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By Bernard Lewis

This report summarizes the fundamental research and technical studies conducted by the Explosives Branch of the Bureau of Mines from July 1, 1943, to June 30, 1949. It is the thirteenth of a series of annual reports, which have aimed to bring to the reader a resume of the research results that have appeared in published form during each fiscal year. The work of the Explosives Branch covers a number of activities - explosives research, explosives testing, flame and combustion research, flammability of gases and vapors, dust-explosions research, and technical studies in the experimental mine. An important part of the work of the branch is fundamental research to advance our knowledge and understanding of explosion processes. Considerable emphasis has been placed on studies of ignition and flame stabilization, as it is felt that an understanding of these processes should assist materially in alleviating explosion hazards in coal mines. The results are also finding important application in the development of jet propulsion. Studies of the explosibility of gases, vapors, and dusts saving thousands of lives and are preventing the destruction of much property. In innumerable instances in which potential explosion hazards exist, safe operating procedures have been recommended from data taken in the Laboratory. Aware of the value to national security of research results of combustion, flame, and explosion, the Army, Navy, and Air Forces are actively supporting important phases of this fundamental research.

Jan 1, 1950

By Henry Kreisinger, F. K. Ovrrz, C. E. Augustine

The Bureau of Mines is conducting investigations to determine how fuels belonging to or for the use of the United States Govern- ment can be utilized with greater efficiency. As a result of these investigations a number of reports have been published, each report treating of one phase of fuel utilization. A list of these publications is given at the end of this bulletin. The efficient utilization of coal depends on the correct design of furnaces and on their proper operation. To attain both of these conditions a knowledge of the fundamental principles of combus- tion is necessary. Therefore, the study of the combustion of coal in industrial furnaces has been made a part of the bureau's fuel in- vestigations. The desirability of investigating the fundamental principles of combustion was suggested by the study of a large number of steam- ing tests made by the fuel-testing division on coals from all of the more important fields in the United States. The results of these tests have been published in Bulletin 325 of the United States Geological Survey and in Bulletin 23 of the Bureau of Mines. As a result of that study a plan to investigate the combustion of coal in a special apparatus in which all conditions could be controlled was presented to the National Advisory Board for Fuels and Struc- tural Materials at its meeting of April 10 and 11, 1906. The plan received the approval of the board, and since the establishment of the experiment station of the Bureau of Mines at Pittsburgh the investigation of the combustion of coal has been carried on intermit- tently. The history of these investigations is given in Technical Paper 63.

Jan 1, 1917

By G. S. Scott

Safety problems in the mining and allied industries have led the Bureau of Mines to investigate over a period of years; the flammability (explosibility) of many types of combustible atmospheres principally at ordinary pressure; the results of these investigations have been made available as a bulletin. However, more recently, the demand for information on the flammability of gaseous mixtures at high and low pressures has increased greatly. In particular, the rapid development of high-altitude aviation has brought demands for information on the flammable (or explosive) characteristics of certain gases and liquids at low pressures. The present report gives the results of about 900 tests made to determine the flammability of the lighter paraffin hydrocarbons mixed with air and nitrogen at pressures of 400 200, 100 and 70 ram. Hg. The gases tested include natural gas, methane, ethane, propane normal butane and isobutane. The minimum pressures at which these gases are capable of propagating flame whorl individually mixed with air also were investigated.

