Search Documents

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

By C. E. Birchenall, H. M. Schadel

THE purpose of this study was to measure the vapor pressure of silver as the first step in the determination of activities in silver alloys and to test the limitations of the method adopted. In order to work at low pressures, below 2x10-2 mm of mercury, the orifice effusion technique was employed. To shorten the time of collection of silver from the atomic beam, radioactive silver (Ag110) was used as a tracer. The rate of effusion of a monatomic vapor from an "ideal" orifice, where the thickness of the orifice edge is negligible compared with the orifice diameter, can be readily calculated from the kinetic theory of gases, G = vM a p/v2pRT where G is the weight of material effusing from the orifice per unit time; p is the vapor pressure at oven temperature, T; R is the gas constant; M is the molecular weight of the vapor; and a is the orifice area. Consolidating constants and expressing as the weight of material effusing from the orifice in a period of time, t, (5.83)(10-2) (vM) (a) (t) (p)/vT where GT is total weight of monatomic vapor effused (g); M is molecular weight of the effusing tracer vapor; a is orifice area (cm2); t is time of effusion (sec); p is vapor pressure of effusing material (mm of Hg); and T is oven temperature (OK). The vapor effuses from the orifice in a hemispherical pattern, and the intensity of the beam in any direction is given by the cosine distribution law.&apos; Considering this, the weight of effused material can be calculated from the amount of material passing through a circular collimator intersecting the beam. If such a collimator is in a plane parallel to the plane of the orifice and with center on the normal to the orifice center, GT = G?/1-cos2? = G?/sin2? where G? is the weight of effused material passing through the collimator, and 0 is one half the apex angle of the cone defined by the collimator circumference and the orifice center. Reducing eq 3 to the more directly measurable quantities of orifice to collimator distance, d, and collimator diameter, D, the expression becomes,

Jan 1, 1951

By W. F. Holbrook

THE problem of sulfur control is important in all blast-furnace operations but particularly for certain grades of steel because of the rigorous specifications. During the past decade the tendency has been to produce pig iron, and, hot metal of lower sulfur content. As most of the sulfur in the ion originates in the fuel, the use of high-sulfur coke demands modifications in practice to meet sulfur specifications. While it is generally known that high temperatures and more basic slags favor desulfurization, operators as a rule produce the most acid slag that will permit proper desulfurization. The viscosity of blast-furnace slag has been thought to be related to desulfurization and has been investigated by Feild and Royster1, also McCaffery and his associ-ates2, but apparently no systematic effort has been made to determine the relative desulfurizing powers of slags over the range of composition encountered in practice.

Jan 1, 1936

By E. C. Houston

The phosphate ores mined in middle Tennessee typically consist of granular rock phosphate particles disseminated in a clayey matrix. In the TVA plant near Columbia, Tenn., the phosphate ore is mined, made into a slurry with the addition of a small amount of sodium hydroxide as dispersant, and treated in a hydroseparator to remove minus 10 micron material. The hydro-separator underflow, comprising a rough concentrate, is transported by pipeline to the plant; the hydro-separator overflow, comprising a tailing, is flocculated by addition of calcium sulphate and is discharged to settling ponds at a rate of about 1400 gpm. Sedimentation in the ponds produces a clarified effluent, which may be recycled for use as process water or discharged to surface drainage. This method of tailing treatment is not entirely satisfactory since poor sedimentation characteristics of the tailing result in poor ultimate utilization of pond storage volume.

