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By Henry G. Granger, Edward B. Treville

The Republic of Colombia is the northernmost country of South America. Its northern coast line exteilds from the frontier of Costa Rica to that of Venezuela, on the Caribbean Sea. On the west it fronts on the Pacific Ocean, along the Panama Isthmus, and down to Ecuador. It is bounded on the south by Ecuador, Peru and Brazil, which latter country with Venezuela form its boundaries on the east. Its area exceeds 500,000 square miles. It is deemed unnecessary to give here a map of the country. Fig. 1, a map of the department of Antioquia, studied in connection with a good modern general map of Colombia, will explain itself. Fig. 1 contains also some of the region of the Cauca valley, described in this paper. Access.—The interior of Colombia is reached through the ports of Sabanilla and Cartagena on the Caribbean Sea, each of which places is connected with the Magdalena river by a short narrow-gauge railroad, running respectively to Barranquilla and Calamar. From these points lines of river-steamers serve the ports of the upper Magdalena, which they reach in journeys of a week to ten days. After leaving the steamer, a short railroad journey, followed by a long and tedious mule-ride, reaches the cities of Bogota and Medellin. Quibdo, at the head of the navigation of the Atrato, and its most important town, is connected by steamer-service with Cartagena, by canoe-routes with the various districts of the Choco, and by mule-road, at present well-nigh impassable, with the heart of Antioquia. On the western coast the port of Tumaco is a starting-point for canoe- and mule-travel to the southern part of the department of Cauca, while Buenaventura is the port of the central section of the valley of the Cauca,

Jan 1, 1899

By O. W. Ellis

THE question of the influence of gases upon the properties of copper has received the attention of a number of investigators, among whom Sieverts,1 Iwasé,2 Lobley and Jepson3 stand preeminent. SOLUBILITY OF . GASES IN. COPPER Sieverts and Iwasé concerned themselves with the solubility of a variety of gases in the metal in the solid and liquid states. They determined the absorption coefficients of these gases and in all cases found a sharp change in solubility at the melting point of the metal. In this respect they disagree with Lobley and Jepson, who have based their opinions upon the appearance of small ingots of the metal which had been fused in an atmosphere of one or other of three gases and had then been rapidly cooled, while surrounded by gas, to the freezing point (rate-possibly 30° to 60° C. per sec.). The ingots that had been fused and cooled under nitrogen and carbon monoxide were free from blowholes and it was assumed that these gases were not absorbed in amounts much in excess of those which would dissolve in the solid metal; the ingots similarly treated under hydrogen were full of blowholes and it was assumed in this case that gas was ejected on solidification of the copper. The effect of varying the rate of freezing upon the character of the test ingots was not examined by these investigators; otherwise, it is felt, their views might have been subject to modification. Sieverts' most important contribution is that the solubility of a gas in any metal is proportional to the square root of its pressure or concentration. Knowing then the absorption coefficients of the various gases in copper, it should be possible to determine the analysis of the

Jan 1, 1928

By W. M. Courtis

THIS district commences near Pigeon River, the northeastern boundary between Minnesota and Province of Ontario, and extends entirely around the north shore of Lake Superior, terminating for the present at the Bruce Mines on Lake Huron. The discoveries of mineral-bearing veins have been confined for the most part to the lake shore, or to the country opened up by the Dawson Red River road. As yet the country back from the lake has been but little explored, on account of its roughness, being intersected by steep, rocky trap bluffs, 1000 or more feet high, and alternating white cedar and tamarack swamps. The forests are exceedingly difficult for prospectors. In many places Titanic piles of rocks, protected by chevaux-de frise of dead cedars, with their hooked, tough, sharp branches, and- a covering of spongy moss, sometimes several feet thick, successively guard against the discovery of hidden treasure. The Hudson's Bay Company for nearly a century have maintained trading-posts at Fort William and other points, which probably opened the way to the first discoveries that were made at Prince's Bay, near the western limit of the district. At this point a large vein was worked by Colonel Prince, the owner, as early as 1846. The richest part of the vein seems to have been on Spar Island, but work was stopped on account of excess of water. Sir William Logan states that a mass of ore weighing several hundred pounds and carrying 3 per cent. of silver was taken out. On the mainland small quantities of native and sulphide of silver were found, together with iron and copper pyrites, zinc blende, and galena, in a large spar vein. On the main shore a drift 165 feet long and 90 feet in depth

