Search Documents

By R. W. Smith

It is well known that certain silicates such as the feldspars and beryl can be readily floated from quartz at a low pH value using a long chain cationic collector in the presence of a fluoride.1-3 However, the mechanism whereby the fluoride activates feldspars and beryl is not known. Indeed, only a few authors have even speculated about possible mechanisms.1,3,4 As a first approach to the problem, it is perhaps best to look closely at the interesting character of hydrofluoric acid and how it dissolves silica and silicic acid. Hydrofluoric acid, unlike hydrochloric acid, is a weak acid with a dissociation constant of about 3.53 x 10-4 at 25°C.5 The reason for the weak acidic character of HF lies in the very small size of the fluoride ion.6 The pKa value is 3.45 which means that at pH 3.45 half the HF is present in molecular form and half in ionic form. The anion present is probably HF2.-6 At pH values below the pKa value, molecular concentration increases rapidly at the expense of the HF2- anion. It is known that HF readily attacks glass, silicates, quartz and silicic acid. The equation usually cited pertaining to the first step in HF attack of silica is6-'

Jan 1, 1965

By G. F. Huff, G. R. Bailey, J. H. Richards

An improved bomb-sampling technique for obtaining samples for oxygen analysis from liquid steel is described. Analyses of samples taken from open-hearth furnaces by the improved method show sufficient agreement with laboratory data to indicate the accuracy of the method is better than that of other existing sampling methods. THE bomb-sampling method of determining the oxygen content of a liquid-steel bath was studied by obtaining and analyzing more than 200 samples from normal open-hearth heats. Of these samples, about 60 were obtained with a bomb of conventional design;' the remainder were taken with a somewhat modified bomb designed to give greater protection against slag contamination. In the new device, the contacting faces of the cast-iron mold halves are machined so that they fit closely; the opening at the top of the bomb is covered with a thin steel cap; and the top of the bomb is further covered with a wood block held in place by heavy steel wire. After the bomb has passed through the slag layer and has entered the steel bath, the wire melts and the wood block floats to the surface. Thereafter, the steel melts through the thin cap and flows into the bomb cavity where it is deoxidized with aluminum wire. An assembled bomb, ready for sampling, is shown in Fig. 1. To standardize sampling procedure, the samples were usually taken through the center door and at the bottom of the furnace; that is, the bomb was on the bottom when the metal cap melted. After each addition to the furnace, at least 20 min elapsed before a sample was taken. The oxygen contents of all the samples were determined by using the vacuum-fusion method, two or more specimens from each sample being analyzed. The specimens were cubes of metal cut from a region in the interior of the bomb sample, as shown in Fig. 2. Drillings for carbon analysis were obtained immediately above the oxygen-analysis region. Reproducibility of Results In determining the reproducibility of the results obtained with the modified bomb, the following four factors were studied: 1—variation in the oxygen concentration of duplicate specimens taken from a single sample; 2—variation in the oxygen concentration of duplicate samples taken in quick succession: 3—effect of the amount of aluminum wire

Jan 1, 1953

By C. R. Breck

THERE has been a running discussion over the-past several years with respect to the life and adequacy of our natural gas reserves.. Some of the experts agree on one phase of the subject at least--that eventually it will be necessary to augment deliveries of natural gas in the northern markets by the development of a more or less comparable synthetic gas made from coal. The purpose of this paper is to point out: 1. It may be later than a good many people think-the demand for additional domestic and commercial pipeline gas in at least one section of the North will probably be felt rather keenly before an adequate synthetic pipeline-gas project, developed on economic lines, could be completed, even if ' initiated in the near future. 2. The evidence is considerable that such a project would be technically sound and economically self-supporting, although the margin of profit at first might be so small and the magnitude of an economic enterprise so great that financing would be impossible without Government aid in some form or other. The part of the country referred to is the heavily populated section in the northeast of the United States. To simplify an examination of the situation, let us take the potential marketing areas within range to the north and east of the three pipelines: 1. Tennessee Gas Transmission Co. as it enters Erie County, New York state. 2. Texas Eastern Transmission Corporation just before the tap that supplies the general Philadelphia area. 3. Transcontinental G& Pipe Line Corporation as it enters the state of New Jersey The sources of gas for these three pipelines are in Texas and Louisiana. The ultimate maximum combined capacity of the three lines at the points stated is approximately 1,200,000,000 cu ft per 24 hr at the maximum load factor probable of attainment in normal operation. The areas supplied by the three lines north and east of the points stated, or assumed as eventual markets, are: 1. Central New York state, from Buffalo to Albany (both inclusive).

