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By George Asmus

Closed front, or open front for blast-furnaces, has been for a number of years a much discussed question among the furnace-men in every country where iron is made. As blast-furnaces are costly structures, and as the whole question is one of economy, I hope to be excused for entering a little into details. The "fore-hearth" is a prolonged opening in the lowest part of the hearth, from two to three feet wide, four to six feet long, and two to three feet high. It is a more or less fire-proof box, cooler than

By R. P. Rothwell

THE first difficulty mentioned is that in some instances two or more beds of coal separated by sandstone or slate rocks of considerable thickness in one part of a basin, are found running together in another part. Of course, we may happen to strike first the part of the basin where there is but a single seam, and in this case the bed would appear 60 divide into two or more branches within a short, distance. Such cases are not rare in the anthracite coal-fields. I would suggest as an explanation of this phenomenon the gradual sinking of the peat-marsh-the embryo coal-bed-on one side, and the moving forward of the marsh, so that on one part of the bed the formation of peat would still be progressing, while another part, being under water, would be covered with mud and sand. Thus we have different portions of the same bed of different ages. Now if the sinking of the marsh be stopped for a time, the bed will become thicker in the portions left exposed, and if the sinking now changes in direction, so that the part that had previously gone down commences to rise, we should have the phenomenon of a bed, continuous throughout, with one portion overlying another, and separated from it by rock strata. These are exactly the conditions observed in splitting beds. While one side of the lake is sinking, and the peat marsh moving on in that direction, the other side may be rising,

By K. E. Brown, J. P. Brill, T. C. Doerr

A wide range of intermittent gas-lift tests way conducted in a 1,500-ft experimental well through 11/4- and 11/2-in, nominal size tubing. The well was equipped with two gas-lift valves, four Maihak electronic pressure transmitters and surface facilities to measure casing and tubing pressures, temperature, liquid production and the rate and volume of gas injected. For each tubing size, tests were conducted varying the slug length, gas volume injected and liquid viscosity and surface tension. From these tests, an empirical "fallback" or liquid loss correlation has been developed. No general fallback correlation could be obtained, and the correlation is presented in the form of one curve for each slug length of a given liquid and lubing size. A conceptual model has been developed which combines the fallback correlation with equarions which govern liquid slug pow. A mathematical simulation of the model in the form of a digital computer program is used to calculate total recovery, gas volume used and clearance time for a given test. Tubing pressures at the gas-lift valve and at the gm-slug interface are calculated as a function of time. Tubing pressures at the surface during slug clearance ore also calculated. The results compare favorably with the test data and verify the conceptual model. The extent to which the model can be used for other tubing sizes, depths, liquids and gas-lift valves can only be determined with additional experimental data. Data are also necessary so that a fallback curve can be constructed for the particular test conditions studied. INTRODUCTION The flow of liquid slugs in vertical conduits has long been an established production method in the petroleum industry. Under the name "intermittent gas lift", many advances have been made in engineering design. However, the unsteady-state nature of liquid slug flow has discouraged attempts to describe the problem analytically. The result has been that intermittent gas lift is dominated by rules-of-thumb engineering practices developed over many years. The advent of slim-hole completions has increased the demand for a more rigorous solution to the intermittent problem. Small-diameter conduits offer more frictional per intermittent cycle. Small-diameter conduits are defined to be 1%-in. nominal size tubing or smaller. When oil is produced from the reservoir in which it is found, and transported to surface tanks by intermittent gas lift, three separate flow stages are encountered: flow of the fluids to the wellbore through a porous medium, vertical flow of a liquid slug from the point of gas injection to the surface, and horizontal flow of the liquid slug through the surface flowlines from the wellhead to the surface tanks. The three stages are depicted schematically in Fig. 1. The present study deals with liquid slug flow in both the vertical and horizontal conduits, ending when the bottom of the liquid slug reaches the surface. Due to the large number of variables involved, the analytical study of intermittent gas lift is extremely complex. The possibility of flow regimes other than slug type, the nature of the force fields acting on the system, the interfacial instabilities involved, the varying operational principles of existing gas-lift valves and the complete unsteady-state nature of the physical phenomena occurring in an intermittent gas-lift cycle relate some of the difficulties encountered.

