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By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949

By AIME AIME

FEW indeed are the sections of the country where trained or partly trained workers have not already been hired by a war industry plant or will be within the near future. Yet right in the midst of the heavily industrialized East lies the anthracite area, home of a million people, whose productive power has persistently been by-passed either by private industry or by the Government Plant Site Board. The chief reason given for not locating war plants in the area is that it is not within the strategic zone, but in numerous instances elsewhere this rule has been waived. Furthermore, the anthracite region is well protected on all sides by mountains and is at all points more than 100 miles inland. Continued depression in the anthracite industry and a crippling blow dealt by the war emergency to the production of silk and rayon goods, the chief manufacturing activity of the area, have resulted in a heavy migration, particularly of trained young workers, into near-by industrial areas. At least 50,000 people are currently unemployed, with the likelihood of an increase in coming months, and as many families are on relief.

Jan 1, 1942

By AIME AIME

EITHER the 2300 people who came to the Annual Meeting were in a better frame of mind or they were resigned to their fate, or it was a better meeting than usual. Whatever the reason, at the 1nstitute?s 148th meeting the attendance was better than ever before, things went more smoothly than in some previous years, and complaints appear to have been almost entirely absent. Patience was sometimes reauired but. almost without exception, it was forthcorning the well-known recession seems to have given many members enough leisure time to come to the meeting without depriving them of the tangible wherewithal to come.

Jan 1, 1938

By Harry H. Power

INDUSTRY has the right to expect the petroleum engineering schools to supply more than the minimum technical qualifications necessary to obtain or discharge the responsibilities of a particular job. The basic training, social and economic orientation, should go far beyond these minimum requirements. Petroleum engineering students should also be well grounded in the history of the oil business so that they may understand the industry's progress since the advent of the Drake well. Furthermore, according to P. H. Bohart, the schools "have a definite duty to help the students form a workable philosophy of life, which includes an appreciation of the service of science to mankind, and a belief in the obligation of the individual who enters a profession to exalt himself by continuing his studies and growth so that he may never cease making contributions to the advancement of science and industry."

Jan 1, 1948

By James Bowron

CONSIDERING the importance of the steel trade and the strategic position occupied in it by the Birmingham District, it may be surprising to many to realize that even the first pig iron smelted with coke was made in Alabama on Feb. 28, 1876, although merchant pig iron had been produced in Rockwood, Tenn., in 1867, a plant which is still in active operation. The heavy deposit of Clinton ore extending from Pennsylvania into Alabama, varying greatly in accessibility on account of geological changes such as erosion or anticlinal upthrow, varies equally as much in thickness and in quality. The brown ores extensively scattered through the South also vary materially in quality, some being relatively low in phosphorus and high in manganese, and vice versa. The red ore varies materially in phosphorus, but the iron produced from these ores was always considered to be too high in phosphorus for treatment by acid Bessemer or open hearth and did not contain sufficient for the basic Bessemer process. Under these conditions there remained only the basic open hearth as a possibility, and for many years it appeared impossible to use it, because, with coke smelted iron, the silicon was too high to permit its use in basic lined furnaces.

Jan 1, 1924

By John Fritz

MEMBERS of the American engineering societies who were in London and Paris during the last days of. June and early July were present at many interesting gatherings. The official delegates of the Founder societies were the specially honored guests of the foreign engineering societies, but other American engineers took part in the meetings. The members of the delegation were: Arthur S. Dwight, Charles F. Rand, William Kelly, representing A. I. M. E.; Ambrose Swasey (general chairman of deputation), Ira N. Hollis, Jesse M. Smith, representing A. S. M. E.; F. B. Jewett, A. E. Kennelly, G. O. Squier, representing A. I. E. E.; Charles T. Main, Robert A. Cummings, John R. Freeman, D. C. Henny, representing A. S. C. E.