Jan 1, 1877

By John Park

THE mining .district is located in the northeasterly part of Nevada, between the Jarbidge River on the west and the East Fork of the Jarbidge on the east. The northern boundary of the district is but a few miles south of the Idaho state line-the gold-bearing area extending from this point south, for 5 or 6 miles. The Jarbidge Mountains, in which the ore deposits occur, range from 5000 to 11,000 ft. in elevation, the most important mines being situated about 7000 ft. or higher. The town of Jarbidge lies along the Jarbidge River and is reached by stage from Rogerson, Ida., the nearest railroad point. During the summer months, the camp may be entered from the south by way of Deeth, Nev., but no regular transportation facilities are available over this route. HISTORY The mineral deposits were not discovered until 1909, when D. A. Bourne, panning along the river bank, found gold in the gravel at the mouth of a small stream flowing into the Jarbidge. He prospected in the vicinity of this stream, later known as Bourne Gulch, and shortly after located the North Star claims. During the following spring and summer (1910), the camp of Jarbidge grew from nothing to a town of 2000 people and the hills surrounding it were practically all taken up by mining claims. Most of the work done during. the first year or two consisted of trenching and open-cut prospecting. Tunneling was started on a number of claims and many veins were uncovered. Mills were built and operated on a few properties, notably the Pavlak and the North Star. These ran only a few months, however, when they were closed down because of extraction and financial difficulties.

Jan 1, 1925

By S. F. Emmons

Geological Sketch.-The rhyolite area near Silver Cliff includes what may be called the Silver Cliff plateau, with Round mountain and the intervening valley. The plateau is about 2 miles long and 1 mile wide. From its northern part rise the White hills, which have no special topographic importance, as their highest point is only 400 ft. above the northern edge of the rhyolite mass. Round mountain, on the other hand, is a quite sharply pointed conical hill, so steep-sided as to constitute an important topographic feature, although its elevation above the plains around it is barely 700 ft. The summit of Round mountain is dense banded rhyolite, with steep, irregular clip; the southern end is breccia containing fragments of the banded rock. There are slight exposures of glassy forms of rhyolite on the lower slopes. On the east, the Archaean rocks extend half-way up the side of the mountain, and the contact between them and the rhyolite is vertical, or dips steeply to the west. This mountain is supposed to be at the vent from which the rhyolite of the plateau was poured out. The Silver Cliff plateau occupies the site of a former basin, in which at one time there was probably a lake. At the time of the rhyolitic outburst of the Rosita hills there was a local eruption of the same character in this region, commencing with showers of volcanic ash and of rock-fragments, which filled the lake and built tip about it hills which have since been removed in great measure by erosion. At present the southern half of the plateau is capped by solid lava to a depth in places of 150 ft. The cliff of blackened rhyolite on the southern edge, where the main discovery of ore was made, is from 30 to 50 ft.

Jan 1, 1913

By R. S. Archer

THE PROPER representation of equilibria involving graphitic carbon in the constitutional diagram of the iron-carbon system is admittedly an unsolved problem. The complete solution of the problem will probably require the establishment of more experimental evidence than is at this time available. The object of this paper is to present the author's observations on some of the phenomena in question and his interpretation of this and other recorded evidence. The chief of the recently disputed questions upon which the author has experimental evidence concerns the occurrence of graphitization at temperatures below the A1 point. In a paper1 presented at the September, 1919, meeting of this Institute, the following is found: "the results given would seem to indicate that the graphite eutectoid lies at a smaller value of carbon content than has been previously supposed. At least this is true unless there is either a marked formation of graphite eutectoid at these rates of cooling, or a decomposition of pearlite into graphite, both rather unlikely suppositions, but not impossible ones." In a discussion of this paper, H. A. Schwartz2 takes the position that the possibility of graphitization occurring below the A 1 point is an open question, but that complete graphitization (to less than 0.10 per cent. combined carbon) commonly occurs above this temperature. Another opinion from the malleable castings industry is found in a recent paper3 by Touceda: "Also the carbide of iron can be broken up into its two soft constituents at the temperature referred to. This temperature is called the critical temperature, or critical range, and for air-furnace hard-iron castings it is in the vicinity of 1440° F. It is the