By G. H. Billings

There exists an unconfirmed opinion among many ironmasters that the combination of a small quantity of manganese, chromium, titanium, tungsten, aluminium, nickel, and some of the metalloids with iron has a beneficial effect upon the quality. And the impression prevails in some localities that the excellence of steel greatly depends upon the influence of some of these elements. Brit as the recorded experiments are so meagrely described, and made under such various conditions, the student in search of information upon the subject is somewhat bewildered by the contradiction of the opinions expressed. Observing some interesting phenomena while experimenting with an alloy of iron, copper, and nickel, I was led to determine the effect of some of the metals upon iron as free from contamination by other elements as it is possible to procure in practice, in order that the result of an alloy of an individual metal with iron might be more closely studied; for it is almost an impossibility to determine the influence of a small amount of one element upon a metal combined with a large amount of another, and the mere presence of another sometimes makes this difficult. And as most of the experiments recorded upon this subject have been made with iron containing sufficient carbon and other elements to interfere with the effect of that metal the influence of which it was desired to observe, I have endeavored to avoid these sources of error as far as practicable. In determining the specific gravity of the alloys in these ex-

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By P. B. Baxendell

The appraial of producing properties and profitability ntzalysis of a proposed capital expenditure are based on the same principles. In both problems a projection of future cash income is. cornpared to one or more capital expenditures. Several different methods have been in use either to compute a price to obtain a given earning power on the investment or to compute the earning power which will result from a given capital expenditure. One of these, the "Average Annual Rate of Return" method, computes in a simple manner the ratio of the present value of the future earnings after amortization to the present value of the undepreciated balances of the investment over the life of a project. This method, not well known generally, appears to have some rather unique advantages in reducing the computation work required, eliminating trial-and-error solutions, and providing a more accurate answer when applied to oil industry investments subject to the unit-of-production basis of amortization. Its derivation is given and its versatility demonstrated in the solution of certain everyday investment problems. A number of charts, useful in applying this method to profitability analysis and appraisal work, are provided. The current trend in the market values of producing properties is shown. INTRODUCTION Making sound capital expenditure decisions requires an objective means of measuring the productivity of individual investment proposals. Since the best measure of the economic worth of such proposals is their ability to produce profits, it is common practice to grade proposed capital expenditures according to their annual earning power as a percentage of the outstanding capital. The same principles which govern the determination of the rate of return of proposed capital expenditures also apply generally to the problem of determining the appraisal value or purchase price of income-producing oil and gas properties. Both problems are of prime importance in the producing phase of the oil business, where management is faced daily with decisions to drill or not to drill certain development wells, or with the determination of the appraisal value of producing properties. The common feature in both problems is that a projection of future cash income is compared with a known or estimated capital investment to determine itsiearning power or annual rate of return. In the case of development drilling, the cost of the proposed well can usually be estimated with a fair degree of accuracy and the problem consists of finding the rate of return on the invested capital. In the case of appraising producing properties, on the other hand, the desired rate of return is usually known in advance and the problem consists of determining the purchase price which, for the given income projection, results in the fequired rate of return. Certain accounting procedures common to the oil and gas producing business make these two problems and their solutions somewhat different from corresponding problems in other industries, and, in certain ways, simpler. The main difference is in the amortization policy which, for oil and gas production, is frequently on a unit-of-production basis, compared to the amortization on a time basis used in many other industries. The purpose of this paper is to discuss briefly the various methods currently in use for the measurement of productivity of invested capital in producing properties and, in more detail, the derivation and application of what will be called the "Average Annual Rate of Return Method". This rather interesting and not too well known method has some very definite advantages in the solution of many problems common to the oil industry. For the sake of simplicity, federal income tax considerations have been disregarded in the examples used, since they do not affect the principles involved. The use of the production payment route in the sale or purchase of producing properties, which has been amply covered in many other publications, has also not been included in this analysis. METHODS FOK MEASUKING THE EARNING POWER OF INVESTED CAPITAL, Of the many different methods used to measure the earning power of invested capital, four are applicable to oil or gas production ventures. Depending on whether these four methods utilize one or two interest rates, and whether a fixed amortization pattern is used, they may be classified as follows.