Jan 1, 1921

By WM. E. Mlligan

IN the last year, much information had become available as to the extent that zinc participated in the war effort. The importance of foreign zinc in this program had been indicated by Bateman (M&M April 1945) as of the order of 400,000 tons annually in zinc or contained zinc. Pehrson (M&M April 1945) reviewed the domestic ore-reserve situation with respect to most minerals and metals and showed the extent to which commercial zinc ores had become depleted in this country. This picture was further darkened by O.P.A. figures appearing in E.&M.J. July 1945 in which figures for total production during the three previous years were broken down into percentages produced under ceiling and various quota price categories. True, factors other than depleted ore reserves contributed to this picture. Among the more important of these, were shortage and high cost of labor, both skilled and unskilled, and the general difficulty and cost of maintaining adequate equipment and supplies. The cost of production in the Tri-State district was most affected.

Jan 1, 1946

By AIME AIME

THE Fall Meetings of the Institute of Metals Division and of the Iron and Steel Division were held in Cleveland from Tuesday, Oct. 20, to Thursday, Oct. 22, as a part of the National Metal Congress. The registration at the technical sessions was something over 450 and the attendance at the joint dinner of the two Divisions on Wednesday evening taxed the capacity of the dining room. The president of the British Institute of Metals, W. R. Barclay, consulting metallurgist to the Mond Nickel Co., Ltd.; of London, was in attendance at several of the technical sessions and was one of the after-dinner speakers at the banquet. He commented on the desirability of greater international amity and cooperation in these troubled times and of the role that technical societies, such as the A. I. M. E. and his own British Institute of Metals, can and indeed are playing in bringing this to pass, with their membership and contacts reaching to all parts of the world. He also referred to the new reciprocal membership arrangements in effect between the A.I.M.E. and the British Institute of Metals.

Jan 1, 1936

By Gene D. Clayton, Robert R. Dimock

A time-consuming and expensive preshearing program to minimize the adverse effects of blasting on slope stability at Kennecott Copper Corp.'s Ruth Pit in east-central Nevada has been eliminated in favor of down-the-hole, nonelectric delayed blasting which can produce a smooth wall effect and improve blast fragmentation. The new blasting approach resulted from a Kennecott engineering investigation aimed at improving the stability of the extremely variable rock conditions found throughout the pit by reducing the vibrational energy imparted to the walls with conventional bench blasts.

Jan 4, 1977

By P. F. MINISTER

AT Lime Spur, Mont., the East Butte Copper Mining Co. has been quarrying limestone for twenty years. The quarry is beside the Northern Pacific R. R. in the Jefferson River canyon, 4 ½ miles east of Cardwell, at Lime Spur, Montana. HISTORY This quarry was opened early in 1900 by Dan Morrison of Whitehall, the discoverer of the Morrison cave, to supply a demand for smelter flux. Limestone was sold to the Pittsmont smelter of The East Butte Copper Mining Co. and to the Butte Reduction Works. As no particular effort was made at the quarry to select the rock that delivered to the smelters was unduly high in magnesia and impurities. The East Butte com¬pany, therefore. Bought the quarry. in 1909 and confined operations to the high-grade beds in order to supply rock of the desired purity for its own smelter and the Butte Reduction Works until the latter shut down. It also developed a market for some of its rock with the sugar factories. The latter market increased until in later years all rock, larger than 4 in. in size over a bar grizzly, was being shipped to the sugar factories, and the rock smaller than 4 in. was being used as a flux in the blast furnaces at the Pittsmont smelter. In 1924, the East Butte concluded a contract with the Anaconda company for the treatment of its ores, and the Pittsmont -smelter -was shut down: which made the minus 4-in. rock a useless by-product. Since there was not enough revenue in the sugar rock alone and also because of limited waste room it became necessary, if Lime Spur was to continue to operate, to increase- the proportion of plus 4-in. rock and to develop a market for the minus 4-in.