Jan 1, 1953

By J. M. Roberts, N. Brown

The stress-strain behavior of zinc single crystals was measured over a strain range of 10-6 to 10-2. The phenomenon of macroyielding was observed in detail and plastic strains were detected at almost zero-stress. Closed hysteresis loops were observed during loading and unloading in the strain region of about 10-5. From the hysteresis a frictional stress on the dislocation of about 6 psi was obtained. A preliminary analysis indicates that impurities are primarily responsible for the friction. Nonelastic Strains as much as 10 -4 were recovered depending on the amount of prior deformation. Part of the recovered strain occurs instantaneously upon unloading and the remainder occurs at zero stress. The time dependence of the recovered strain was measured. THIS investigation is concerned with the details of plastic deformation preceding the ordinary yield point as measured with the usual strain sensitivity of about 10-4. The approach leads to internal friction observations in the hitherto neglected frequency range below 10-1 cycles per sec. It is believed that if the phenomenon of macroscopic yielding is to be understood, then the stress-strain curve in the neighborhood of the macroyield point should be greatly magnified. It may then be possible to determine whether macroscopic yielding is a unique event or whether it is a process which begins gradually at a lower stress. In the case of low-carbon steel a unique event obviously occurs at the macroscopic yield point as indicated by a drop in the load, but copper appears to exhibit a gradual transition from the elastic to the plastic state. In zinc the yield point is rather abrupt although the data indicates that some plastic deformation precedes large scale yielding.' One of the purposes of this investigation is to determine whether there is an abrupt transition from the preyield microstrain region to the region of macroscopic deformation. Such a rapid transition would support the concept that there is a critical stress for yielding. The concept that yielding is a unique event associated with such phenomenon as activating a Frank-Read source, freeing the dislocation from solute atoms, dislocations cutting through dislocations, or dislocations moving freely by one another, has been expounded widely on theoretical grounds. It is hoped that highly sensitive measurements of strain in the neighborhood of the macroscopic yield point will shed some light on the event known as the "Yield Point". EXPERIMENTAL METHOD 1) Specimens—High-purity zinc was cast into spherical graphite moulds in air and grown into spherical single crystals by the Bridgman method under a positive pressure of Argon gas. Spectro-graphic analysis of cleaved sections from four crystals showed a purity of 99.994 pet Zn. The specimens were acid machined with an 1/8 in. gage section in a form similar to those used by Parker and co-workers.2 Bausch type grips were fastened to the specimen by Epon VI adhesive. The specimens were oriented so that only [1120] (0001) slip occurred. Fig. 1 shows two of the specimens in the grips. Prior to each test, the gage section of the specimen was given a concentrated HNO3 chemical polish followed by alcohol rinsing and air blast drying. 2) Test Method- The shear tests were performed on an Instron testing machine and the experimental set-up was made very "hard". Strain could be measured to a sensitivity of 10 -6 by means of a capacitance gage extensometer. The design and calibration of this type of extensometer to measure microstrain, as applied to pure shear and tensile tests of metals, will be the subject of a separate paper—therefore, only a brief account will be presented here. The method essentially consists of attaching a

