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AARONS, J. BOYD, Major. AGNEW, FRANK VANS. ALLEN, HERMAN H., Private, D Co., 8th Reserve Engineers. BANKS, H. R., Lieutenant, Canadian Engineers, B. E. F. BARBOUR, PERCY E., Deputy Supt. (Captain), New York State Troopers; Captain, 22d Regiment, N. Y. N. G. BARLING, H. B., 1st Lieutenant, Engineer Officers' Reserve Corps. BIGELOW, BRAXTON. BLOOMFIELD, E. C., Lieutenant. BORROW, F. K. BROOKS, ALFRED H., Captain, Engineer Officers' Reserve Corps. BROWNE, DE Courser, 1st Lieutenant, Ordnance Dept., Fortress Monroe, Va.

Jan 8, 1917

AARONS, J. BOYD, Major. AGNEW, FRANK VANS. ALLEN, HERMAN H., Private, D Co., 8th -Reserve Engineers. BAINS, THOMAS M., Major, Engineer Officers' Reserve Corps. BANKS, H. R., Lieutenant, Canadian Engineers, B. E. F. BARBOUR, PERCY E., Deputy Supt. (Captain), New York State Troopers; Captain, 22d Regiment, N. Y. N. G. BARLING, H. B., Ist Lieutenant', Engineer Officers' Reserve Corps. BIGELOW, BRAXTON. BLOOMFIELD, E. C., Lieutenant. , BORROW, F. K. BROCK, R. W., Major, 19th Reserve Battalion of Canadians. BROOKS, ALFRED H., Captain, Engineer Officers' Reserve Corps. BROWNE, DE COURCY, 1st Lieutenant, Ordnance Dept., Fortress Monroe, Va.

Jan 9, 1917

AARONS, J. BOYD; Major. AGNEW, FRANK VANS. ALLEN, HERMAN H., Private, D Co., 8th Reserve Engineers. AMBLER, HARRY A., Second Training Camp,, Ft. Sheridan, Ill. BAINS, THOMAS M., JR., Major, Engineer Officers' Reserve Corps. BANKS, H. R., Lieutenant, Canadian Engineers, B. E. F. BARBOUR, PERCY E., Deputy' Supt. (Captain), New York State Troopers; Captain, 22d Regiment, N. Y. N. G. BARLING, H. B., 1st Lieutenant, Engineer Officers' Reserve Corps. BARRETT, LESLIE P., Lieutenant, A. E. F., France. (Unattached.) BENSEL, J. A., Major, Engineers' Reserve Corps. BIGELOW, BRAXTON, Royal Engineers, B. E. F. BLOOMFIELD, E. C., Lieutenant. BORROW, F. K. BOWLES, MARTIN F., 2d Lieutenant of Infantry, Camp Funston, Kans.

Jan 11, 1917

By Jack Fox

Three years ago we attended the V International Mining Congress in Moscow. This year we attended the VI International Mining Congress in Madrid. By almost any criterion, this was a most successful convention. There were 1717 registrants, not counting the ladies. I don't know how many of the latter there were, but they certainly made a welcome addition to the group. Once again, the International Organizing Committee put together a very impressive technical program which the Spanish National Committee backed up with a brand new Palacio de Congresos admirably equipped with simultaneous translation devices and an organization that provided an excellent social program, a tremendous set of post- meeting excursions, and very impressive opening ceremonies, entertainment and closing ceremonies. There was also an exhibit on the subject of Spanish and Spanish American mining history in the Palacio de Congresos.

Jan 1, 1970

ANDERSON, ALEXANDER, Captain, Royal Garrison Artillery. ANDERSON, GEORGE K., JR., Lieutenant, 30th Co., 3d Replacement Regiment. ARMSTEAD, H. H., Captain, Quartermaster Corps, U. S. N. A. ARMSTRONG, HAROLD KERR, Student Flight Officer, U. S. Naval Reserve Flying Corps, Dunwoody Naval Training Station, Minneapolis, Minn. BAKER, HARRY A., Captain, Co. M, 53d Pioneer Infantry. BASSETT, THOMAS E., Corporal, 340th. Field Artillery, Battery A, 89th Division, A. E. F. BATES, Wm.. T., 3d Reserve Officers' Training Camp. BAUMMGARTEN, K., 1st Lieutenant, 1st Corps School A. P. 0. 703. BAYLESS, G. E. S., Supply Dept., U. S. Submarine Base, New London, Conn. BENSEL, J. A., Major, U. S. R., Board of Control, War. Construction Activities, Norfolk, Va. BILLICK, DON C., Co. C, Ordnance. Supply School. BILLINGSLEY, PAUL, 1st Lieutenant, National Army, Statistics Branch,. General Staff. BLANDY, S. H. B., B. E. F.

