standardized, and such errors as occur in the results obtained are for the most part attributable to the methods of sampling rather than to those of assaying, while duplicate assays made by skilled workers usually agree closely. When it is a question of estimating the "free" or amalgamable gold of an ore, as opposed to the total gold, there is but little uniformity in the methods employed by different workers, and often equally little in the results obtained when duplicate determinations are attempted, no satisfactory standard method having been generally adopted. The methods in use are of two general types—"panning" and "amalgamation." Panning For the estimation of the value of the visible gold by panning or washing, a weighed sample may be taken, ranging from an ounce to several pounds; a kilogram or 2 lb. is a favorite quantity for laboratory tests, while a prospector often uses a full miners' pan, say nearly 20 lb. or 10 kg. In the case of rich quartz, ground to about 30 or 40 mesh, a Mexican horn is convenient, using 1 to 8 02;. of material, and a 6-in. frying pan is favored by many prospectors in dry districts. Bateas, plaques, and dishes of various patterns are used for the same purpose. With these, fairly close results may be obtained by using for ocular comparison standards consisting of weighed amounts of gold of similar character as regards purity, fineness of division, and the general shape of the particles, which standards are preferably obtained from gold of the same locality, or the same deposit, as the ore or gravel being tested. Men working in one particular district sometimes become surprisingly expert in thus judging the value of an ore by the eye, the weights of both ore and gold being guessed. On the other hand, many have been led to overestimate the value of ore and gravel from unfamiliar localities, where the gold has been very finely divided or of unusually high silver content, and a novice may

Jan 1, 1916

THE 143d* meeting of the American Institute of Mining and Metallurgical Engineers was held in New York, Feb. 19-22, 1934. It consisted of the annual business meeting, 45 technical sessions at which 217 papers were presented (more than ever before), two sessions of the Board of Directors, two meetings of Section delegates, three formal lectures, luncheon Monday, Tuesday and Wednesday for members and guests, three group dinners and five group luncheons, eight committee meetings, the annual reception and dinner dance, an informal dance, a smoke-dinner and the annual meeting of the Woman's Auxiliary. Attendance showed an improvement over the previous year, as follows: Total, 1534 in 1934, and 1475 in 1933; dinner dance, 543 and 426; smoker-dinner, 425 and 394; informal dance, 295 and 250; women's registration, 160 and 133; luncheons, 1034 and 734. The Coal Division held a general session and three sessions on Coal classification. It also met jointly with the Committee on Ground Movement and Subsidence. At the general session, John B. Dilworth presented a report of the Committtee on Methods of Valuing Coal Proper- ties and R. H. Sweetser a report of the Committee on Evaluation of Coal for Blast-furnace Coke. C. B Huntress, Executive Secretary of the National Coal Association, was the principal speaker at a luncheon on Monday, at which Eli T. Conner, Chairman of the Division, presided H. N. Eavenson, newly elected President of the Institute, and Edward W Parker, Secretary-Treasurer, of the Anthracite Institute, also spoke. The Executive Committee of the Division met Tuesday afternoon. The Sectional Committee on Classification of Coal met on Thursday morning and the Technical Committees on Scientific and Use Classification of Coal on Thursday afternoon. The Committee on Mining Methods held two general sessions, one for presentation of a half-dozen interesting papers on strictly mining subjects, the other on Aerial Transportation. It also participated jointly in a session on ground movement and subsidence with the committee of that name and the Coal Division The Institute's Standing Committee on Aviation had its inception at the session on Aerial Transportation

Jan 1, 1935

By Thomas S. Carnahan

The mining property of the Utah Copper Co. is situated in the West Mountain mining district, Salt Lake County;Utah, in the Oquirrh Range of mountains. Geology In a general way the rock formation of the district consists of a series of beds of quartzite and limestone intruded by a body of monzonite porphyry roughly elliptical in shape, with an east-west axis over a mile in length and a north-south axis of about 3,000 ft. This porphyry intrusion, accompanied by strong mineralizing action and fracturing, resulted in the formation of orebodies in the adjacent sedimentary rocks, and was itself sufficiently mineralized to make it one vast orebody. The Utah Copper Co.'s mining property comprises within its boundaries practically the entire outcrop of the monzonite mass, of a commercial grade. Genesis of Porphyry Ore Following an intricate system of fracturing, mineral solutions circulated freely through the porphyry, depositing small quantities of copper and iron, and resulting in a considerable silicification of the monzonite. The quantity of copper originally deposited was undoubtedly too small to have ever given the porphyry a commercial value, had not secondary enrichment, due to the leaching of the copper from the surface of the mass and re-deposition in the sulphide zone, been active over a long period of years. A large portion of the leached material has probably been removed by erosion, but there still remains a blanket of leached and oxidized porphyry of varying thickness covering the sulphide ore, known as capping. Over certain sections of the orebody, this capping contains commercial quantities of copper carbonates, but most of it contains little or no copper.