By John F. Blandy

Although the question of the "waste of anthracite coal mining " has been so frequently discussed, and a committee was appointed at the first meeting of this Society to consider and report upon the subject, still but little progress seems to have been made in arriving at a conclusion as to how it ran be reduced. That committee made a preliminary report at the August meeting, 1871, in which it divided the question into three parts, namely: Waste in mining, in preparing for market, and in transportation. I shall not here refer to the first item, as so much depends upon the peculiar features of each separate mine, and the skill of those in charge; but in reference to the second, that of preparing the coal for market in breaker and screens, I wish to make some remarks. There is no use considering the question, whether the coal should be broken up to suit the fancy of consumers; all miners are satisfied that it should not be, but the consumers decide that they want it that way, and the miner must submit, and simply utter his maledictions upon the head of the man who first suggested a breaker or screen, if that is any consolation to him. What is called waste in this process of preparation, is the dust and fine coal, which results from the breaking and screening, and, as we all know, this is a very important percentage of what passes from the slope to the top of the breaker. Now, if this dust and fine coal can be utilized—the slate which is picked out is not to be taken into consideration as waste—then we get rid of this item entirely. There is no question in my mind that this article can and will be used as a steam generator at least, and I think, therefore, that in depositing

By R. A. Thomas, R. L. Solbod

The importance of transverse diffusion on the finger development in a miscible-phase displacement at an adverse mobility ratio of tbree was studied in a porous plate 1/4-in. thick, 3-in. wide and 18-in. long. Fast displacement rates (29 ft/D) and slow rates (1.6 ft/D) were used to determine the effect of residence time on the geometry of the fingers. The shape of the fingers was observed directly by use of the X-ray technique. At fast rates numerous narrow fingers were observed, but at slow rates a single somewhat bulging finger was produced. The amount of material moved transversely by diffusion across the plate was sufficient to modify the finger geometry in the slow-rate run because of the long residence time. These results are in contradiction to some of the postulates in the literature. The composition of the effluent stream, however, was not affected by the flow rate. This result is not inconsistent with the observed change in the shape of the finger in a short model, but it seems likely that a short model does not offer adequate and proper scaling of the reservoir. The model used was probably a valid one for studying the effect of transverse diffusion on the finger geometry, but a longer model would be needed for proper scaling of the effect of the change in the finger shape on the efficiency of displacement as measured by the composition of the effluent stream. INTRODUCTION Fingering can be defined as the uneven advance of the injected phase as it moves into a porous medium displacing the resident phase from the pore spaces of the rock. The use of this term is usually restticted to the situation in which the displacing phase is less viscous or more mobile than the fluid being displaced. Under these conditions, not only are fingers formed, but the length and width of the fingers grow with distance traveled in the porous medium. This subject has become one of great interest to the oil industry because of the present trend toward the use of various forms of miscible-phase displacement to increase oil recovery. Since in nearly all of the known modifications of the miscible-phase displacements an unfavorable mobility ratio exists (the displacing phase has a lower viscosity than that of the crude oil), the conditions are proper for fingering to develop. An appreciable amount of fingering appears to be a severe handicap to these processes for it increases the volume of agent required for the process to be a success, and such an increase puts a severe strain on the economics of the proposed processes. In some cases, such as for a mobility ratio of 200 unfavorable, it has already been demonstrated that the proposed process would not be economic if the fingering in the field were to be of the same magnitude as that observed in the laboratory. A number of aspects of fingering have been studied and reported in the literature. While the phenomenon of fingering cannot be regarded as a completely understood subject, considerable information exists on the effect of the path length and the mobility ratio on the growth of fingers. Less-complete data are available on the effect of the diameter of the flow path on the character and amount of the fingering, and even less agreement in results exists on the effect of rate of flow on the nature of fingering. This paper deals with one aspect of this latter subject. OBJECTIVE The objective of this study was narrowed down to one rather specific feature of the behavior of fingers in miscible-phase displacement in porous media. The variable studied was the effect of rate of flow on the nature and the development of fingers. It should be made clear at this point that, while rate was the apparent variable, the real variable was residence time; that is, at low rates the fluids are present at a given spot in the porous medium for a longer time interval than at fast rates. The purpose of the study, therefore, was to determine the changes which occur in the fingering and the possible benefits which might accrue from a longer residence time during that period when fingers are