Jan 2, 1920

By H. A. Schwartz

FROM time to time, one of the authors has had occasion to investigate the graphitizing reaction and has published the results mainly as discussion1 of the work of other investigators. In view, therefore, of the diversity of both observations and interpretation, it seemed well to attempt a revision of the entire subject in the Research Laboratory of the National Malleable Castings Co. The work consisted of a careful study of a single, impure, iron-carbon alloy. The material, which may be considered typical low-carbon white cast iron of the malleable industry, was an air-furnace iron of the following composition: carbon 2.30 per cent., silicon 1.20 per cent., manganese 0.29 per cent., phosphorus 0.156 per cent., sulfur 0.048 per cent. The freezing range extended from 1213° to 1132° C., the latter figure agreeing with Gontermann's data .2 We have attempted to define the equilibrium diagram of this alloy, in the stable condition as related to the metastable diagram, from a temperature somewhat below the eutectic freezing point to a temperature below Ar1 and for a graphitic-carbon content from practically nothing to the original total carbon of the specimen (see Fig. 6). More especially we desired to locate the line in the stable diagram corresponding to the Acm line of the metastable system, which is designated by analogy, the Atm line (tm from temper carbon) ; also to determine the location of Aim with respect to Acm toward their lower extremities at Ar1 in order to determine whether or not graphitization is completed by the separation of an iron-carbon eutectoid analagous to pearlite in the iron-cementite system. This would involve further a comparison of the locations of the stable and metastable A1 points.

Jan 8, 1922

By Wilbur E. Sanders

At some period during the operation of metalliferous and other commercially valuable mineral-deposits in connection with their underground mining, when the developments therein have become so extensive that their description is tedious and confusing, some scheme for naming or numbering the various workings and their parts is necessary for convenience of reference. A simple and symmetrical yet expansive system of classification must be devised, one that is capable of being extended to cover all possible exigencies and conditions of future operations within the property. Such a scheme, properly arranged, greatly simplifies communication between the various departments of the mining business, as, for instance, between the administrative and the operating departments of the concern, and is of the greatest assistance to the officers of the mine in enabling them to locate and describe particular points and parts of workings and specific kinds of work. Again, in the proper segregation and differentiation of mine-accounts, when they are carried out with that detail which will furnish ready information concerning the cost of a particular piece of work, or the various items and totals of expense connected with the development, operation and repair of each or all of the mine-workings, some such method of clesignatioi~ becomes a necessity. Moreover, such a plan is acl- mirably adapted to the needs of the mining engineer, who, in connection with his reports upon mining-properties, is sometimes required, in his descriptions of certain blocks of ore, to locate lists of assays of samples taken from many and various places, and to designate workings and parts of workings that are located in different parts of the mine, sometimes at points wide apart. To write out in full a sufficient description of any particular

Jan 1, 1907

By W. M. Courtis

This district commences near Pigeon River, the northeastern boundary between Minnesota and Province of Ontario, and extends entirely around the north shore of Lake Superior, terminating for the present at the Bruce Mines on Lake Huron. The discoveries of mineral-bearing veins have been confined for the most part to the lake shore, or to the country opened up by the Dawson Red River road. As yet the country back from the lake has been but little explored, on account of its roughness, being intersected by steep, rocky trap bluffs, 1000 or more feet high, and alternating white cedar and tamarack swamps. The forests are exceedingly difficult for prospectors. In many places Titanic piles of rocks, protected by chevaux-de-frise of dead cedars, with their hooked, tough, sharp branches, and a covering of spongy moss, sometimes several feet thick, successively guard against the discovery of hidden treasure. The Hudson's Bay Company for nearly a century have maintained trading-posts at Fort William and other points, which probably opened the way to the first discoveries that were made at Prince's Bay, near the western limit of the district. At this point a large vein was worked by Colonel Prince, the owner, as early as 1846. The richest part of the vein seems to have been on Spar Island, but work was stopped on account of excess of water. Sir William Logan states that a mass of ore weighing several hundred pounds and carrying 3 per cent. of silver was taken out. On the mainland small quantities of native and sulphide of silver were found, together with iron and copper pyrites, zinc blende, and galena, in a large spar vein. On the main shore a drift 165 feet long and 90 feet in depth