Jan 1, 1916

By J. Federico Price, Joseph E. Aparicio

This paper describes the production of a specific iron oxide pellet that has given very good and consistent results as feedstock for HYC-Process Direct Reduction Plants. The sponge iron originated from these pellets has been used for the economic production of almost 15 Mt of low carbon steel via electric arc furnace meltshops. An overview of mining, beneficiation, pelletizing, direct reduction and steelmaking for this case is given with emphasis on the charactertitics of the self-fluxing oxide pellets.

Jan 1, 1982

By A. D. S. Gillies

One of the most difficult places to ventilate in any mine is the working face area. With an everchanging configuration, continual modification and extension to the ventilation system is necessary to maintain an adequate supply of fresh air and to avoid mixing and recirculation in the face area. In coal mines, methane emissions and high dust levels as coal is broken and removed from the face area can produce unhealthy and dangerous conditions if ventilation is not adequately monitored.

Jan 1, 1982

By Persifor Frazer

The rocks which cover the east flank of the South Mountain are chloritic schists typical in character. A specimen of this rock from near the Bechtel shaft, Hamilton Ban Township, Adams County, Pa., was selected and analyzed in my laboratory by Mr. C. Hanford Henderson, with the following results: Ignition,........2.740 CaO,..........7.040 SiO,,..........41.280 MgO,.......... 7.486 AI,O,,.........18.480 K,O,..........2.208 Fe,Os,.........9.440 Na,O,.........3.523 FeO,......... 8.200 100. As one penetrates the range by moving westvard, these schists are replaced either by epidotie quartz or by orthofelsite. In the former case, a belt of copper-bearing rock is traversed, but not in the latter case. Inasmuch as this junction of the chloritic schists on the southeast and orthofelsite on the northwest, separated by the epidotic quartz, is several times repeated, we find two or three copper belts arranged in general parallelism to the axis of the chain, because the copper horizon is generally at this junction. Thus, in going west from Fairfield, after entering the low spurs on the South Mountain, one is fairly within the chlorite measures. At the " Virginia Mills " a chlorite schist comes in with a dip of S. 1.5 E.-74 Half a mile up Middle Creek, large numbers of fragments of chlorite schist, decoruposed epidotic matter, and quartz are encountered. The former rock, where in place, dips E. 40" S.-57o. About 4000 feet west of the intersection of this road with the so-called Tape-Worm Railroad, near the house of one Singly, large masses of chloritie schist are found loose on the road. A hundred yards farther west, near a triangle in the road, the latter is less in quantity and much epidotic quartz appears, after which a very large display of orthofelsite succeeds on the left bank of Middle Creek. All these last-mentioned rocks, however, are in fragments. Crossing the stream again a few hundred yards farther On, the chlorite fragments at first preponderate, and then large numbers of both rocks

Jan 1, 1884

By GERALD A. WARING

ALASKA'S coal consumption is now about 130,000 tons annually. About one-quarter of this amount is used in the southeastern part of the territory and in settlements on the western coast and comes from Seattle and from British Columbia mines. About 60,000 tons is sub-bituminous coal from the Healy River mine in central Alaska, and is used mainly at Fairbanks, sixty miles to the north, for heating and the development of electric energy, for the city and the gold-dredging operations of the Fairbanks Exploration Co. The remaining 40,000 or 50,000 tons is bituminous coal from Matanuska Valley, in the south-central part of the territory. These coal deposits extend intermittently for about forty miles along the valley, which trends eastward from the upper end of Cook Inlet.

Jan 1, 1934

By Milton Williams

IT is generally recognized that fluid is lost from rotary drilling mud s to permeable strata during normal drilling operations;1,2,3 but that this fluid is the filtrate from the mud, rather than the mud itself, has been shown by various workers.1,4,5 . The presence of this filtrate in oil-bearing or gas-bearing strata is undesirable and harmful. The decreased permeability of the stratum to oil effected by the presence of water has been pointed out by several investigators,6,7 and since, in the production of the reservoir fluid, the greatest pressure drop occurs immediately adjacent to the borehole, it follows that infiltered water is particularly objectionable in this region. Again, this filtrate tends to make electrical logs less reliable, since oil in the proximity of the borehole is probably flushed out to an appreciable ent by the water.8 Observation of side wall cores may be misleading for the same reason. Drill-stem tests in low-pressure areas may be of doubtful value where no oil is recovered, unless sufficient time is allowed for production of water lost from the mud. The infiltered water may hinder drilling operations by softening shales and causing sloughing; the "tight hole" occasioned by excessive deposition of filter cake in the hole is a common occurrence. The filter cake remaining on the face of the producing formation may itself sometimes be detrimental to production.9 In view of these implications of the importance of filtration of mud, an investigation was undertaken to determine the factors involved in the infiltration process, and to correlate these in such a manner that the values obtained in routine filter tests employing a conventional filter of the "wall-building tester" type,10 together with data on size of hole, drill pipe, and rate of mud circulation, could be used to estimate water loss and distance of penetration of the filtrate into strata.