By Richard P. Rothwell

Fires in mines are so serious in their consequences and of such frequent occurrence, that their causes and the means of extinguishing them are certainly questions of the greatest interest to a large part of the engineering profession. We have already, in this country, many mines which have been burning for years, and though our hard anthracite is so difficult to ignite that for a quarter of a century after it was first discovered it mas not known how to burn it except with the aid of an artificial blast, yet most of the fires which have occurred underground have been in anthracite mines, and in the coal itself. The injury which these fires have caused to properties in various parts of the anthracite regions, and the cost of extinguishing them, would amount to many millions of dollars, and they have also occasioned the loss of many valuable lives. It is not surprising, therefore, that the subject has already attracted much attention, and the exercise of great ingenuity; and the present communication is made less with the expectation of announcing anything new, than with the object of putting upon record the present state of our knowledge on this subject, or, in other words, of indicating how defective are the present means of combating underground conflagrations. Causes of Mine Fires.—Even upon the surface, fire is a terrible foe to contend with, and there is probably no other which inspires such thorough and well-founded alarm. With what feelings, then, must we look upon this destructive element, when its field is in the narrow galleries of a mine, where the poisonous products of combustion, spreading in every direction, protect, in the most effectual manner, the fire itself from the attacks of extinguishers, while, if the face of attack be ventilated so as to enable then] to approach the seat of the fire, the air current simply increases the extent and violence of the conflagration. Fires underground originate in as various ways as those on the surface, and it is scarcely necessary to say that, except in the rare cases where they are the result of design, they are invariably classed as " accidents," and most generally as " unavoidable accidents." In reality, by an intelligent understanding of their causes and with due precautions, they can almost always be prevented. Ignorance and

By Joshua E. Clayton

This remarkable gold and silver bearing district is situated on the middle fork of Boise River, in Alturas County, Idaho Territory, about eighteen miles north of Rocky Bar, and sixty-five to seventy miles, as the crow flies, east of Boise City, the capital of the Territory. This district lies in the very heart of one of the most wild and mountainous regions of Idaho. For many miles in every direction nothing can be seen but bold granite mountains, with deep narrow gorges cutting into their sides in every direction, rendering them almost inaccessible except to .the hardy mountaineer and adventurous prospector. The mountain sides are covered, in most part, by dense forests of pine, fir, and spruce timber. In every canon there are clear streams of pure running water that empty into the principal forks of Boise River. The only line of approach to this mountainous region at present is from the southwest, by way of Rocky Bar, the county seat of Alturas County, to which place there is a good wagon-road. From thence to Atlanta City, eighteen miles, the road, or pack-trail, passes over the high, steep range that separates the south and middle forks of Boise River. During severe winters this line of approach is closed up by deep snows for months at a time, thus leaving the district isolated, in the bosom of the grand old mountains. The geological formation is granite, of a coarse, friable texture, and in many places is traversed by numerous dikes of syenite, and three or four varieties of porphyry, which cut through the granite in easterly and westerly directions. The metal-bearing reins also have an easterly and westerly trend, bat are occasionally intersected by the dikes. The largest number of the gold and silver lodes are confined to a