By J. F. Kemp

IN submitting an additional contribution to the discussion on ore-deposits in the recent volumes of the Transactions, it is my desire to adhere closely to matters of material importance as affecting the actual processes. Judging from the discussion by Professor Van Hise, and from one or two reviews or other articles by associates of his in geological work, the impression seems to prevail that, in so far as my paper* referred to ,his masterly essay,†I was guilty of misconceptions regarding both the part attributed by him in it to the igneous rocks and the ubiquitous presence of the ground-water. I should regret extremely to be wanting in these particulars or to have misunderstood one for whose great services in this and other branches of geology no one has a higher esteem than myself. I have, however, in the most careful way, and with these points in mind, read his essay again, anti, taking it as a whole, I cannot gain any different impression of relative magnitudes than the one first received. The importance of the igneous phenomena and the restrictive influence of the processes described by " cementation " in their effect upon the ground-water, as set forth in Professor Van Hise's " Discussion " (Trans., xxxi., 292), impress me as being in very marked contrast with the same things in his first essay. If the point seems to anyone of sufficient importance, it can easily be decided by reading the originals. My paper was the result of some years of observation, reading and reflection, and was meant to be an independent contribution, controversial only in some subordinate particulars. In depicting the drama of the deposition of ores, I cannot but feel that Professor Van Rise assigned to the chorus and the scene-shifters some characters which, it seems to me, should

Jan 1, 1913

By W. E. Forsythe

Different forms of optical pyrometers are discussed and the advantages and disadvantages of the different types for measuring high temperatures are pointed out. These advantages and disadvantages lead to the selection of the disappearing-filament type of optical pyrometer for most work. Attention is directed to the necessity for the use of a monochromatic screen with a pyrometer, which leads to a discussion of the meaning and use of the effective wave length of the screen. Methods of calibrating the optical pyrometer are outlined and it is shown that an optical pyrometer can be calibrated just as definitely as any other temperature-measuring device. Accuracy tests are included, in which it is shown that excellent results can be obtained by even untrained or slightly trained observers with this form of optical pyrometer. The various corrections that are necessary in this kind of work are indicated, including corrections for stray light, for absorption of windows, of smoke, and so forth. The troublesome problem of measuring the temperature of bodies that do not radiate like a black body is discussed and the corrections for reducing such readings to the true temperature are given for a number of different materials. Introduction The fundamental idea of temperature depends upon our temperature sense and bodies are said to be hot or cold depending upon the reaction of our hands or some other part of the body to the heat from the source investigated. For measuring the temperature some instrument must be devised, since the temperature of the source studied is apt to be so hot as to greatly injure any part of the body that comes near it, to say nothing about direct contact with it. Definition of Temperature.—The temperature scale is based upon two fixed points, the temperature of freezing water and the temperature of boiling water. This temperature interval, depending upon the scale