Jan 1, 1949

By THOMAS G. FEAR

THE COAL DIVISION started its share of the annual meeting Monday morning with a study of coal classi fication. A. C. Fieldner was in the chair. The report of the tellers of the ballot for division chairman, stating that Thomas G. Fear had been elected to that office, was read by M. D. Cooper. Mr. Fear acknowledged the honor in a few words. In reviewing the history of the Coal Classification Committee the chairman pointed out that this was its third symposium, the last previous one having been held at the 1930 Annual Meeting. Throughout its work the com¬mittee has had the active cooperation of the Canadian workers who are interested in the subject which should result in a uniform scheme of classification in Canada and the United States. F. E. Lathe, of the National Research Council, Ottawa, abstracted the first two papers of the session entitled "Determination of the Alkali-Soluble Ulmins in Coal," by Edgar Stansfield and K. C. Gilbart, and "Moisture Determination for Coal Classification," by the same authors. The third paper "Condition of Water in Coals of Various Ranks"&apos; was presented by its author, A. W. Gauger. Written discussions of these papers were presented by H. C. Porter and Gilbert H. Cady. In the oral discussion which followed, W. T. Thom, Jr., brought out the advisability of considering age as a factor in classification. Mr. Fieldner favored retaining bed moisture as a partial classification basis, stating that a review of many coal analyses revealed a remarkable consistency in this item in samples from a given mine particularly where the moisture content was not high. Mr. Porter pointed out that the structure and porosity of coal often have much to do with its moisture content and that these vary in different parts of a seam, particularly in anthracite. Mr. Gauger expressed doubt as to whether the Stansfield method gives the true moisture content of coal, which is needed for classification purposes.

Jan 1, 1932

By Thomas Leonard Watson

SULPHIDE ore-bodies of more or less lenticular shape occurring in metamorphic crystalline schists, gneisses, and. slates, and conforming closely in strike and usually in dip to the inclosing rock, have been recognized and described along the, Atlantic seaboard from Quebec to Alabama. The ore-bodies do not entirely conform, in all cases, to the structure of the inclosing schists, but they sometimes cut across the foliation in dip, though conforming more closely with the direction of strike. In composition the principal sulphide mineral is usually pyrite or pyrrhotite; or both, accompanied by copper, frequently gold, and almost always some sphalerite and galenite. Other. metallic ores are, so far as these sulphide bodies have been investigated, less common; silver is not uncommon, and in some of the pyrrhotite masses nickel is present in quantity sufficient to be commercially valuable. Cobalt frequently accompanies .the nickel, usually in smaller amount, and the two vary much in relative proportion. Quartz and calcite are probably the most common of the, non-metallic minerals. A number of silicate minerals are frequent representatives in one place or another; garnet, amphibole, biotite, pyroxene, zoisite and others. The sulphide bodies of Virginia, comprising both pyrite and pyrrhotite, are among the most extensive along the Atlantic seaboard. Among the pyrite bodies may be mentioned the well-known and extensively worked mines of Louisa and Prince William, counties, located on&apos; the main pyrite belt (A, Fig. 1) of the middle and northern, eastern Piedmont region in Virginia, and among the pyrrhotite bodies is the famous " Great Gossan Lead "(B, Fig. 1) of the Floyd-Carroll-Graysou coun-

Sep 1, 1907

By F. G. Cottrell

(New York Meeting, February, 1912.) ABOUT a year and a half ago, at the San Francisco meeting of the American Chemical Society, in connection with the excursions to local smelting-works, I had occasion to show some lantern-slides illustrating the recent commercial development of electrical methods for precipitating the suspended matter from smelter-smoke, the underlying phenomena of which were clearly brought to the attention of the technical public by Sir Oliver Lodge as long ago as 1884. In the Journal of industrial and Engineering Chemistry, August, 1911, most of these views were reproduced, together with an account of the work from its beginning up to July, 1911. To-day I wish particularly to show you some of the further developments of the work since that time; but in order to make these clear they will be prefaced by a brief abstract of the article above referred to. The removal of suspended particles, front gases, by the aid of electric discharges is by no means a new idea. As early as 1824 we&apos; find it suggested by Hohlfeld 1 as a means of suppressing ordinary smoke, and again a quarter of a, century later by Guitard.2 These suggestions, which do not seem to have stimulated any practical study of the question, were soon entirely forgotten, and only brought to light again by Sir Oliver Lodge,3 many years after he himself had independently rediscovered the same phenomena and brought them to public attention 4 in a lecture before the Liverpool Section of the So-