By O. R. Wagner, R. O. Leach, H. W. Wood, C. F. Harpke

PAN AMERICAN PETROLEUM CORP.TULSA, OKLA. CASPER, WYO A field test has been made in which additional oil recovery was obtained from a previously-waterflooded "oil-wet" sandstone reservoir. This recovery improvement was accomplished by adjusting the reservoir wettability through chemical treatment of the flood water. The test was made in the Muddy sand of the West Harrisburg Unit, Neb. The chemical used, sodium hydroxide, was injected as a slug of dilute caustic solution through a water-injection well. The natural wettability of the reservoir and the chemical requirements for reversing wettability were determined in the laboratory from contact-angle studies using field water and oil samples. Laboratory flood tests with a synthetic system had shown that reversing the wettability of an oil-wet consolidated core would lead to improved oil recovery. The field performance indicates that the mechanism by which increased oil retovery is obtained in the field is the same as that observed in the lahoratory. Laboratory studies indicate that higher ultimate recoveries and decreascd water-injection requirements result when the adjusting agent is added early in the life of the flood. However, a previously waterflooded area was intentiorzally chosen for the field test so that unambiguous conclusions could be made about the effects of chemical injection on wettability and the extent of oil-recovery improvernent afforded by wettability reversal. Forces existing at the fluid-solid and fluid-fluid interfaces in a porous medium have an important effect on oil recovery during a water flood. Modifying these interfacial forces in the reservoir to improve oil recovery has been the object of much research. Several papers' ' have discussed the use of surfactants to lower the water-oil interfacial tension. This paper describes work concerned with improving oil recovery by modifying the forces at the fluid-solid interfaces— that is, by changing the preferential wettability. An earlier paper: presented evidence to show that some reservoir systems could be changed from preferentially oil-wet to preferentially water-wet by the action of simple chemicals added to the water to increase waterflood oil recovery. The process was attractive for further study because it used only inexpensive chemicals and because it called for a gross "wettability reversal" rather than for a precise adjustment. The present paper is an extension of the earlier work. Laboratory flow tests were made using treated water and oil in a consolidated core to determine the amount of additional oil recovery and the producing performance which might be expected from reversing the wettability of an oil-wet reservoir during a flood. A contact-anglc study using water and oil from the Muddy "J" sand of the Harrisburg field, Banner County, Neb., indicated the reservoir to be preferentially oil-wet and susceptible to wettability reversal through chemical injection. Based on these studies, a field trial of wettability-reversal water flooding was initiated. in the Harrisburg field. The primary purpose of the trial was to determine if wettability-reversal flooding would improve oil recovery in an actual field situation. The field trial was also an important test of the laboratory tecnique used to determine the effect on oil recovery of certain wettability manipulation, as well as a test of the contract-angle method of determining reservoir wetra-bility. The paper is presented in two parts. The first part covers the laboratory experiments leading up to the field trial, and the second part covers the field trial. PART I—LABORATORY STUDY The laboratory experiments consisted of displacement tests using an idealized fluid system and of a contact-angle study with crude and water from the Muddy "J" sand of the West Harrisburg Unit, Banner County, Neb. The displacement tests were designed to determine the effects of a particular wettability manipulation, oil-wet to water-wet, on oil displacement in a water flood. The contact-angle measurements were made to determine the natural wettability of the reservoir and to determine if beneficial wetting changes could be brought about by a chemical addition to the flood water. PROCEDURE DISPLACEMENT TESTS The displacement tests were perfornled in a consolidated sandstone core using a refined oil and water. The wetting properties of this system could

By G. Thodos, R. B. Grieves

A method has been developed for the accurate calculation of the cricondentberm and cricondenbar temperatures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain any number of components including paraffins and isoparaffins, olefins, acetylenes, naphthenes and aromatics. This approach is based upon the mole fraction of the low-boiling component in the mixture and graphically presents the ratios of the cricondentherm and cricondenbar temperatures to the pseudocritical temperature as {unctions of a boiling-point parameter. The only requirements are the critical temperature, normal boiling point and the approximate vapor pressure behavior of each component. For mixtures of more than two constituents a stepwise calculation procedure is necessary where the pseudocritical temperature is based upon the critical temperature of the pure low-boiling component and upon the actual cricondentherm or cricondenbar temperature of the mixture of all the remaining higher-boiling components. From an analysis of 22 binary systems (123 compositionsl, the average deviation of calculated cricondentherm temperatures from reported values is 0.87 per cent, based on degrees Rankine; and for 10 multicomponent mixtures containing from three to six components, the average deviation is 0.98 per cent. From an analysis of 18 binary systems (104 compositions) the average deviation of calculated cricondenbar temperatures from reported values is 0. 79 per cent; and for 15 multicomponent mixtures, 1.47 per cent. Equations, derived from the graphical relationships, are presented which enable rapid calculations for both binary and multicomponent systems. INTRODUCTION With the increasing tendency towards the use of high pressure processes, the need for an accurate method of calculation of the properties of a multicomponent hydrocarbon mixture in the critical region is becoming more essential. Critical region phase relations are also significant in gas condensate reservoirs, for which a knowledge of the fluid phase boundaries and regions of retrograde condensation make it possible to evaluate optimum operating conditions. The possibility of liquefaction in the underground structure may be established, and information on the feasibility of the use of repressurizing may be determined. A typical phase diagram for a multicomponent hydrocarbon mixture is presented as Fig. 1. This figure also shows the regions of retrograde behavior encountered by following lines AB and AC. If accurate methods of calculating the temperatures and pressures at the critical, cricondentherm (maximum temperature) and cricondenbar (maximum pressure) points of multicomponent hydrocarbon mixtures of known composition were available, it would be possible to estimate closely the entire phase diagram of any mixture. Several methods have been presented in the literature for the estimation of the critical temperatures and pressures of multicomponent mixtures containing all types of hydrocarbons and including the fixed gases.4-8,21 Considering the cricondentherm and cricondenbar points, the work is more limited. Etter and Kay5 have developed rather complex equations for