Jan 1, 1936

By Karl Sundberg

ElectRical investigations carried out in regions containing sedimentary rocks showed that sediments generally are good electrical conductors, a fact which at the present time is used for structural investigations by electrical methods. It is of fundamental importance, not only for these investigations but also for electrical prospecting in general, to know the electrical properties of various soils and rocks. It will be useful, therefore, to discuss this question with the hope that the general points of view discussed in this paper will perhaps be completed by further observations and determinations of material from various localities. This paper is based principally on the study of literature, and the purpose is primarily a discussion of the main factors that determine the electrical conductivity of soils and rocks. It will follow, however, that the factors discussed here also frequently decide how far a certain orebody can be regarded as a good electrical conductor compared with the surrounding rocks. All rocks are more or less porous, and the pores are filled with liquids and gases. Their electrical conductivity, therefore, depends on the following factors: 1. The electrical conductivity of minerals composing the rock. 2. Electrical conductivity of the liquid filling the pores. 3. Proportion of the volume of liquid filling pores of the rocks to the solid rock material. 4. Shape of the pores. 5. Arrangement of the particles of gas and liquids. 6. Temperature. Dry minerals, with the exception of certain ore minerals, are complete nonconductors from the point of view of applied geophysics; in the present investigation we deal with rocks which have no conducting minerals, and factor 1, therefore, is not important. The same is true of soils. The liquids contained in soils and rocks in most cases are waters, sometimes oil. As oil is a nonconductor of electricity, the impregnating waters will determine the electrical conductivity of soils and rocks.

Jan 1, 1932

By W. E. Forsythe

Different forms of optical pyrometers are discussed and the advantages and disadvantages of the different types for measuring high temperatures are pointed out. These advantages and disadvantages lead to the selection of the disappearing-filament type of optical pyrometer for most work. Attention is directed to the necessity for the use of a monochromatic screen with a pyrometer, which leads to a discussion of the meaning and use of the effective wave length of the screen. Methods of calibrating the optical pyrometer are outlined and it is shown that an optical pyrometer can be calibrated just as definitely as any other temperature-measuring device. Accuracy tests are included, in which it is shown that excellent results can be obtained by even untrained or slightly trained observers with this form of optical pyrometer. The various corrections that are necessary in this kind of work are indicated, including corrections for stray light, for absorption of windows, of smoke, and so forth. The troublesome problem of measuring the temperature of bodies that do not radiate like a black body is discussed and the corrections for reducing such readings to the true temperature are given for a number of different materials. Introduction The fundamental idea of temperature depends upon our temperature sense and bodies are said to be hot or cold depending upon the reaction of our hands or some other part of the body to the heat from the source investigated. For measuring the temperature some instrument must be devised, since the temperature of the source studied is apt to be so hot as to greatly injure any part of the body that comes near it, to say nothing about direct contact with it. Definition of Temperature.—The temperature scale is based upon two fixed points, the temperature of freezing water and the temperature of boiling water. This temperature interval, depending upon the scale

Jan 1, 1936

By Burt Hartmann

The nation's ever-expanding construction and mining activity has placed an increasing demand upon engineers and geologists to design and construct stable slopes in earth materials-soil and rock. Man's attempt to handle these slope stability problems has been based primarily on practical experience and the resulting theories formulated to explain the phenomena. Too many instances occur when man is faced with a slope stability problem that has not yet been experienced and doesn't lend itself to solution by any existing theory. At this point he must extend himself in using his engineering judgment to arrive at a reasonable and safe design. As past experience has shown, all of the "safe designs" are not really safe. Sometimes they result in embarrassing failures. Measurements provide the key to understanding and controlling natural phenomena. We cannot hope to gain control of the slope stability problem until we understand the causes of slope failure, their behavior with respect to time and their relative magnitudes. Measurements required for an adequate definition of any slope problem must be of the highest reliability because of the importance of decisions which must be based on them. For this reason, direct measurements of movement, shear strength, water pressure, etc. of the unstable mass are preferable to indirect measurements of other physical properties. Movement instruments which can be positioned inside of the slope mass (within boreholes) are among the most useful in diagnosis and/or monitoring of slope movements. The higher the sensitivity and il-measurement precision possible with borehole instruments, the quicker the required information can be obtained and the more exactly may hazardous conditions be observed. A high density of measuring points in a single drill hole is deemed essential for diagnostic purposes. Behavior gradients may thus be obtained. The Pressure Meter (Fig. 1) can be used to measure a relative strength