Jan 8, 1918

By Paul Weir

FOR the first time in 1938, bituminous coal production for the week ending Nov. 19 surpassed that of the corresponding week in 1937, and indexes of industrial activity indicated the possibility that the remaining weeks of 1938 would run ahead of the corresponding weeks of the preceding year. But regardless of this year-end pickup, total production in 1938 was approximately 25 per cent less than in 1937. The estimate of 340 million tons for 1938 places the bituminous industry slightly above the production level of 1933 and approximately 10 per cent above the modem low of 1932. Anthracite production is not subject to the same extent as is bituminous coal to fluctuations arising out of the rate of industrial activity, hence the decline from 1937 has not been so great being approximately 14 per cent under 1937. The estimate for 1938 production is approximately 45 million tons, but this represents the lowest level reached in the last fifty years with the possible exception of several strike years.

Jan 1, 1939

By P. J. Closmann

Steam zone growth as a function of time has been calculated for the case of constant rate steam injection into a preheated reservoir. To simplify the calculation a linear temperature profile has been assumed in the cap and base rock at the start of steam injection. The results indicate that at early times augmentation of steam zone growth due to preheating should be greatest. At longer times the steam zone development becomes close to that calculated with no preheating. INTRODUCTION With the increasing application of thermal recovery processes to recover viscous oil, cyclic steam injection has become important in many large-scale projects. In this process, the cycle of steam injection followed by oil production is repeated a number of times. At the beginning of the second and later cycles, steam is injected into a reservoir that has already been heated but that has lost part of its heat both in produced fluids and by conductive heat loss away from the injection zone. In such a case, the temperature level of the injection zone and the temperature distribution of the surrounding rock will affect the growth of the steam zone developed during the subsequent steam injection. Knowledge of the size of steam zone developed is important in determining the amount of oil displaced and the extent of heating in the reservoir. It is also useful to be able to compute the size of the steam zone for cases where thief zones take most of the injected steam. This paper presents a fairly straightforward method of estimating the steam zone developed in a preheated formation, based on certain simplifying assumptions. Some cases of steam injection into a reservoir at its original temperature have already been considered elsewhere.1-3 Because it is difficult or impossible to obtain an accurate representation of the temperature distribution in the reservoir some time after initial heating has taken place, in this work, a linear temperature profile in the cap and base rock is assumed (Figs. 1A and 1B). The linear profile has the advantage of yielding heat flow equations that

Jan 1, 1969

By G. Reinberg, C. D. Clarke

Most underground mining operations are dependent on pumping installations to keep the mine unwatered. The reliability of such installations is obviously of paramount importance. The volume of water to be handled is often considerable, and the total head is relatively high. In these cases, both capital cost and operating expense of the pumping installations will become significant factors in overall mining costs. To insure reliability and to keep efficiencies, and hence operating costs, within acceptable limits it goes without saying that mechanical maintenance of a mine pumping installation must receive scrupulous attention at all times. Large mine pumping installations today almost invariably use multistage centrifugal pumps, since positive-displacement units would not be economically competitive except under very unusual conditions of small volume combined with extremely high heads. Centrifugal pump maintenance, under ideal circumstances, would be confined to parts subject to normal running water, i.e., bearing surfaces, stuffing box packing, and shaft sleeves. Under adverse conditions, however, metal may be lost from the wetted surfaces of a pump by erosive or corrosive action of the pumped fluid, and maintenance costs can easily attain enormous proportions.

Aug 1, 1956

Executive A R LEDOUX, Chairman ARTHUR S DWIGHT CHARLES F RAND E P MATHEWSON J V W REYNDERS Membership E DEGOLYER, Chairman W Y WESTERVELT, Vice-chairman WILLIAM H BASSETT H G MOULTON C MINOT WELD Finance WALTER H ALDRIDGE, Chairman GEORGE D BARRON GALEN H CLEVENGER Library GEORGE C STONE,' Chairman JOHN H JANEWAY ALEXANDER C HUMPHREYS, ROBERT LINTON FREDERICK F SHARPLESS