By T. Sterry Hunt

At the meeting of the Institute in Easton, October, 1873,I made a communication on the Ore Knob copper mine, in Ashe County, North Carolina (Transactions, vol. ii, p. 123), in which I called attention to the chemical decomposition alike of the pyritous lode and the inclosing gneiss rock to a depth of 60 feet, by which the feldspar of the latter had been converted into clay, and the whole rock very much softened. Such a decomposition is well known to be almost universal in the crystalline rocks of the Appalachians south of the Potomac; and if it is only seen in rare and exceptional cases farther to the northward, this, as I have elsewhere pointed out, is due to the fact that the decomposition began and ended in the ages anterior to the drift period, and that the decayed portions which still remained were at that time removed from the surface, except in some localities which were protected from the emding agency. I have lately had an opportunity of studying a remarkable instance of this kind in an examination made last month for the corporators of the Hoosac Tunnel.* The locality is at the western base of Hoosac Mountain, the western slope of which rises rapidly 1300 feet above the town of North Adams, in Berkshire County, Massachusetts, itself 700 feet above the sea level. Through this mountain, as is well known, a tunnel for the Troy and Boston Railroad has lately been opened, a distance of 25,081 feet from east to west. The rock of the mountain consists of mica schist and micaceous gneiss, including in its western half a great mass of harder feldspathic and quartzose strata in part a granitoid gneiss, the strata for the most part dipping to the eastward with variable angles, but with occasional western dips, apparently due to inversion. The crystalline strata of the mountain crest and sides are in many places exposed, and present rounded surfaces, often deeply grooved and striated, but with no appearance of decay. At the western base of the mountain, however, the gneissic rock is in a state of complete decomposition, which was well displayed in opening the tunnel, which, for a distance of several hundred feet, was driven through highly inclined strata so much decomposed that they were excavated with pick and shovel, and without the aid of blast-

By A. L. Holley

The intention of this paper is not to discuss this important subject in all its bearings, but merely to point out why mechanical tests of steel, as ordinarily made, are not, alone, of any special value to engineers—certainly not to general mechanical engineers. The agents of the Barrow Hematite Steel Company, one of the largest and most successful Bessemer establishments in England, have recently distributed a report, made by Sir William Fairbairn,

By R. W. Nelson

Methods for determining permeability presented by W. D. Kruger3 in a paper entitled "Determining Areal Permeability Distribution by Calculation" have considerable merit. They can be expected to contribute significantly to analysis of flow in heterogeneous systems. Some rather subtle yet important conditions must be met, however, to assure that the computed permeabilities are correct. The conditions which insure a unique permeability distribution may have been overlooked in the method as proposed and presented in the subject paper. The subtlety of the special requirements may permit good agreement between computed and measured pressures in the reservoir; but the computed permeability may still be in error. The general theory and discussion of the requirements for a unique determination of the permeability distribution are presented elsewhere in more detail.7'8 Accordingly, only major features will be presented here in the notation of Kruger. GENERAL DESCRIPTION OF REQUIREMENTS A brief mention of the route to be followed in showing the special requirements may be helpful. The equation to be solved is a quasilinear, first-order, partial differential equation in the unknown permeability. This equation can be solved through an extension of Lagrange's method by reduction to a system of subsidiary ordinary differential equations. Through consideration of the identity of one of the Lagrange subsidiary differential equations with the stream function, a special interrelationship can be shown. The interrelationship has special significance with respect to the boundary condition. If the boundary function satisfies part of the subsidiary differential equation, no unique solution for the permeability distribution exists. In the physical problem this requirement for uniqueness indicates that the permeability measurements used as a boundary condition can not be along a stream tube. The boundary condition must be along a line, or series of lines, which completely traverse the region and pass through every stream tube.