Jan 1, 1961

By WILLIAM WATERS

L HISTORY. THE Pierrefitte mines, situated in the South of France, in the district of the Hautes-Pyrenees, owe their name to the fact that the first mining operations of any extent, and of comparatively recent date, were carried out in the neighborhood of the vil¬lage of Pierrefitte, which is a branch terminus of the Midi railway. The Pierrefitte mines, however, embrace a wide extent of country and several different concessions, on most of which comparatively little exploration-work has been done. The portion of the property presently to be described is a zone running roughly E-W., over a distance of about 5 miles from the valley of Cauterets to the valley of Estaing, the ridge dividing these valleys being a spur of the main chain of the Pyrenees, and running more or less at right angles to it. According to local tradition, which various indications tend to confirm, these mines are of ancient date, the first workings being attributed to the Romans, who are supposed to have sought not only the lead but also the silver which is contained in the ore. Old slags have been found in the neighborhood which might well have been produced from the cupellation of lead-ores. These old workings, while of considerable extent at times, do not seem to have extended beyond a depth of 100 ft., even this depth being somewhat exceptional. The old notarial records of the district show that mines were known to exist, and that they were even worked, in the sixteenth century, but since the mines were abandoned (by the Romans or others) considerably prior to this period, very little

Nov 1, 1908

By R. K. Govila, E. H. Parkison

THE interplanar angles for hcp metals vary with c/a ratio, and therefore must be computed separately for each particular metal or alloy. Manual computation of these angles is laborious and time consuming, and for this reason computer programs have been developed to accomplish this task.1"3 However, these programs have certain disadvantages. For example, they require prior knowledge and understanding of ALGOL or FORTRAN languages. Further, they will not print out specific angles but instead give all angles between given limits—thus program2 prints out a total of 26,649 angles between planes with indices and in the range from (4 4 4) to (4 4 4) for any given c/a ratio. The purpose of this note is to present a simple and inexpensive computer program for accomplishing this task. This program is written in BASIC language4 which does not require any prior knowledge of computer programming, and is ideally suited for nonprofessional programmers. It also provides flexibility for the user by allowing him to select any indices for as many or few planes as desired for any given c/a ratio. The computer program proposed below is based on the relationship in which + is the angle between any two planes and . TO illustrate use of the program, consider the problem of calculating the interplanar an-

Jan 1, 1970

Jan 1, 1967

By B. F. Zwick

The entire production of oil in Ecuador so far has come from the Santa Elens Peninsula, Province of Guayas. Both the shallow fields of the northern and the deeper fields of the southern part of the peninsula have been in constant exploitation, though the former are of doubtful economic value. In Table I herewith, which commences with the total amounts produced by the various companies up to 1940, annual company totals are given for the succeeding years. The figures for 1944 have been partly estimated. Table 2 gives figures on casinghead gasoline. Shell Company of Ecuador (formerly known as Anglo-Saxon) has continued active exploration in the Oriente region east of the Andes, and during 1944 the Company's first wildcat well was spudded in. International Ecuadorean Petroleum Co. (formerly International Petroleum Co., Limited) has pursued an active exploration campaign since the latter part of 1939, and a drilling string was placed in operation about a year later. A second string of tools was added during 1943 and a third a few months ago. Ten wildcats, all dry, have been completed in this period, two wells are drilling at the present time and other locations are on the program. Seven of the wells thus far drilled are in the area between Guayaquil and the Santa Elena Peninsula, one up the Daule River beyond Balzar, one on Puna Island in the Guayas Estuary and one in the northern province of Esmeraldas. Both the present drilling wells are in the Guayaquil-Santa Elena zone. The situation in regard to concessions has changed during the past four years because I.E.P.C. has made its selections from the extensive Daule-Guayas Study Concession, as a result of which large tracts were returned to the Government; because of the expropriation of the holdings of the "Ecuapetrol," a German concern whose acreage has passed into other hands; the Peruvian-Ecuadorean boundary settlement, which has reduced Shell's holdings somewhat; and the transfer of most of the holdings of the Cia. Minero-Petrolera del Pacifico to I.E.P,C. The greater part