Jan 1, 1968

By Alwyn Birchmore Cox, Ian William Wark

Different parts of the world in which mineral separation by flotation is practiced experience vastly different natural temperatures, and in some districts there is a big difference between summer and winter temperatures. It will be shown in this paper that the temperature is of considerable importance where it is desired to separate pyrite or arsenopyrite from other minerals. It is probable that some of the differences obtained in the flotation of these minerals at plants working under otherwise similar conditions are due to temperature variations. The influence of temperature on the flotation of galena, chalcopyrite and sphalerite by xanthates is less marked than its influence on pyrite flotation. Experimental Method The methods used have been described previously.l-4 In each test the clean mineral specimen was immersed in a solution prepared by adding the reagents in the following order: (1) sodium carbonate and hydrochloric acid as necessary to buffer the solution and to give approximately the pH value desired, (2) sodium cyanide, (3) copper sulphate, (4) ethyl xanthate, followed by (5) a final adjustment of pH value. After ½ hr. the mineral was tested for a xanthate film by bringing a bubble of air into apparent contact with the submerged polished surface. If true contact (spreading) was not obtained within ½ min. and after cleaning the surface by wiping with a small linen pad, it was concluded that the adsorption of a xanthate film had been prevented. Following the method already described (ref. 2), curves have been constructed such that for a solution composition corresponding to any point below the curve, contact between mineral and air is possible, whereas for a solution composition corresponding to any point above the curve, contact is impossible.

Jan 1, 1939

By William Ian Wark, Alwyn Birchmore Cox

DIFFERENT parts of the world in which mineral separation by flotation is practiced experience vastly different natural temperatures, and in some districts there is a big difference between summer and winter temperatures. It will be shown in this paper that the temperature is of considerable importance where it is desired to separate pyrite or arsenopyrite from other minerals. It is probable that some of the differences obtained in the flotation of these minerals at plants working under otherwise similar conditions are due to temperature variations. The influence of temperature on the flotation of galena, chalcopyrite and sphalerite by xanthates is less marked than its influence on pyrite flotation. EXPERIMENTAL METHOD The methods used have been described previously.1-4 In each test the clean mineral specimen was immersed in a solution prepared by adding the reagents in the following order: (1) sodium carbonate and hydrochloric acid as necessary to buffer the solution and to give approximately the pH value desired, (2) sodium cyanide, (3) copper sulphate, (4) ethyl xanthate, followed by (5) a final adjustment of pH value. After ½ hr. the mineral was tested for a xanthate film by bringing a bubble of air into apparent contact with the submerged polished surface. If true contact (spreading) was not obtained within ½ min. and after cleaning the surface by wiping with a small linen pad, it was concluded that the adsorption of a xanthate film had been prevented. Following the method already described (ref. 2), curves have been constructed such that for a solution ' composition corresponding to any point below the curve, contact between mineral and air is possible, whereas for a solution composition corresponding to any point above the curve, contact is impossible.

Jan 1, 1938

By G. R. Fritterer

Investigators in the field of temperature measurement have long sought a thermoelectric couple fulfilling the following requirements: 1. It should be useful up to and including high industrial temperatures; i. e., 1000 to 1800 C. 2. Its thermoelectric variation with temperature should be linear and be maintained after heating to high temperatures for long periods of time. 3. It should be reproducible; i. e., different couples of the same elements should have similar calibration curves. 4. Its thermoelectric power should be large so as to allow the industrial use of rugged recording instruments. 5. Chemical reactions with, and physical changes within the elements of the couple should not alter its calibration. No thermocouple proposed to date exhibits simultaneously all of these characteristics, whereas the couple about to be described fulfills all requirements to a satisfactory degree. New Thermoelectric Materials A thorough survey of the literature on thermoelectricity revealed that present-day thermocouples could not meet the specifications mentioned above because their thermoelements are metallic. Metals have a marked tendency to deteriorate chemically and their melting points limit their use to low temperatures. Refractory substances, however, are usually resistant to chemical attack and are quite stable at high temperatures. Hence a survey of refractory substances having thermoelectric possibilities was made. One class of thermocouples considered was that in which carbon and a carbide of some metal or nonmetal were the thermoelements. Previous investigators neglected to study this field but certain recommendations were made by them for the use of couples in which carbon served as one element. These proposals are listed in Table 1. The couples suggested are unsatisfactory because of their low thermoelectric powers, the low melting points of their metallic elements, etc. The