Jul 1, 1912

CONTENTS PAGE FULTON, CHARLES H., and READ, J. BURNS-A New Roasting Furnace for Zinc Flotation Concentrate. Discussed by Charles H. Fulton, Arthur S. Dwight, B. M. O&apos;Harra, Kurt Stock 1 STOCK, KURT.-Redistillation of Zinc. Discussed by G. E. Dalbey, Kurt Stock.. 3 BEASLEY, F. E.-High Zinc in Lead Blast-furnace Slags. Discussed by R. C. Canby, R. L. Lloyd, C. R. Haywood, G. E. Dalbey, A. S. Dwight, E. P. Mathewson, A. L. Walker, B. M. O&apos;Harra, and C. P. Linville 4 STEELE, E. W.-Application of Pulverized Coal to Copper Refinery Furnaces. Discussed by F. R. Pyne, E. P. Mathewson 11 LINVILLE, C. P.-Recovery of Arsenic and Other Valuable Constituents from Speiss. Discussed by C. R. Hayward, C. P. Linville, G. E. Dalbey, A. S. Dwight, Edward F. Kern, Karl Eilers, E. P. Mathewson 12 A New Roasting Furnace for Zinc Flotation Concentrate Discussion of the paper of CHARLES H. FULTON and J. BURNS READ, presented at the New York Meeting, February, 1925, and issued, as Paper No. 1362-D, with MINING AND METALLURGY,. October, 1924. G. E. DALBEY, East Berlin, Conn. What would be the, effect on the formation of sulfates of an increased water vapor content in the roasting gases? CHARLES H. FULTON.-I cannot answer that from our experience. The question of the formation of sulfate in the roasting of zinc is mainly one of temperature and the concentration of S02 and S03 in the gases. We found we could roast almost completely to sulfate if the concentration was kept at the proper point. We, however, did not care to do this because we wished to make a 5 to 6 per cent. S02 gas for sulfuric-acid work. The sulfating of the zinc oxide in the proper concentration of gases goes on very rapidly. There are certain places in the furnace system such as the Cottrell and in a part of the dust chamber in which the roasted

Jan 6, 1925

By Ralph H. Sweetser

BENEFICIATION of iron ores from the blast-furnace point of view means more than the usual enrichment of the iron contents by the removal of a large part of the clay, carbonic acid gas, silica, or moisture of the natural ore; it includes all these, but it also embraces several other mechanical .processes made , necessary by the exacting requirements of present-day blast-furnace practice. The increasing use of iron- bearing by-products, to as much as a third or more of the total ore burden, has introduced still another series of processes for improving the blast-furnace ore burden. As we look back over the past three decades of blast- furnace practice &apos;in. this country, we see that many of the blast-furnace troubles were directly due to lack of proper preparation of the iron ore burden,, and we realize that beneficiation in one form or another would have remedied the trouble. This was particularly true in the smelting of magnetic iron ores, where run-of- mine ore included such big lumps of &apos;magnetite along with rich fines that the furnace operations were greatly retarded and control of the furnace such as is usual today, was completely unknown.

Jan 1, 1930

By Thomas J. Menner

Jan 1, 1983

By Frank Milliken

IN September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1007 to 1019. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was dissemi-nated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was prob-ably less than 6o per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a com-plete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof com-prised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. 1, which gives percentages of tonnage and copper content.

Jan 1, 1940

By AIME AIME

THE annual meeting of the A.I.M.E. was fittingly closed with a joint meeting of the Metropolitan sections of the four National societies on Feb. 18, at which this subject was adequately discussed by leading engineers before an audience that completely filled the Engineering Auditorium. The large amount of publicity that has been given the Diesel electric loco- motive, and the often garbled reports of its performance and possibilities that have been circulated, makes it particularly fitting that the facts should be given the profession as determined by those who have aided in developing and operating this latest form of prime- mover in railroad operation. C. A. Stein, general manager of the Central R. R. of New Jersey, opened the meeting with a discussion of the problem of electrification, and the relation of the short haul, switching, and terminal service to heavy electrification. Referring directly to the problem of the Central R. R. of New Jersey, some subtitution for the steam locomotive is necessary within the city limits of New York because of local ordinances against the smoke nuisance. While the improvement in the design of the steam locomotive has been marked-the efiiency today is over fifty times that of the locomotive of 100 years ago-it has now probably reached the point of maximum perfection. If anything, it is open to the criticism of having Coo many appliances to get out of