Jan 1, 1952

By Keith L. Harris

Buoyed primarily by growing consumer spending, the economy rebounded from a weak second quarter. According to preliminary estimates released by the Department of Commerce, real gross national product (GNP) grew $2 1.9 billion during the third quarter, producing a seasonally adjusted annual growth rate of 2.4%, compared with a rate of 0.6% in the second quarter of 1986 and 4.1% for the third quarter of 1985 (table 1). Third-quarter real personal consumption expenditures and Government purchases of goods and services rose $42 billion and $7 billion, respectively, but those gains were partially offset by the continuing decline of gross private domestic investment, off $16 billion, and the growing trade deficit, up $11 billion. Three quarters of the growth in consumer spending occurred in the durable goods sector as consumers responded to discounted financing offered by automobile manufacturers attempting to lower inventories of 1986 vehicles, Increased purchases of other durable goods, such as furniture and home furnishings, also contributed to the strength of the durable goods sector. The success of the automobile inventory reduction program as well as weak factory output led to a $20 billion decline in inventory growth. Investment for housing and producers' durable equipment expanded, however, and mitigated some of the impact of slower inventory depending on gross private domestic investment, Capital spending for nonresidential structures declined for the third consecutive quarter. The declining capital spending and the growing trade deficit continued to be significant and interrelated problems for the economy. Real capital spending for new plants and equipment during 1986 is expected to decline 2.5% after rising 8.7% in 1985 and 15.8% in 1984 (table 2). It is likely that capital expenditures bottomed out in the second quarter and that they will expand in the third and fourth quarters. The first-half decline was partially attributed to uncertainty arising from the pending tax- overhaul bill. Furthermore, there is little impetus for corporations to invest in new capacity since factories are operating at less than 80% of capacity (table 3) largely because of the continuing growth of imports. The growth rate of the trade deficit dropped sharply in the third quarter to less than half that of the previous quarter. Low oil prices, declining auto- mobile and steel imports, and increased exports of agricultural goods contributed to this decline. The continued low growth of the economy caused the Federal Reserve System to reduce the discount rate for the fourth time this year (in late August), drop ping it to 5,596, the lowest level in about 9 years. Inflation, as measured by the fixed- weighted GNP price Index, continues to remain low, but rose from the revised second-quarter level of 1.7% to 2.596, mostly because of rising food costs.

Jan 1, 1986

By Joseph M. Kurtak

The Bureau of Mines (Bureau) and the U.S. Geological Survey (USGS) conducted a 4-year (1979-1982) mineral assessment study of the Chugach National Forest (CNF), Ak, as part of the Roadless Area Review and Evaluation (RARE II) Program. The USGS remapped the geology and distribution of mineral resources. The Bureau investigated mines, prospects, and mineral occurrences. This report describes the results of Bureau work in the central 790,880 acres of the Forest. Copper, with by-product zinc, silver, and gold, has been the major metal produced from the study area as well as from the entire Chugach National Forest. The majority of the copper deposits are concentrated within basaltic rocks on Knight Island but the major producers are hosted by sedimentary rocks on Latouche Island. Approximately 182.6 million lb of copper, 1.5 million oz of silver, and an unknown but substantial amount of gold were produced during a 30 year period. Currently no mines in the area are producing. Inferred, indicated and measured reserves having mineral development potential total 4.6 million tons, with weighted average grades of 1.6% copper, 0.30 oz silver/ton, and 0.04 oz gold/ton.

Jan 1, 2011

By Joel A. Hunt

The Bunker Hill Mine, located in north Idaho, consists of over 150 miles of passageways within highly fractured and faulted Precambrian metamorphosed rocks. The Bunker Hill Mine was at one time a major producer of lead and zinc; currently it is on inactive but maintained status. Ground water moving along flow paths that have been disturbed by mining reacts with pyrite and oxygen to produce acid water within the mine. Discharge of this acid water averages more than 5 cubic feet per second, with an average zinc concentration of 160 mg/L and pH of 2.8. Treatment of this acid mine drainage is required by the National Pollutant Discharge Elimination System (NPDES). Cessation of all underground activities at the Bunker Hill Mine will not terminate the production of acid mine drainage. Reclamation alternatives that could either reduce the quantity or Improve the quality of the drainage upon mine closure are highly attractive. This project is directed towards delineation of reclamation alternatives based upon an understanding of the characteristics of ground water recharge near the mine. A variety of field techniques were used to identify areas of rapid infiltration and to investigate the ground water flow system associated with the upper portion of the mine in a portion of the Milo Creek drainage. These techniques include Installation of piezometer nests, dye tracing, surface resistivity, dye dilution, spring surveys, and hydrochemical analyses. Sites of direct Infiltration into the mine have been located. These include mine workings directly below perennial streams, intersections between streams and faults, and a caved area adjacent to an ephemeral stream. Results of these investigations indicate that recharge through these sites is not as rapid as suggested by previous studies. Inflow to the underground workings from the ground water flow system around the margin of the mine may account for more mine water than sites of direct infiltration. Recharge control at areas of direct infiltration could result in a net decrease in the quantity of acid drainage from the Bunker Hill Mine. Locations suggested for recharge control are West Milo Creek above the Guy Caving Area, the intersections of the Cate Fault with South Milo and Milo Creeks, and an area of Milo Creek below the Milo Creek Dam that overlies shallow mine workings.