Jan 1, 1945

By E. R. Funk, H. Udin, J. Wulff

The surface tension of solid silver is measured by a refinement of the Udin, Shaler, and Wulff technique. The tests were made in a purified helium atmosphere at four different temperatures and various times. The average of the results is y = 1140 + 90 dynes per cm for the range 875° to 932°C. A SUCCESSFUL measurement of the surface tension of solid copper was reported by Udin, Shaler, and Wulff.' They performed experiments on copper held in vacuum within 100°C of the melting point. At these temperatures, the creep rate in 5 and 3 mil copper wires was sufficient to permit determination of a balance between the contractile force of surface tension and the extending force of small copper weights joined to the end of the wire specimens. By suspending a series of variously weighted specimens and measuring the change in a gage length during the test, the balancing applied load could be found. This point of zero strain is a measure of the surface tension. The mathematical formulation of this gives: w = r y [1] where w is the weight for zero strain; r, the radius of the wire; and y, the surface tension. A subsequent note by Udin pointed out that eq 1 applies only to single-crystal specimens. Since the specimens used revealed a "bamboo" structure upon

Jan 1, 1952

Organization Place Date 1919 American Railway Engineering Association Chicago, 111. Mar. 18-20 Society of Industrial Engineers New York, N. Y. Mar. 18-21 American Electrochemical Society New York, N. Y. Apr. 3-5 National Foreign Trade Council Chicago, Ill. Apr. 24-26 American Iron and Steel Institute New York, N. Y. May American Institute of Electrical Engineers Lake Placid, N. Y. June

Jan 3, 1919

By Rudolph G. Wuerker

THE Krupp-Renn Process,[1] has been successfully used to treat low-grade iron ores, laterites, titaniferous sands, and other minerals, and before World War I1 25 units were built by the Krupp-Grusonwerk, Magdeburg, Germany. J. J. Howard[2] has shown theoretical advantages of the pyro-metallurgical treatment over conventional approaches; and the process was described by R. Durrer[3].

Jan 1, 1951

By M. K. Foster

Ten horizontal retort zinc blocks of a modified Hegeler design are in operation at Nueva Rosita, Coahuila, Mexico, and produce approximately 170 t of spelter daily, or 62 000 t/year. A block consists of two furnaces of 448 retorts each, making 8960 retorts as the plant complement. Each furnace block is fired with natural gas and air maintaining the combustion mixture in the furnace always slightly reducing. No attempt to recover energy through waste heat boilers is made. The spelter moves to market by rail and truck either in palletized bundles weighing approximately 1060 kg, as loose slabs weighing 26.5 kg each, or as 1088 kg ingots. At present 46% of the metal is exported and 54% is consumed domestically in Mexico. The present day trend toward equalized or alloyed spelter, as well as special shaped castings results in sales of 35% of the entire plant's production. Sulfuric acid is also produced by the Contact Process using vanadium pentoxide as the catalyst. The plant is basically a Monsanto contact system, producing approximately 68 t of 100% sulfuric acid daily. Both 98.5% sulfuric acid and 20% oleum are available. All of the acid made is consumed in Mexico. Shipments are made in 26,900 dm3 tank cars.

Jan 1, 1970

The Board of Directors, at its meeting on March 22, 1918, extended an invitation to the American .Institute of Metals to become the Institute of Metals Division of-the American Institute of Mining Engineers in accordance with the terms of By-Law VII. This invitation was presented to the membership of the American Institute of Metals for letter ballot, and, at the meeting of the Board of Directors of the American Institute of Mining Engineers on April 26 191 ,it-was reported that the replies had been in favor of accepting the invitation. The American Institute of Metals therefore becomes a division of this Institute and the members thereof are entitled-to all privileges of regular