Jan 1, 1930

By H. B. FERNALD

THE first year to which the Revenue Act of 1936 has applied is now passed. It is appropriate to try to give some calm thought to the plan of Federal income taxation as now imposed and what it will mean to the business and industry of the country if this plan of taxation is continued unchanged. Whether or not we like to pay these taxes is beside the point. Taxes are high and may be expected to be high for many years. The important question is whether the taxes to be imposed will destroy or injure business enterprise and development, and, in so doing, lower the standards of employment, living, comfort, and welfare of our people. The power to tax is the power to destroy. That destruction may come suddenly as a cyclone, or slowly as dry rot. What, if any, features are there in the present plan of Federal income taxation that have these destructive tendencies? A few of the points follow that seem to call for consideration.

Jan 1, 1937

By Bradley Stoughton

AT THE meeting of the Board of Directors on May 20, the resignation of Bradley Stoughton as Secretary of the Institute was presented and regretfully accepted by the Board. The letter of resignation follows : Gentlemen: About two years ago, I indicated to the President and some members of the Board my belief that the office of Secretary of the Institute should not be a permanent one. It is my observation of events, not only in our own Institute, but also in several sister societies, that too long a tenure of office by the Secretary inevitably leads to a situation which is not good either for him or for the society. After submitting this in writing to the Directors on February 17, 1920, I was overpersuaded by members of the Board to defer resignation until a more convenient time for the

Jan 1, 1921

By H. E. Kramm

(New York Meeting, February, 1919.) DURING the summer of 1911, I had the opportunity to study in detail the geological conditions of what is known in northern California as " Harrison gulch," in Shasta county. Though the district, as a whole, that is, the western part of Shasta and the eastern part of Trinity county, has contributed during the last 15 years a considerable share of the gold-production credited to Shasta county, very little is known of its geology, perhaps because the country is covered with a dense growth of brush which makes exploration and prospecting extremely difficult. Topographically the district presents a succession of ridges trending approximately N-S.; and alternating with deep narrow canyons. The drainage is partly into . the Sacramento, partly into the Trinity river. Climatic conditions in summer time are almost ideal. It is true, the thermometer may climb to 115°, but the air is dry and the heat is bearable, especially as the nights are always cool. It seldom rains during the summer months, and creeks and springs dry out towards the end of the summer. The winter is severe, lasting from November to April, and usually a thick layer of snow covers the mountains. By reason of the character of its gold-deposits, the region is known to miners as "the pocket country." It contains a series ?of eruptive rocks intruded into slates, cherts, limestones, and conglomerates. Dikes, laccoliths, and batholiths are frequent. In a day's ride it is possible to find all the common igneous rocks from the very acid to the very basic. Serpentines are especially abundant.. The sedimentary rocks are, as rule, broken and shattered as well as folded, and show the effects of intense metamorphism. ? Pocket-hunters " speak of the contact of diabase and slate as the ? pocket-contact." Some rich gold-pockets, however, have also been found in the diabase.

Jul 1, 1912

By W. H. Adams

One of the most attractive subjects for technical writers is the gigantic industry of the manufacture of sulphuric acid. This is no doubt, natural when we take into account that it has grown in this country during the past twenty years, from a production of 60,000 tons in the year 1867, to that of nearly 450,000 tons in 1887. We may well excuse much of the literature which but repeats the same old story, as it serves to bring to the public notice, at proper intervals, the hidden resources of our land; and this constant application of essential truths will sooner or later be the means of freeing us from dependence upon the Old World for necessary chemical products. The present increase in manufacture of this acid in the United States is almost wholly from pyrites ores, which we have in unlimited quantities close at hand. The largest consumption of such acid is for treatment of other native products, petroleum, rock-phosphates, etc.; and, considering the knowledge we have gained during the past twenty years, it is safe to say that the industry is but fairly established, and the causes which have operated to place us in our present proud position are but natural incentives for a further growth and an increased consumption of the many other undiscovered or undeveloped resources of our American soi1. In one of his earlier editions Muspratt says: " It would seem that the manufacture of sulphuric acid, though as extensively carried on as any other business, yet seems to be the least understood; and the ignorance of some manufacturers appears to be only equalled by that of writers, who, in their description of the production of this acid, give figures of apparatus, and vaunt as improvements, things which have been exploded for years. It is possible to find in the works of eminent men drawings of apparatus, for the production of sulphuric acid, which never could possibly have worked one day—some, in fact, could never have worked at all."