Jan 1, 1984

By BUREAU OF MINES

In July, 1918, the attention of the Secretary of the Interior WItS called to the rapidly increasing cost of producing gold and the declining output of that metal in the United States. Realizing the importance of the gold-mining industry, the Secretary appointed a. committee, consisting of Hennen .Iennings, chairman, J. H. Mackenzie, and Charles Janin, of the Bureau of Mines, and H. D. Me- Caskey and F. L. Ransome, of the United States Geological Survey, to,make a thorough study of the gold-mining situation in the United States. The study was to cover the increased cost of recovery and the decreased output of gold, and to consider the different measures that had been proposed to relieve the industry and stimulate production. This report embodies the results of the investigation and study made by the committee. The report presents statistical data compiled from various sources, showing the production of gold in the United States and other countries, with comparative figures for coal, iron, and other mineral products, and describes the sources and distribution of gold output in the United States. It discusses the relation of gold' production to finance and credit, the causes for the decline in gold output, and measures for the relief of the industry. The Interior Department publishes this report in the belief that the widest publicity possible should be given the findings of the committee in order that attention may be directed to the serious conditions revealed therein, and in the hope that wide discussion of the subject may result in some action being taken that will aid in upholding the gold standard ,and the gold industry.

Oct 30, 1919

By H. Kenworthy

Sulfide-ore concentrates containing cobalt, nickel, copper, lead, and iron from the operations of the National Lead Co. at. Fredericktown, Mo., were treated successfully on a laboratory scale to recover more than 90 percent of the cobalt, nickel, and copper. A cobalt -nickel-bearing, lead-copper matte., produced by the St. Joseph Lead Co. at Herculaneum, Mo., was treated to produce a lead-zinc fume, a copper sulfide concentrate, and a cobalt nickel-iron product, netting a recovery of over 75 percent of the cobalt and about 90 percent of the nickel and copper. National Lead Co. bulk concentrates were chlorinated with gaseous chlorine to form anhydrous metal chlorides and sulfur chlorides, sulfur chlorides were recovered by distillation, a high percentage of the ferric chloride was converted to ferric oxide, and the chlorinated residual metals were extracted with water. Metal ions were removed from leach liquors by pH-controlled fractional precipitation as hydroxides. Cobalt solutions "were prepared from cobaltic hydroxide, and procedures were developed to remove contaminating metal ions. Purified cobalt solutions were employed as electrolytes for deposition of high-purity cobalt.

Jan 1, 1953

By Charles Janin

The recovery of gold from sands and gravels is one of the oldest forms of mining; it antedates history and has been practiced by savage peoples. In North America the search for placer gold has been a powerful agency in the exploration and development of unknown regions and has profoundly influenced the course of our civilization. With the progress of invention, the improvements in machinery, and the availability of large capital for the conduct of great operations, the tendency in placer, as in many other branches of mining, has been toward the working of extensive but comparatively low-grade deposits. The early miner washed the rich spots in stream beds or terraces with his pan, his long tom, and his primitive sluice. Then followed the growth of hydraulic mining and the use of giants supplied with water under pressures of hundreds of pounds to the square inch that could work at a profit gravels whose gold tenor was less than 3 cents to the cubic yard. Finally came the dredge that could handle deposits lying so far below water level as to be beyond attack by other methods. Although the gold dredge was first successful on a commercial scale in New Zealand, it has reached its present strength and efficiency in this country and its development is a monument to the daring, per- severance and technical skill of the many men, mine owners and engineers who have each contributed something to the final result. The Bureau of Mines, authorized to conduct investigations for the purpose of increasing efficiency in the mineral industries, had its attention called some years ago to the need of a comprehensive report on gold dredging in the United States. The director of the bureau recognized that such a report should summarize the development of the gold dredge, should describe in detail the essential features of present-day dredges, should discuss the facts that determine whether a placer deposit can be profitably dredged, and should point out the approved methods of prospecting placer ground and of operating dredges. At the request of the director, the author undertook the preparation of such a report and has been intermittently engaged on the task for several years. This bulletin is the outcome of his labors. He hopes that it will prove of interest to designers and builders of dredges, to mining engineers, and to persons who may contemplate investing capital in placer-mining ventures.