Jan 1, 1939

WHEN pouring concrete it frequently happens that space prohibits the placing of a mixer at the point, or points, where the concrete is to be used. Usually in such cases recourse is had to some form of pressure chamber, or concrete gun, to blow the mix by compressed air from the mixer to the point of pouring. Recently such a case arose at one of the western mines. The experience obtained there may be of benefit to others, not expert in the means of transporting mixed concrete, when they run up against similar situations. The first stage in pouring in this instance was a vertical drop of 100 ft. from the mixer on one level to the point where horizontal travel began on a lower level. Standard 6-in. pipe with flange joints was used, hung in the shaft space available. A standard 45" bend near the bottom directed the mix, with free discharge, into an air chamber for the horizontal stage of travel. With an air chamber at the mixer and pressure applied to the falling mix in the vertical section, jamming frequently occurred at the turn and the pipe would have to be taken apart for freeing. To obviate this difficulty the mix was poured slowly without the addition of air pressure, when it was found that the mix got through much better.

Jan 1, 1929

By Allen D. Gorrison

EFFORT to develop fundamental quantitative information and improved technique in the production of petroleum has long been faced with difficulties of a particularly evasive nature, owing to a combination of circumstances. In the first place, petroleum comes from far below the ground, out of sight, so that information derived from indirect observations must be extrapolated to reservoir conditions. If one does not force the analogy too far, the petroleum engineer may be said to be somewhat in the position of the astronomer. The actual phenomena which he wishes to observe in detail appear at a place so deep in the earth?s crust that personal observations and direct experiments are impossible.

Jan 1, 1942

By O. M. Schaus

GRATIFYING progress continues towards the elimination of the hazards confronting health and safety in and about mines. Employers and employees are diligently co-operating. One of the outstanding movements towards this end is the National Safety Competition conducted by the U. S. Bureau of Mines. William W. Adams, of the Bureau, has stated that "Through 1936 there has passed by a dozen years of this National Safety Competition, as it started in 1925 with an enrollment of 210 mines and quarries in 28 states and 68 million man-hours of employment. For 1936 it covered 328 mines and quar-

Jan 1, 1938

By John Birkinbine

Much has been contributed to the Transactions of the Institute concerning the construction and operation of American blast-furnares ; but the following compilation is offered as possibly furnishing additional information upon the general features, dimensions, locations, capacities, etc., of the blast-furnaces of the United States; while, incidentally, the ores upon which they rely are noted in a general way. The paper is presented chiefly as a compilation, and the figures given are selections from most reliable sources, or averages calculated from official statistics, placed for convenient reference, with a view of assisting those who consult the Transactions in determining the present relative merits and importance of various sections of the country. The scope of the paper has been restricted to as few topics as possible, and all the details of special plants, or notable outputs have been ignored. While every effort has been made to give correct figures and data, the changes which are constantly taking place in the iron-producing industry, will, undoubtedly, by the time the paper is in print, develop some errors. It is difficult to determine which of the blast-furnace plants of the country should or should not be considered as upon the active list. A number which have not been in operation for years are still reported as active, some of which will scarcely be put in blast again, and others are handicapped so that they can only operate in times of abnormal profits. It is therefore scarcely probable that there are over 600 blast-furnaces in the United States which can properly be considered as active; but so many considerations affect the various plants, that, it being impossible to determine the exact number, I have relied upon the annual reports presented to the American Iron and Steel Association. Concerning the number of plants which could be stricken from the list, the Secretary of this Association says: "In January last (1885) we enumerated 669 furnaces, which included many stacks which had not been in blast for a very long time, and others which could not be operated except during short periods of exceedingly high prices for pig iron. We have gone over this list very carefully and have eliminated 10 anthracite, 19 bituminous, vol. xiv.—36

Jan 1, 1886

By L. C. Brown, E. B. Hawbolt

If a single-phase alloy is rapidly cooled such that insufficient time is available for an equilibrium transformation to occur, the high-temperature phase may be retained to room temperature or may undergo a massive or martensitic reaction. The massive or martensitic product develops without a composition change and usually has a crystal structure approximating an adjacent equilibrium phase. The characteristics of a massive transformation are intermediate between the equilibrium reaction in which long-

Jan 1, 1969

By J. C. Wilhoit, E. M. Galle

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelastic-ity was used to determine the stresses within the model. Two separate problems were solved: (1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore, induced by an uneyual system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For uneyual principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. INTRODUCTION Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eeninkl have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. whitworth2 and woods3 have obtained numerical solutions. word415 obtained a three-dimensional photoelastic solution, Durelli and Deily 6 obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit7 determined the stresses around the bottom of a short cylindrical cavity. While Miles and McGuire, Harrison and Kieschnick and Hubbert and Willis 10 obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomo-geneous, permeable and anisotropic. Previous