Jan 1, 1923

By V. J. Parks, Leonard Obert, A. J. Durelli

The state of stress in the region where core discing initiates has been investigated through the use of three-dimensional photoelastic models and the results of this study have been compared with those of a previous investigation of rock models. This comparison showed that discing initiates at a point of maximum shear stress, but that the magnitude of the shear stress, as determined photoelastically, is much larger than the shear strength of the rock as deter-mined from conventional triaxial testing. Moreover the shear stress required to produce discing is not constant, but depends on the applied stress field. Possible explanations for these effects are included in this article. In both exploration core drilling and overcore drilling to determine the stress in rock, occasional sections of the core obtained are broken into a series of discs.I* This discing phenomenon has been investigated in the laboratory to ascertain the state of stress required to produce it. The objective of the study was to obtain information that would make it possible to approximate the state of stress in subsurface rock from which disced cores are obtained. Referred to as the discing test, this laboratory study was conducted to determine the applied axial and radial loads required to produce discing in cylinders of rock from several sources. The dimensions of these cylinders are given in Fig. 1. Discing was produced by first applying an axial load to the cylinder and then diamond drilling the core along its axis. The radial load was then incrementally increased until discing initiated. The discs fractured or ruptured* on surfaces approximately normal to the axis of the core (planes A, B, C, D, E, Fig. 2). In many instances, the bottommost disc fractured before the drill had advanced past the points F and F', cre- ating a mush room-shaped fracture surface FEF'. Alternatively, it was also found that the same shaped fracture surface could be created by first drilling in an unloaded core to some point, say F and F', and then triaxially loading the core until fracture occurred on the plane FEF'. Jaeger and cook4 produced similar fracture surfaces in specimens subjected only to a radial biaxial load. From these laboratory studies and observations made in the field, it can be inferred that fracture or rupture initiates in the proximity of the lowest point in the kerf area, (at F and F', Fig. 2) and that the fracture or rupture surface progresses inward from this point. The experiments described above, however, do not provide any information as to the state of stress at the point at which fracture or rupture initiates. In the investigation discussed in the following sections, a three-dimensional photoelastic analysis was conducted to determine the stress distribution in the proximity of the kerf area of a triaxially loaded plastic (epoxy) cylinder containing a short section of core.

Jan 1, 1969

By Frances H. Clark

IN a concern with the varied interests of the Western Union Telegraph Co., where practically all types of metals, both ferrous and nonferrous, are utilized, many types of failures of materials occur. These have to do not only with outside plant construction, such as corrosion and fatigue of line wire and cable, but also with inside plant equipment operating at such high speeds that rapid deterioration of metal. parts due to fatigue and wear results. Both corrosion and fatigue affect the life of copper wire so its normal life in any particular locality is largely dependent on the atmospheric conditions. Tensions vary widely owing to changes in temperature and ice and wind loadings and the wire is Subject to a great range of vibration caused by wind gusts aril vibration front trains or other heavy vehicles transmitted through the earth. High frequency low-amplitude vibrations are sometimes audible as singing in the wire. The other extreme is the vertical slashing or dancing of the wire observed during severe storms where amplitudes of 9, ft. or more at low frequencies have been observed.

Jan 1, 1942

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By A. B. Kinzel

ALTHOUGH the iron-carbon diagram has undergone many changes in the last 20 years, the region below the eutectoid line and up to approxi-mately 1.7 per cent carbon has been little affected. This region is generally considered to consist of cementite and ferrite. Graphite has been noted occasionally in the hypereutectoid steel region, and the ready formation of graphite nodules in malleable cast iron is a phenomenon difficult to interpret in the light of cementite, supposedly stable at sub-eutectoid temperatures. In this case the graphite formation has been partly explained by the presence of silicon, and many have believed that silicon acts to change the stable state rather than to accelerate reactions so as to arrive at the stable state in a briefer period of time. Consider-ation of this phenomenon indicates that cementite is not the stable phase in the temperature composition zone referred to. In the course of examining a low-carbon steel tube taken from a petroleum cracking still, which had been in service for approximately three years at temperatures somewhat below the eutectoid temperature, observations were made that shed light on this entire subject. The tube in question analyzed:1 C, 0.15 per cent; Mn, 0.49; Si, 0.02; S, 0.023; P, 0.015. The microstructure of the tube after service is shown in Figs. 1 and 2. From these it is evident that cementite as such is absent, and that in its place nodular graphite has been formed. In order to check this observation further, samples taken from the tube were heated at 850° C. for varying periods of time. The small samples were put into a large hot furnace, and the total time is recorded. The structure of the