Jan 1, 1933

By Ian William Wark, Alwyn Birchmore Cox

Different parts of the world in which mineral separation by flotation is practiced experience vastly different natural temperatures, and in some districts there is a big difference between summer and winter temperatures. It will be shown in this paper that the temperature is of considerable importance where it is desired to separate pyrite or arsenopyrite from other minerals. It is probable that some of the differences obtained in the flotation of these minerals at plants working under otherwise similar conditions are due to temperature variations. The influence of temperature on the flotation of galena, chalcopyrite and sphalerite by xanthates is less marked than its influence on pyrite flotation. Experimental Method The methods used have been described previously.l-4 In each test the clean mineral specimen was immersed in a solution prepared by adding the reagents in the following order: (1) sodium carbonate and hydrochloric acid as necessary to buffer the solution and to give approximately the pH value desired, (2) sodium cyanide, (3) copper sulphate, (4) ethyl xanthate, followed by (5) a final adjustment of pH value. After ½ hr. the mineral was tested for a xanthate film by bringing a bubble of air into apparent contact with the submerged polished surface. If true contact (spreading) was not obtained within ½ min. and after cleaning the surface by wiping with a small linen pad, it was concluded that the adsorption of a xanthate film had been prevented. Following the method already described (ref. 2), curves have been constructed such that for a solution composition corresponding to any point below the curve, contact between mineral and air is possible, whereas for a solution composition corresponding to any point above the curve, contact is impossible.

Jan 1, 1939

By William E. Ford, Edward Salisbury Dana

IN the representation of crystals by figures it is customary to draw their edges as if they were projected upon some definite plane. Two sorts of projection are use8; the ah- graphic in which the lines of projection fell at right angles and the chirographic where they fall at oblique angles upon the plane of projection. The second of these projections is the more important, and must be tr2atcd here in some detail. Two points are to be noted in regard to it. In the first place, in the drawings of crystals the point of view is supposed to be at an infinite distance, and it follows from this that all lines which are parallel on the crystal appear parallel in the drawing. In the second place, in all ordinary cases, it is the complete ideal crystal which is represented, that is, the crystal with its full geometrical symmetry as explained on pp. 10 to 13 (cf. note on p. 13). In general, drawings of crystals are made, either by constructing the figure upon a projection of its crystal axes, using the intercepts of the different faces upon the axes in order to determine the directions of the edges or by constructing the figure from the gnomonic (or stereographic) projection of the crystal forms. Both of these methods have their advantages and disadvantages. By drawing the crystal figure by the aid of a projection of its crystal axes the symmetry of the crystal and the relations of its faces to the axes are emphasized. In many cases, however, drawing from a projection of the poles of the crystal faces is simpler and takes less time. The student should be able to use both methods and consequently both are described below.

Jan 1, 1922

By Irwin Roman

Numerous results and formulas have been published for analyzing seismic records, but most of them apply only to large-scale phenomena such as are encountered in studying earthquakes. In a few cases,' formulas have been published for some of the simpler structures. In the present paper, an attempt will be made to analyze several types of structures without using methods more advanced than those of a first course in calculus. In tracing a disturbance through a medium, it is almost always possible to base the analysis on Fermat's Principle of Extreme Time, which states that waves of displacement travel between points in such a manner as to make the time of travel an extremum with respect to all neighboring paths. In the simpler cases, comprising most of those used in optics or geophysical prospecting, this time is a minimum and the principle is often referred to as the Principle of Least Time. Within a homogeneous medium, having a uniform speed of transmission of the disturbance in all directions and throughout the medium, the paths are straight and are refracted at the interfaces in accordance with the Snell law of refraction, which states that the ratio of the sine of the angle, made by the ray with the normal to the interface, to the speed of transmission is the same on both sides of the interface. Thus, in any medium composed of homogeneous sections, this same ratio has a constant value at all points. In particular, if all interfaces are horizontal, it is apparent that the angles of incidence are the angles made by the ray with the vertical direction. Furthermore, the incident ray, the refracted ray and the normal to the interface are all in the same plane at each refraction,

Jan 1, 1934