Jan 6, 1918

By Jack L. Taylor

WITH the exception of the work of Vogel,&apos; and Rolla and Iandelli, very little information has appeared in the literature on titanium binary systems with the rare earth elements. Rare-earth additions to titanium alloys may possibly parallel the beneficial effects on the physical properties of certain steels. Having this in mind, some knowledge of solubility limits and intermediate phases, if any, would be useful. An investigation of the titanium-rich Ti-Ce system was started. Alloy Preparation The iodide titanium from the New Jersey Zinc Co. and the cerium metal from the Institute for Atomic Research Ames Laboratory used in this work were supplied with the typical analysis shown —iodide titanium: 0.0065 pct Mn, 0.0022 pct Fe, 0.0015 pct Cu, and 0.0042 pct Pb; cerium metal: <0.01 pct Fe, <0.03 pct Si, <0.05 pct Ta, <0.02 pct Pr, <0.03 pct Ca, <0.02 pct Mg, with no trace of Nd, La, or Th. The cerium metal, stored in oil, was washed and scraped just before weighing into capped cups machined from iodide titanium. The cold hearth helium-arc furnace described by Schramm et al3 was used for melting. The alloy buttons from the arc-melted cup were cut in two, mounted, and examined. Homogeneous alloys were demounted and rolled to approximately 1/4-in.sq bars. Sections l/8 in. thick were cut from the bar to provide samples. The Ti-Ce alloy buttons analyzed for cerium were of the following composition: 0.19, 0.36, 0.48, 0.61, 1.15, 2.52, 3.06, 3.70, 4.30, 9.20, 14.26, and 18.50 wt pct. Nominal

Jan 1, 1958

By R. W. Baldwin

On page 309, column 1, the second equation should read: Ma-M1 = dlog_Pa M2-M1 d log P2

Jan 1, 1961

By R. Simon, L. Yarborough

This paper presents a correlation for predicting the critical pressures of gas-solvent-reservoir oil systems of the type encountered in gas and solvent injection processes. Experimental data from 14 systems were used to develop the correlation which expresses critical pressure as a function of composition, C7+ mol weight, and C7+ characterization factor. Critical pressures predicted by the correlation for the 14 gas-solvent-reservoir oil systems have an average deviation of 2.8 per cent of the experimental values. The correlation war used to study a wide variety of other hydrocarbon mixtures reported in the literature whose critical conditions are in the range of interest in oil recovery work (100 to 280F and 2,000 to 6,000 psia). Critical pressures predicted by the correlation had an average deviation, expressed as per cent of experimental value, of 5 per cent for 20 miscellaneous mixtures from the literature, and 6.4 per cent for I7 methane-butane-decane mixtures reported by Sage and Lucey. INTRODUCTION Predicting critical points of hydrocarbon mixtures is an important part of phase behavior calculations. If the critical point can be predicted for a specific mixture, the separation between the bubble-point and dew-point regions will be defined, and physical properties of the mixture can be calculated by using the principle of corresponding states. Numerous correlations for predicting critical points of hydrocarbon mixtures have been published. Six of these correlationsl-8 were for light hydrocarbons, and two correlations7,8 ere for high boiling-point petroleum distillates. Organick9 And Eilerts" presented correlations which combined the published data from both light and heavy mixtures, and these correlations became the only available methods for predicting critical pressures for wide boiling range mixtures. In the course of the authors&apos; work on secondary recovery by gas and solvent injection, experimental data were obtained for 14 mixtures of dry gas, ethane-propane-butane solvents, and various reservoir oils. The critical pressures and critical temperatures of these gas-solvent-reservoir oil systems were in the range of 1,900 to 4,800 psia and 180 to 265F. The critical pressures predicted for the 14 mixtures by the correlations of Organick and Eilerts had an average deviation from the measured values of about 13 per cent. The authors felt that it was necessary to develop a better correlation for engineering calculations and the resultant correlation, which is presented on Figs. 1 and 2, predicts the critical pressures of the 14 mixtures with an average deviation of 2.8 per cent. The validity of the correlation was tested by applying the correlation to other hydrocarbon mixtures reported in the literature. This subject is discussed later in the paper. The authors feel that there is also a need for an improved critical temperature correlation for gas-solvent-reservoir oil systems. However, developing a critical temperature correlation is a significant study in itself and is not included in this paper. EXPERIMENTAL DATA The compositions and critical points obtained by the authors for 14 gas-solvent-reservoir oil mixtures are shown on Table 1. The methane concentrations in these mixtures varied from 20 to 63 mol per cent. The intermediate hydrocarbon group, consisting of ethane, propane, and butane, varied from 20 to 64 mol per cent, and the concentration of the C,, fraction from 10 to 20 mol per cent. The physical properties of the C,, fraction covered the range from light, paraffinic, nonasphaltic (Mixtures 5, 6, 7, 8, 9 and 10) to heavy, aromatic, and asphaltic (Mixtures 13 and 14).