Jan 1, 1926

By Blamey Stevens

(San Francisco Meeting, October, 1911.) My previous paper is entitled, The Laws of Igneous Emanation Pressure. The present paper lays no claim to the exactitude and completeness of a law, since it is of a provisional nature and may be disregarded when experiments have established a basis for more exact reasoning. The general physical states in which aqueous emanations may occur are first considered. The possible physical conditions under which the mineral elements may occur in emanations are then discussed, and a classification of deposits, dependent on emanation, is proposed. A system of scientific experimental investigation is outlined, and it is shown that the physical and chemical properties of emanation may be exactly determined thereby. The investigation is urged as feasible and simple, and not necessarily requiring large and costly apparatus. It is the only step necessary to make possible the formulation of a complete set of laws of igneous emanation. Process of Emanation. In a rising column, magma ranges in temperature from 900° to 1,200°C. Exhalation must begin at some fairly great depth. What this depth may be we can only surmise, since no experimental evidence is available. Exhalation, however, continues as the magma flows upward, until at another level the occluded gases have all escaped. This depth is probably upward of 5,000 ft. (See Fig. 1.) All exhalations must come from between these two levels. As the whole emanation is the sum of the exhalations and residues, the residues must come from below the uppermost level. They will be most abundant when coming, from those parts of the intrusion which have solidified below the lower level.

Apr 1, 1912

By Charles H. Morgan

THE case of Henry Cort comprises: (1) the nature of Cort&apos;s inventions;, (2) their value to England and to mankind,; (3) the remuneration received therefor by him or his family; and (4) the suitable permanent record and recognition of his services by the representatives of the art lie founded-a debt long over-due, and still unpaid. I. CORT&apos;S INVENTIONS. Under this head, it is unnecessary here to enter into details. The facts have been repeatedly published, and a brief outline of them will be sufficient for my present purpose. . Henry Cort, born in 1740 at Lancaster, England, became a navy broker in. London about 1765, and gained from that business in about ten years. something more than £20,000, which lie devoted to perfecting the manufacture of iron, building a mill at Fontley, near Portsmouth, and prosecuting, between 1777 and 1783, the experiments which culminated in .his two patents, one for puddling iron and the other for shaping it by rolling between grooved rolls.: Careful study of the contemporary evidence, including Cort&apos;s specifications, the testimony (in act as well as word) of his business rivals, the public declarations of eminent authorities, and the history of the times, leaves no possible doubt that Cort was the real inventor, of

Mar 1, 1905

By Grimes, J. A.

EXTENSIVE discovery &apos;and rapid exploitation of orebodies within the past half century have attracted many able geologists to the mining industry and furnished them a wealth of data from which to develop theories concerning ore genesis. By tosting and elimillating theories which are not sufficiently sup- ported by fact, or which are based on inaccurate observation of field data, the trend of geological opinion has . moved strongly in certain directions until, at the present time, large numbers of geologists subscribe to a broad concept of .ore genesis that I would summarize as below:

Jan 1, 1928

By Paul E. Richardson, Edwin E. Maust

Cyclic voltammetry and surface potential (photovoltage) measurements have been carried out on galena electrodes in sodium tetraborate solutions with added HC1 and NaOH to adjust the pH over the range 2 to 13. The first technique shows that the surface species formed on moderate anodic polarization and reduced on subsequent cathodic polarization are the same over the entire pH range. At anodic potentials, a soluble metal species and excess sulfur are formed; at cathodic potentials, sulfur is reduced to a soluble species. More importantly, excess surface sulfur is formed spontaneously under zero current conditions in alkaline solutions. This has been shown to occur on both polished surfaces and on virgin surfaces produced by in situ cleavage under the electrolyte. The photovoltage gives some insight into the charge and potential distribution at the galena surface. This is found to depend on past electrochemical history and the n- or p-type semiconducting character of the electrode and is interpreted in terms of changes in the surface stoichiometry that occur during reduction or oxidation. The effect of surface stoichiometry on subsequent xanthate interactions is discussed.