Jan 1, 1934

By H. J. de Haan, L. Schenk

Scope for Thermal Recovery in Shell's Heavy Oil Fields in Venezuela The main heavy oil reservoirs on the East coast of Lake Maracaibo (Fig. I), known as "Bolivar Coast", initially contained some 20 billion bbl of oil in place with gravities in the range of 10 to 15° API. The current total production rate is about 400,000 B/D. Since the recovery to date is on an average only 12.5 percent of the initial oil in place, these fields offer a vast potential for secondary recovery methods. The reservoirs are characterized by moderate depth (generally 1,000 to 3,000 ft; maximum 5,000 ft), good formation properties such as net oil sand thickness (50 to 300 ft), high porosity (30 to 40 percent) permeability (1 to 3 darcies) and oil saturation (initially about 80 percent) and high oil viscosity (100 to 10,000 cp in situ), all of which are favorable for the application of thermal recovery processes. Since 1957, steam drive, steam "soak" and underground combustion have been tested or are being tested in this area.1-3 This paper deals with a major steam drive test in the Tia Juana field. The test was commenced in Sept., 1961, on the basis of encouraging results of laboratory experiments and pilot field tests, which will be discussed briefly. Early Laboratory Investigation of the Steam Drive Process In 1956 a series of model experiments was carried out in the Koninklijke/Shell Laboratorium, Amster- dam, to investigate the displacement of heavy oil by steam.' The prototype studied was a horizontal, un-consolidated heavy oil reservoir, subjected to a linear steam drive. The model, representing a slab from this reservoir along the main flow direction, consisted of a steel tube filled with oil-saturated sand, provided with layers of rock at the top and bottom to simulate conductive heat losses to cap and base rock. Lateral heat losses, perpendicular to the main flow direction, were minimized by insulating the sides of the model. Heat flow and viscosity and gravity forces were scaled by taking the steam injection rate and sand permeability inversely proportional to the geometric reduction factor of the model, and using materials (oil, steam, cap rock, etc.) identical with those of the prototype. The main feature of the process was a frontal displacement mechanism that was observed within wide ranges of injection pressure and rate, oil viscosity, initial oil saturation and sand permeability. The high stability of this front can be attributed to the high volumetric steam flow rates, combined with the reduction in oil viscosity. High recoveries were obtained due to the low residual oil saturation of about 15 percent in the zone swept by steam. The latter value pertains to the specific test conditions (heavy oil, uncon-solidated sand) and may be lower for light oil, due to the effects of steam distillation. The applicability of this experimental approach is limited, as it does not take into account the fact that

Jan 1, 1970

By W. T. Swensen

The Anaconda Company, through its wholly owned subsidiary The Anaconda Company (Canada) I,td., has investigated, optioned and partially developed a large tonnage of iron ore amenable to magnetic concentration. The reserves are located in north central Ontario and occur within a twenty-two mile belt of layered and intricately folded metamorphic rocks, close to the north contact of an igneous complex of granite and pegmatite. There are two main ore deposits. Briarcliffe is a steep to vertically dipping body 100 to 500 feet wide and over a mile long. The Two Mile Lake deposit is flat dipping and confined to an open, asymmetrical syncline; it is approximately a mile wide and 250 to 4.00 feet thick. On its flat easterly plunge, it is saucer-like in shape and is amenable to open-pitting for an east-west distance of several thousand feet. Magnetometer surveys, confirmed by drilling, indicate at least a three mile eastward extension of this deposit. Location and Access: The property is located in the Kowkash Mining District of northwestern Ontario, roughly forty-four miles north of the community of Nakina on the main line of the Canadian National Railroad. (Fig. 1) Access during the exploration period was entirely by airplane from Nakina. (Fig. 2) More recently, Nakina itself was connected to the highway network in the Longlac-Geraldton area. The property is roughly 190 miles by existing and proposed railroad from the Great Lakes waterway system. The Trans-Canada pipeline moving natural gas from western to eastern Canada passes through Geraldton roughly 70 miles south of the property. Topography: The surface features in the area are typical of a sizeable portion of the Precambrian Canadian Shield area. Many lakes, low swampy areas, and glacial moraine-type features are common in this recently glaciated area. The average elevation is between 800 and 900 feet above sea level, and the relief is probably less than 100 feet with the greater portion of the area less than 50 feet. The topographic "highs" are formed either by outcrops that were resistant to glacial erosion or by moraines, eskers and drumlins which were deposited upon the recession of the glaciers. The better mineralized zones, composed chiefly of quartz and magnetite, commonly form ridges resistant to erosion and weathering. Previous Work: Because of the obvious outcrop of the magnetite-rich beds and knowledge gained from early developments within the general region, it is conceivable that the presence of the iron formations has been known for a good many years. The area is included in studies made by L. F. Kindle* in 1929 and 1930 for the Ontario Department *Kindle, L.F., Kowkash-Ogoki Gold Area, Ontario Department of Mines Annual Report, Vol. XL, Part IV, 1931; map 40f

Jan 1, 1961

By Edward H. Robie

Jan 1, 1971

By Westwater, J. S.