By Carl Henrich

Jan 1, 1893

By Paul R. Bluekamp

The Mather Mine property is composed of a 5.2 sq km (2 sq mile) area within the Cities of Ishpeming and Negaunee which are located in the Upper Peninsula of Michigan. Production in this mine started in 1943; it ran continuously until its closing in 1979, having produced slightly over 55 million tons of iron ore. This mine was a joint venture between several steel companies and The Cleveland- Cliffs Iron Company (CCI), with CCI being the fee holder and operator. For the first 17 years of operation, the ore was shipped in its natural state directly from the mine to the steel mill. By 1960, iron ore pellets were on the market and they proved so superior to the natural soft Mather ore that the latter became difficult to sell except for the coarser portions. It was decided to develop a pelletizing process for the Mather ore, and this was accomplished by 1965 when the first Mather pellets were produced. From this date, all but the coarse fraction of the Mather ore was shipped as pellets. The geological setting is that of a large east-west trending synclinorium which plunges to the west. The lowest member of this trough-like structure is, for the most part, a quartzite-like graywacke, the upper 20 m of which grades into a softer, fine grained slate. Lying conformably on this graywacke footwall member is an iron- formation member which is over 1,300 m in thickness. This iron-formation is cow posed of thin alternate bands of iron oxides and chert and is intruded by a number of diorite sills - some up to 122 rn (400 ft) in thickness. The north limb of this synclinorium dips at approximately 45&apos; and bottoms out at about 1,000 m from surface in the central part of the mine. There are two sets of faults, many of which are intruded by diorite dikes, which trend east-west and southeast-northwest. Displacements are varied, reaching a maximum displacement of 243 m (800 ft). The ore is found lying directly on the slatey footwall and its position is largely controlled by the faults and dikes, with the bulk of the ore being on the upper side of these structures. The ore is composed of soft earthy hematite and martite with vertical thicknesses up to 122 m (400 ft) although the average thickness would be closer to 46 m (150 ft). The ore averaged 60% iron and 7% silica on a dried analysis. The Mather Mine is located on the north limb of the syncline and was worked from two shafts, the deepest of which. was 1,09 7 m. These two shafts are about 2 km apart and serviced a total of 8 working levels between them during the life of the mine. The level spacing was about 61 m (200 ft). The main haulageways were driven parallel to the ore/footwall contact in the hard cow petent graywacke wherever possible. On the lower levels, deeper into the footwall, naked development was common. This material graded into roof bolting ground towards the upper stratigraphic portion. As drifting progressed further into the upper stratigraphic portion of the footwall, progressively stronger steel sets had to be used. From the main haulageway, cross-cuts were turned into the orebody on 61 m (200 ft) centers and extended as far as needed to recover the ore available to that particular cross-cut. The main haulageways and cross-cuts were driven 3 m (10 ft) high, 3 m (10 ft) wide at the top and 4.6 m (15 ft) wide at the bottom. This configuration would accomodate a set composed of a 2.7 m (9 ft) cap on top of two 2.7 m (9 ft) legs angled out at 18&apos;. A sill plate was used under each leg to prevent its sinking into the ore below. The type of steel used was dependent on the expected weight to be experienced. Sets were placed on 1.63 m (5 ft 4 in.) centers; however, in extremely heavy areas, it was sometimes necessary to install sets on 0.8 m (2 ft 8 in.) centers. On the top two levels (5th and 6th), the ore was considerably hard-er and was mined by sub-level stoping and long hole drilling. Very light steel sets were used in the main haulageways and cross-cuts and timber was used in the production drifts. Some con- crete production drifts were installed on 6th level, but proved to be uneconomical. However, as mining reached greater depths, the ore became softer and more massive, reaching its maximum vertical heights on 11th and 12th levels. On levels 7 through 10, yielding steel sets were used extensively in the slusher drifts. While they were satisfactory on 7th and 8th levels, their success diminished with depth and they were