Jan 1, 1918

By Keith Harris

The U.S. economy grew moderately in the second quarter of 1985 with real gross national product (GNP) recording a seasonally adjusted annual growth rate of 2.0%, up from the 0.3% growth of the previous quarter but significantly below the 7.1% growth of the second quarter of 1984 (table I). Personal consumption expenditures grew 5.3%, with purchases of durable and nondurable goods rising 7.4% and 5.1 %, respectively; nonresidential and residential fixed investment--the two components of fixed investment--grew 11.8% and 5.6%, respectively; and Government spending rose 3.6%. However, these gains were tempered by a major decline in the growth of business inventories (from $19.1 billion to $8.3 billion) and the continuing growth of the net export deficit (from -$28.4 billion to -$33.3 billion). While the high value of the dollar compared with other currencies has been a major cause of the expanding trade deficit, its value, as measured by the monthly Federal Reserve Board (FRB) multilateral trade-weighted dollar index, has declined over 17 index points from its February peak to 140.94 in July. The July dollar value was still high historically. The rate of inflation, as measured by the fixed-weighted price index for GNP, remained low at 4.1%, down from 4.3% in the first quarter, and employment continued to grow at a rate sufficient to keep up with new additions to the labor force. Civilian unemployment has remained steady at 7.3% over the past 6 months. Industry Statistics The FRB recently revised its index of industrial production and changed the base year from 1967 to 1977,1/ The revised total index shows a 0.1 % higher annual growth rate between 1967 and 1984 than the previous index. In the slower growing or declining industries, such as metal mining, primary metals, and fabricated metals, however, downward revisions in the indices and rates of growth have occurred. The previous and revised annual rates of growth between 1977 and 1984 for several of the sectors of interest to the mining industry are shown in table 2.

Jan 1, 1985

By Charles W. Merrill

The U .S. Treasury stocks of silver have been reduced at such a rapid rate to meet industrial and coinage requirements that they face exhaustion in 3 or 4 years. Alleviation of the silver problem will require increasing supply or reducing demand. This paper examines possible long-range resource development and research programs and improved secondary recovery. The possible reduction or elimination of silver in coinage and development and introduction of substitutes in the arts and industry are also discussed.

Jan 1, 1965

By Walter K. Utt

The process of drilling and bolting the roof is currently one of the most dangerous jobs in underground mining, resulting in about 1,000 accidents with injuries each year in the United States. To increase the safety of underground miners, researchers froth the Spokane Research Laboratory of- the National Institute for Occupational Safety and Health are applying neural network technology to rite classification of mine roof strata in terms of relative strength. In this project, the feasibility of using a monitoring system on a roof drill to assess the integrity of a mine roof and warn a roof drill operator when a weak layer is encountered is being studied. Using measurements taken while a layer is being drilled, one can convert the data to suitably scaled features and classify the strength of the layer with a neural network. The feasibility of using a drill monitoring system to estimate the strength of successive layers of rock was demonstrated in the laboratory.

By Charles W. Merrill

The U.S. Treasury stocks of silver have been reduced at such a rapid rate to meet industrial and coinage requirements that they face exhaustion in 3 or 4 years. Alleviation of the silver problem will require increasing supply or reducing demand. This paper examines possible long-range resource development and research programs and improved secondary recovery. The possible reduction or elimination of silver in coinage and development and introduction of substitutes in the arts and industry are also discussed.

Jan 1, 1965

By Henry Kreisinger, WALTER T. RAY

This preliminary bulletin was written as the first of a series of several on the significance of drafts in steam-boiler practice, the succeeding bulletins to be along the same lines but of a more advanced character. The conclusions arrived at are tentative, and are the result of a study of one of the many problems growing out of a general plan of the United States Government to increase the efficiency with which the coals of the country are being used. Greater efficiency requires better boiler and furnace design. The experimental study of drafts on which the conclusions presented in this bulletin are based formed part of the fuel-testing investigations that were carried on by the technologic branch of the United States Geological Survey and have been transferred to the Bureau of Mines. The experiments made seem to indicate that it is possible to double or treble the capacity of a plant without making any radical changes the furnaces and boilers. These increases require about double and treble the quantities of air to be put through the fuel beds and boilers. It also seems probable that rebafHing the boilers will often permit the capacity to be doubled or trebled, while still getting more steam than formerly per pound of coal for uses outside the boiler room. These experiments were undertaken with the object of clarifying ideas concerning the passage of air through fuel beds and boilers. Measured weights of air were passed through two beds of lead shot, series, one of which remained always the same and represented a boiler; the other being varied as to size of shot and depth of bed, and representing a fuel bed. Careful observations were made of the weight of air passing through the beds per minute. All data were plotted in many charts, so as to permit the study of them from several points of view. A number of laws were deduced bearing on the relative amounts of power required to force air through fuel beds of various thicknesses, composed of various sizes of coal, and through boilers of various lengths and areas of gas passages. An important part of the discussion relates to an increase in the capacity of boilers by increasing the amount of power applied to pressure and exhausting fans and thus forcing several times as much air through the fuel beds and boilers. may be possible, as a result of these investigations, to raise the rate of working the boiler heating surface to three or even four times its present value. Such an increase would undoubtedly mean new designs of grates, stokers, furnaces, and boilers, especially fitted for high rates of working. Fan equipments designed to supply three or four times as much air under several times the pressure would be provided with more efficient engines, thus giving an additional factor favoring high-capacity working. It must be borne in mind, as stated above, that the results are tentative. It will cost money to force gases at high speeds through fuel beds and boilers, and there will soon be pressing need of such quantitative data as will enable the largest possible part of the energy imparted by the fans to be advantageously utilized. We desire, to thank our superiors, especially Messrs. L. P. Breckenridge and D. T. Randall, for their helpful criticism and suggestions.