The Mather mine of The Negaunee Mine Co. embraces nearly all of Sections 1 and 2, T47N, R27W. within the limits of the cities of Negaunee and Ishpeming on the Marquette iron range of Michigan's Upper Peninsula. Operations of the Negaunee Mine Co., the stock of which is jointly owned by Bethlehem Steel Co. and The Cleveland-Cliffs Iron Co., are under the direction of the latter company. The opening of the Mather mine was described by C. W. A1len. Mather "A" shaft was completed to an initial depth of 2352 ft in early 1943. The shaft capacity of over one million tons yearly is in prospect of being realized by orderly development and mining, and sinking of the second or "B" shaft then started in accordance with previous planning. Mather " B, " also a vertical shaft, was designed as a twin to Mather "A" shaft and the sinking technique developed at Mather "A" was utilized in "B" shaft operation.

Jan 1, 1949

By Fulton Flick

THE micrography and macrography of aluminum and its alloys present certain difficulties. Many of the difficulties attendant on the micrography have been removed by methods developed during the past few years, notably those of E. H. Dix, Jr.1 The development of grain size in aluminum and its alloys may be equally troublesome, yet comparatively little detailed attention appears to have been given to it. Satisfactory reagents. are available for the development of such structures in ferrous and most non-ferrous metals, but those applied to aluminum and its alloys, i. e., alcoholic or aqueous solutions of sodium hydroxide or hydrofluoric acid are not entirely satisfactory. Hanson and Archbutt,2 in speaking of these two reagents, state that "These two reagents give fairly satisfactory results, but they sometimes produce badly tarnished surfaces from which the surface deposit is difficult to remove." It has been our experience that neither of these reagents is to be entirely relied on for developing structures suitable for study or photography. This means that when the etch fails to produce satisfactory results the, specimen must be repolished, through the 000-paper at least, and then etched with another reagent. This procedure entails a con¬siderable loss of time, and the final results may not be all that might be desired. However, the reagent to be described, although not a panacea for all etching troubles, has improved results so markedly that it is felt that it is worth offering as a grain-size etch generally applicable to aluminum and aluminum alloys. Czochralski3 in 1915 mentioned the application of a solution of 10 to 20 c. c. concentrated hydrofluoric acid in 100 c.c. absolute alcohol, etching in this reagent being followed by dipping in concentrated hydrochloric-acid solution.

Jan 2, 1925

CORPORAL SHEPPARD B. GORDY Sheppard B. Gordy, a brief biography of whom was printed inn the January Bulletin, entered the employ of the Braden Copper Co. immediately on his graduation from the Sheffield Scientific School in 1912. He remained with this company four years, working up through the various grades to assistant foreman and foreman to one of the individual mines. The last year he was in its employ, he acted as general mine foreman. He was for a short time with the Chile Exploration Co. and then went with the Andes Exploration Co. (Anaconda) and remained with CORPORAL SHEPPARD B. GORDY. the latter, doing mine exploration and development work, until he sailed for home in June, 1918, to give a more personal and active service to his country in her need. He declined a tender of induction into an officers' training camp, at the urgent request of Professor McClelland supplemented by Mr. Potter, because they demonstrated to his satisfaction that he could give more valuable service to his country in helping out with the aircraft production. Being within the draft age, in order to carry out this plan, it was necessary for him to be called by his Local Board and sent to camp. This call came Aug. 26. Two weeks before that time lie had gone to Dayton, Ohio; to begin the study of aircraft production, and was sent by the Dayton Board to Camp Sherman, Chillicothe, Ohio, where he died of pneumonia on Oct. 9.

Jan 3, 1919

By R. G. Bentsen, D. A. T. Donohue

The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today.1-4 Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming. To use dynamic programming, we must be able to predict not only the production rate-time curve resulting from a given stimulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism. We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process. Oil Production Response Model The advantage of using a mathematical model is its generality and ease of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results. With this in mind, we kept our model as simple as possible, yet generally representative of the actual physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated. In

Jan 1, 1970