Jan 1, 1981

By Albert S. Trube

Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of reservoir fluids well in advance of more accurate laboratory data. One such factor is the isothermal coefficient of expansion of an undersaturated hydrocarbon liquid which may be contained in a particular reservoir. This coefficient, or liquid "compressibility", has often been assumed to be relatively insensitive and nearly constant. Although this assumption may be nearly correct in the case of high specific gravity liquids, it cannot apply in the case of medium to low specific gravity liquids. Any treatment of the nature of liquid compressibilities must give consideration to the variable nature of the isothermal expansion coefficient and the fact that it can be both pressure sensitive and temperature sensitive. The isothermal coefficient of expansion, or compressibility, of a substance is defined as -c = 1/V (?V/?p)T......(1) The value of Eq. 1 may be approximated for a finite pressure change by using the well-known relation, c = V1 - V1/Ve (p2-p1), ........(2) in which p1 > p1 and V2 > V2 and V1 + V2/2. The instantaneous compressibility may also be estimated from the slope of a curve on which log V is plotted vs pa. In this instance, it has been shown that c = In V1/V2/p2-p1 ...........(3) Eq. 3 may be used for variable compressibilities by plot-ting V vs p on semi-log paper. In this case, the instan-taneous or point compressibility is c = 2.303 m.......... . (4) in which m is the slope of the curve at a point in log cycles per psi. ISOTHERMAL COMPRESSIBILITY OF UNDERSATURATED LIQUID In the case of gases, the compressibility has been defined by Muskat&apos; and others as Co = 1/p - ?z/z?p ..........(5) This was later generalized through application of the theorem of corresponding states&apos; to co = 1/pr - (?z/z?pr) T8 ........(6) in which c, is defined as the pseudo-reduced compres-sibility and is numerically equal to (c.p,) and the sign is arbitrarily changed for mathematical convenience. Eq. 6 is general and applies to gases and liquids. In the case of liquids, c. = c1,pe, but if Eq. 6 is used, values of z and ?z/?p, must be determined for the liquid in question. The difficulty of obtaining accurate values of ?z/?p,, particularly in the region where T, is approaching 1.00, was pointed out in the previous paper&apos;. This method of approach is unreliable for extension into computations of liquid compressibilities. On the other hand, c, can also be defined as follows: - Cr = 1/Vr (?Vr/?pr) Tr ......(7) and from which, Cr = 1/pr (?pr/?pr) Tr .....(8) In accordance with the theorem of corresponding states, Vr = V/Vr, p, = p/pr and pr = p/pr. Ref. 2 pro-vides an excellent source of reduced density, reduced pressure and reduced temperature data for a wide variety of fluids. For the purpose of this investigation, the set of fluids2 having ze = 0.27 was chosen because it in-cludes most of the heavier hydrocarbons usually found in those complex mixtures loosely defined as "reservoir oils". Data on undersaturated liquids in Ref. 2 were rearranged to conform with Eq. 8. To simplify the computation of cr, the isothermal p, data were plotted vs the log of pr, in which case for any straight line or tangent cr = 1/M pr pr .....(9)

Jan 1, 1958

By Henry Howe

FIG. 1 shows a volute aging break which developed spontaneously in a hardened and tempered steel helmet between 19 and 38 days after it had been tested ballistically. A similar break, shown in Fig. 2, developed spontaneously in a similar helmet about 40 days after the ballistic testing. In this case the rupture occurred abruptly and with a loud report. The path of rupture in this second case, though much the less regular, is the more interesting of the FIG. 1. FIG. 2. two, in that it is an approximation to two parallel volutes centered at the point of impact of the projectile, just below D. Several weeks later, after the photograph for Fig. 1 was taken, a similar doubling of the volute crack occurred in this helmet, starting from the end of the eyelash crack near A and spreading thence to the left contra-clockwise for about ½ in. The negatives from which these pictures are made have not been touched up in any way, save writing the letters on them. In both cases the trajectory of the bullet was normal to the initial surface at the point of impact, and in both the helmet passed the ballistic

Jan 2, 1919