Jan 1, 1976

By W. A. Barrows, Carl Zapffe

Jan 1, 1913

By R. W. Raymond

(Pittsburg Meeting, March, 1910.) IN the long list of our illustrious and lamented dead, there are names which recall personality as well as career and achievement; social as well as scientific merit; devotion to the Institute itself as well as to some one of the professions which it represents. These men we remember because they did not forget us; besides our pride in their wider work and fame, we are proud of what they did with and through us; especially do we rejoice if our early recognition of them opened the way to a recognition by the world; and in their departure we claim to sorrow, not merely as members of an appreciative public, but also as. bereaved personal friends. In common with thousands, we regret our loss, but we do not regret only-we mourn and miss. To this group of those whose death has brought to us the double sense. of public and private grief belonged our strong, bright, dear brother, in whose memory this inadequate tribute is offered. Charles Benjamin Dudley was born July 14, 1842, at Oxford, Chenango county, N. Y. He came on both sides of New England blood, his father being from New Hampshire and his mother from Connecticut. Emigrating from the rocky hills of their native States, they. settled upon the more fertile soil of what was then regarded as the West, and, with thousands of other pilgrim sons, imitating the pilgrim fathers, contributed to the foundation of new commonwealths. The Empire State owes much to this element of its population. Dudley&apos;s early education was obtained, like that of the sons of the pioneers generally, by attending the village school and academy in the autumn and winter, while he worked upon the farm during the rest of the year. But his ambition looked forward to a college-course; and this was almost within his reach when a passion still stronger took possession of him. The out-

Jun 1, 1910

By J. A. Clum, R. W. Heins, T. D. Tiemann

The use of Na-montmorillonite clay hinders (Western Bentonite) in the pelletizing of iron ore concentrates is well established as is the idea that alternative binders must be found. 1-6 This note summarizes work done7 in evaluating a Wisconsin montmorillonite clay binder. The clay occurs in irregualr beds overlying the Prairie du Chien Dolomite and the St. Peters Sandstone near Hersey, St. Croix County. The raw Wisconsin clay contained 65% quartz and 35% clay minerals. The Na20to CaO ratio was 0.234. Suspension viscosity tests of the raw clay gave results only slightly better than water alone, even after treatment with activator materials. Sedimentation treatment reduced the quartz in the decantate to 5% after 240 min (four hours). Twenty minutes of sedimentation produced a decantate with 27.5% quartz which was found as effective as the 5% quartz decantate in pelletizing behavior. The 20 min decantate was used in subsequent tests. The decantate was filtered and dried at 110°(230°F). The minus 200 mesh portion of this was added directly to the magnetite concentrate. Pellets were made in a laboratory sized disc pelletizer from pastes consisting of ore concentrate, balling water (9%) and binder (clay, or clay + resins, or resins). The pastes were premixed in a Waring blender. The binders were: (1) 1% of a commercially used Western Bentonite; (2) 1 % or 3% of the Wisconsin clay (raw, or 20 min decantate); (3) 20 min decantate washed with activator solutions, (to exchange Na for Ca in the clay); (4) decantate with activator added in the balling water; (5) decantate with organic resins; (6) organic resins. Measurements of the 0.46 m (18 in.) Green Drop Number, the Dry Strength and the Fired Strength (fired at 1260°C (2300°F) for 30 min) were made. The dry and fired compressive strengths were determined on an Instron testing machine using a C-load cell and a F-load cell, respectively. The cross-head speed was 0.004 m/sec (0.1 in./min) for both. The results of each measurement were averaged for 15 pellets. A summary of those results is presented in [Table 1]. More detailed results and procedures are presented in another report.7 In addition to the effects on pellet strength due to various binders the effect of varying magnetite concentrate characteristics is noted in [Table l]. There, a few comparative data are shown for Cornwall, PA Magnetite, which has a generally liner particle size than the Black River Falls magnetite which was used for most of the tests.

Jan 1, 1979

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae&apos;d is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m&apos; is the slope of the line tangent to the curve at the point (p&apos;, 2&apos;).

Jan 1, 1940