Jan 1, 1911

Real economic growth for the year will most likely exceed the Administration's estimate of 3.2%, up from 2.9% in 1986, unless consumers change their spending patterns more than expected as a result of the October stock market decline. The economy grew at a real annual rate of 3.7% in the first three quarters of the year, Analysts agree that the stock market decline will slow economic growth-- most have lowered their growth expectations for 1988 by about 1%; but few would argue that the economy will slow significantly in the fourth quarter of 1987. [ ] During this economic recovery, personal consumption expenditures provided the main impetus for growth and a deeping trade deficit, the main hindrance to growth. In 1987, however, personal consumption expenditures grew at a lower rate than the overall economy. Mush of the economic growth resulted from a reduced trade deficit and growing investment by business in equipment to improve productivity and to meet the domestic and foreign demand for products. The declining value of the dollar resulted in a better competitive position for U.S. goods but also contributed to a rising rate of inflation as imports rose in price. Inflation, as measured by the fixed-weighted index for gross national product, was still far below the rates in the early 1980k, however. More than 2 million jobs were created during the year, predominantly in the service sectors of the economy, and the monthly unemployment rate in September fell to the lowest level in a decade. Then, after 13 months of decline, the unemployment rate edged up 0.1 percentage point to 5.9% in October.

Jan 1, 1987

By E. C. Yeager, E. O. Wagner, A. W. Koth, V. F. Parry, J. B. Goodman, D. G. Gernes, W. L. Patty

"In July 1943, the Bureau of Nines received an appropriation to investigate the beneficiation of Minnesota iron ores through the use of lignite. The broad objective was to find a way to link the large deposits of lignite in North Dakota with the low-grade iron ores of Minnesota. It was proposed that sponge iron might be made through new methods of processing, and one of the objectives was to determine the possibilities of gaseous reduction of fine ore. The problem of obtaining high-hydrogen reducing gases from lignite was assigned to the Subbituminous Coal and Lignite Section of the Bureau of Mines in August 1943.Through the advice of technical consultants and men familiar with the mineral resources of Minnesota and North Dakota, a tentative program of development was outlined. The first proposal was to study the gasification of lignite briquets in a standard water-gas machine. Previous experience with gasification of lignite indicated that the raw fuel would not be suitable for use in the conventional water-gas process on account of degradation, but gasification of lignite briquets appeared possible. Through the cooperation of the Northern State Power Co„ a series of tests was made at the company's plant in Grand Forks, N. Dak., on lignite-char briquets made by the Lehigh Briquetting Co. at Dickinson, Dak. These briquets are made by the Lurgi process, and they have been used satisfactorily as a domestic fuel. The object of the tests was to compare gasification properties of lignite-char briquets with those of gas. coke made from Kentucky coal, normally used in the Grand Forks plant. The tests revealed that the lignite-char briquets were not suitable for gasification, in the standard water-gas process because of disinte-gration and low efficiency caused by loss of fine carbon.While these investigations were underway, a joint Minnesota-North Dakota Development Commission was formed to aid in planning investigations on development of mineral resources of the two States. Some members of this commission were technical men, who with consulting engineers on the Bureau's staff made up an unofficial technical committee, and assisted in solving certain problems connected with gasification of lignite and beneficiation of iron ores. This committee has been of 'real assistance in guiding the investigation.A technical meeting was held in Minneapolis on November 10 and 11, 1943, for further discussion of objectives and certain technical problems. Results of tests on lignite briquets were presented, and several reports analyzing other methods of gasification were discussed. The Reyerson-Gernes process for the continuous gasification of lignite in an externally heated retort was considered from several angles. This process differs from others in that the natural moisture in the coal is utilized to help gasify the coal, and the volatile matter is largely decomposed. Although this process had been carried out successfully in a small steel retort, no definite design for a commercial-scale retort had .been developed. It was first proposed that the process might be carried out in a Glover-West retort. However, it was brought out that a Glover-West retort would require modification to simulate the process correctly, and that good results might not be obtained even then owing to the leakage of gas through the refractory walls and to an anticipated low rate of heat transfer at the gasification temperature suitable for lignite. Further, the probable leakage of inert furnace gas into the water-gas would be adverse to the Objective to obtain a gas that could be purified to 96 percent hydrogen."