Jan 1, 1888

By GEORGE A. KIERSCH

The awesome destructive power of known and projected weapons of war presages a new need for geologists and engineers, who may be called upon to locate vital industry underground, thereby protecting it from sky-borne destruction. The Corps of Engineers is now conducting special tests to establish design standards covering the general field of underground installations as well as surveys a of construction methods and the operational hazards connected with such plants. National planning must dictate a policy that is either tactical, where surface manufactured parts; are stored underground and during art emergency assembled, or operational with both the manufacturing and assemblage completed in subsurface plants. Both plans of operation require the use of subterranean plants. Relocation of vital plants underground will probably involve only a small percentage of the production capacity of this nation. The cost of rebuilding in new location will obviously limit its adoption

Jan 1, 1949

By Fred R. Ingram

FOR the purpose of this discussion, let us consider that the Rocky Mountain region covers the area in the seven Mountain States, Idaho, Montana, Wyoming, Utah, Colorado, New Mexico, and Arizona, and before we discuss the needs of these states, let us define Industrial Hygiene. Industrial Hygiene is that branch of preventive medicine concerned with the protection of health, improvement of efficiency, and prolongation of life of the industrial worker; in short, adult health conservation. It includes in its broad meaning not only the prevention of occupational diseases, such as silicosis, lead poisoning, cadmium poisoning, and many others, but such relative problems as overcrowding, fatigue, and personal and mental hygiene; exposure to abnormal temperatures, pressures, and humidities; ventilation, heating, and lighting. It is a science which requires the combined activity of medical personnel (doctors and nurses), engineers, and chemists to evaluate the exposures and determine the means of eliminating the hazard. The engineer surveys the workplace, takes air samples at the breathing level of the workman, and analyzes the work exposure. The chemist determines in his laboratory the exact amount of toxic material collected in the sample, which represents the exposure of the workman. The doctor must diagnose the occupational disease, recognize its cause, and evaluate the disability. Together, all three must correlate the data obtained and devise efficient methods, medical or engineering or process changes, for controlling or minimizing the dangerous condition and for studying the effectiveness of these measures. The plant doctor, in addition, must aid in the readjustment of the incapacitated worker and provide facilities for prevention. Industrial hygiene, however, is of no avail without the understanding co-operation of management.

Jan 1, 1945

By Richards J. W.

J.W. RICHARDS, South Bethlehem, Pa. (communication to the Secretary?).-Mr. Howland's paper, data and conclusions have interested me intensely, and have led me to study carefully the record-of his 26 furnaces therein given. Mr. Howland is undoubtedly right in his conclusion that when expressing the amount of carbon burned at the tuyères in percentage of the total

Jan 1, 1917

By Paul W. Zimmer, Carl E. Dutton

Iron ore in the Menominee district is mined from two iron-formations of middle Precambrian age. The older formation is present in the northeastern part; is composed mainly of hematite, magnetite, quartz, and minor silicates; and contains about 34 per cent iron. The rock has been so coarsened by meta- morphism that concentration of magnetite and hematite is feasib!e, and pellets containing more than 60 per cent iron are being produced. The older formation is also present in the southeastern part where it has 1:een only slightly metamorphosed. Ore containing more than 50 per cent iron was formerly mined from local residual concentrations of iron oxides from which silica had been sufficiently leached, or replaced by iron oxide, or affected by combinations of these processes. The younger iron-formation occurs in the western part of the district and, if unaltered, is interlayered siderite and chert. The ore in this area also contains more than 50 per cent iron and formed as local residual concentrations but in two stages. The siderite was converted to iron oxides (hematite and "limonite"), and silica was contemporaneously or subsequently removed by leaching, or replacement, or combinations of these processes.

Jan 1, 1968

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith's data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy's obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:'l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969