Jun 1, 1946

By H. Foster Bain

The war has brought about many changes in the Western States, and some have deep pr sent or potent al economic significance. The West has been feeling severe growing pains for a number of years. Especially since the beginning of preparation for national defense and through the period of

Jan 1, 1945

By David K. Hylbert

This study investigated stratigraphic and structural causes of roof falls in room-and-pillar drift coal mines in nine mines in eastern Kentucky. A contract modification provided for remote sensing studies in the Dunkard Basin of West Virginia and Pennsylvania. Results of stratigraphic and structural studies of an earlier contract (H0133018) were applied to several new mines. It was found that similar rock sequences contributed to unstable roof conditions. Structure contour and isopach maps were found useful In projecting these trends together with fence diagrams. Using Landsat imagery, a direct relationship was found between lineament direction and the trends of rock jointing, roof fall zones, "snap top" zones and sandstone channels in the examples cited. It was found that, by analyzing lineament intersections, from 50 percent to 65 percent coincided with roof falls.

Jan 1, 1980

By James T. McCartney, Joseph D. Davis

For more than 10 years coke-oven technologists have been investigating the expanding properties of coal on a scale larger than that afforded by laboratory test tubes. Koppers 4/ was among the first to realize that coals can not be differentiated satisfactorily with respect to expansion in coke ovens by the simpler test-tube methods; in his first method 80 grains of fine coal were coked in a cylinder heated from the bottom, so that the zone of fusion (plastic layer) advanced from the bottom to the top. The scale of test was too small; it has been modified by other investigators, but without significant improvement in practical application of the results. Somewhat later Koppers and Jendne 5/ experimented with a small-scale coke even, one wall of which was movable, in which the layer-coking in a coke oven could be simulated closely. This oven was heated from both sides. Their results with this oven showed a peak in the time-pressure curves near the end of the coking, period when the two plastic layers, advancing from opposite walls, meet. They also found that although the smaller oven was heated from one side only and did not show the Pressure peak characteristic of two-sided heating, it still gave results entirely too high. Russell built an oven similar to the movable-wall oven of Koppers and Jenkner and compared results obtained in it on Beckley expanding coal with these obtained on the some coal in the Altieri 7/ small-scale apparatus. Both tests were conducted at the same constant pressure, but heating was from two sides in Russell's oven and from one side in the Altieri tester. Russell found that the two types of test gave comparable results under constant pressure conditions even though the heating procedures were quite different. He showed later, however, that a "borderline" coal 8/ that contracted in the Altieri tester at constant pressure developed a peak pressure of 4 pounds per square inch in the movable-wall oven heated from both sides at constant volume. He concluded from this that testing at constant volume gave results more accurately indicative of dangerous expansion tendencies than those at constant pressure. He also found that heating from both sides in this oven gave higher pressure than heating from one side only.

May 1, 1942

By Robert M. Becker

This report (the second in a series of five) presents the mathematical development in extending the theory of sample reliability from a sample consisting of a fixed number of items to a sample consisting of a fixed amount of items. Examples of a fixed amount of items per sample are samples consisting of a fixed weight or a fixed volume of unequal size particles. The probability distribution functions (those here called the compound binomial and compound multinomial functions) are developed from fundamentals. Their distributions are generalized to include some measured characteristic of the items. Infinite population moments are derived from moment-generating functions, while finite population moments are developed from corresponding infinite population moments using the finite probability operator defined in part 1 of this series.

Jan 1, 1964