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By A. J. Bowie

Jan 1, 1879

By Stanley J. Gasior, Albert J. Forney, Joseph H. Field

Most bituminous coal mined near Eastern industrial areas requiring high-Btu pipeline gas is caking and therefore unsuitable for fixed-bed pres- sure gasification by present techniques. If the caking property of such coal can be destroyed, the resulting fuel can be gasified in a fixed bed at pressure with steam and oxygen as a preliminary step in making a high-Btu gas. To find a practical way to convert strongly caking coals of granular or small lump size to noncaking fuel was the object of this study. In previous work, strongly caking coals of 1/8- to 1½ -in. size were converted to a noncaking coal char by treatment in a static bed in about 3 hours1 and coal of 18-100 Tyler mesh in a fluidized bed in about 5 min.2 An inert gas such as steam, nitrogen, carbon dioxide or a mixture of all three with a small amount of oxygen was used in both studies. In our work a strongly caking bituminous coal from the Pittsburgh seam of 4-8 Tyler mesh size was converted to a noncaking form in free-fall in about 2 sec by dropping it through a countercurrent flow of steam containing 4% to 7% oxygen at 1150º-1200°F and 300 psig. This method should also be applicable to smaller-sized material.

Jan 3, 1965

By Paul Tyler

STRATEGICALLY situated in almost the heart of the leading fertilizer-consuming area of the United States, Tennessee long has ranked second only to Florida as a phosphate-producing state. Since 1932 its share of the national output of phosphate rock has increased steadily, and in 1937 its production mounted to an all-time record. More significant even than the increase in tonnage are the forward strides in technology. The Tennessee Valley Authority's research program has led to quasicommer-cial operations using hydroelectric power to manufacture concentrated phosphatic fertilizer that is used to further the farmer education program designed to streamline the fertilizer business and halt the appalling waste of farm land by soil erosion. Even more stimulating to chemically minded imaginations is the production of elemental phosphorus by a private company that not only has succeeded in extracting it from the phosphate rock in electric furnaces but actually has contrived to capture it and to transport it safely in tank cars. New values have been created for low-grade phosphate deposits, and the economic life of reserves has been lengthened while the waste of former years goes back into the mills for recovery of its values by modernized methods. Tennesse's phosphate-mining industry dates from the discovery of blue rock in Lewis County in December 1893. Its known reserves are of the order of 101,500,000 tons, which compares with the production of 825,099 tons in 1937; that is, 21 per cent of the phosphate-rock output of the whole nation. The total output reported from 1894 until July 1, 1938, was approximately 19,000,000 tons. Official estimates of reserves are overly conservative and evidence submitted before a joint Con-gressional committee in November 1938 places "probable" reserves at more than 6,000,000,000 tons.

Jan 1, 1939

By Herbert Clark Hoover, Lou Henry Hoover

DIFFERENT methods of parting gold from silver, and, on the other hand, silver from gold, were discussed in the last book; also the separation of copper from the latter and further, of lead from gold as well as from silver ; and, lastly, the methods for refining the two precious metals. Now I will speak of the methods by which silver must be separated from copper, and likewise from iron.1 The officina, or the building necessary for the purposes and use of those who separate silver from copper, is constructed in this manner. First, four long walls are built, of which the first, which is parallel with the bank of a stream, and the second, are both two hundred and sixty-four feet long. The second, however, stops at one hundred and fifty-one feet, and after, as it were, a break for a length of twenty-four feet, it continues again until it is of a length equal to the first wall. The third wall is one hundred and twenty feet long, starting at a point opposite the sixty-seventh foot of the other walls, and reaching to their one hundred and eighty-sixth foot.

Jan 1, 1950

By Herbert Clark Hoover, Lou Henry Hoover

PREVIOUSLY I have given much information concerning the miners, also I have discussed the choice of localities for mining, for washing sands, and for evaporating waters; further, I described the method of searching for veins. With such matters I was occupied in the second book; now I come to the third book, which is about veins and stringers, and the seams in the rocks1. The term "vein" is sometimes used to indicate canales in the earth, but very often elsewhere by this name I have described that which may be put in vessels2; I now attach a second significance to these words, for by them I mean to designate any mineral substances which the earth keeps hidden within her own deep receptacles.

Jan 1, 1950

By Spurr

CONTENTS. [ ]

Jan 1, 1913

By C. O. Brawner

FACTORS THAT INFLUENCE STABILITY AND STABILIZATION METHOD The most effective stabilization method and design can only be developed if the cause(s) and mechanics of the slide are known. Therefore, it is important that the stability be evaluated by an engineer who has had extensive rock stability experience. The most important factors that influence stability are structural geology, ground water, blasting and the mining method or methods. Structural Geology - The majority of failures in rock slopes occur along discontinuities in the rock (joints, bedding planes, shear or fault zones, etc.). Therefore, on all surface mining projects, the development and maintenance of a comprehensive structural geologic mapping program should be a first priority program that is considered a part of the operations function. This program should include mapping all major features - faults, shear zones and through going joints. All structural features which could influence stability should be mapped and presented in a structural domain format for the entire mine (Canmet, 1977). Where planes, wedges or blocks will be undercut by the mining excavation, shear strength and strain to failure tests should be performed on the joints, fault gouge and gouge-rock contact surfaces. These tests must be performed on the samples in the direction of potential slide movement and must determine the range of peak and residual shear strength values. A preliminary assessment of friction angle can be obtained from measurements of failed surfaces in the field (Figure 1) or from core sliding tests (Barton, 1981). An assessment must be made of the past geologic history of

Jan 1, 1983

By J. B. Newkirk, A. H. Geisler

Certain of the permanent magnet alloys provide ideal systems for the study of the kinetics of the precipitation reaction and the correlation of structure with properties. One such system, Cu-Ni-Fe, was found by Bradley1,2 to exhibit a coherent transition state in the precipitation process analogous to that reported for Al-Cu alloys somewhat earlier.3 The attractiveness of some perrnanent magnet alloys for study lies in the fact that vertical sections of the ternary phase diagram in certain regions of composition (Fig I) have as their prototype the binary Ni-Au diagram. Alloys of this type decompose into products that have the same crystal lattice type but only slightly different lattice parameters. The advantages that such alloy systems oA&apos;er for study over the usual in which an intermetallic compound is formed are many: 1. Since the precipitate has the same crystal strutture as the matrix, complex atomic movements are not required to form the new lattice. 2. Similarly, complex orientation relationships are not involved for both the matrix and the precipitate would be ex. petted to have the same orientation. 3, Small &,registry of the decomposition products at equilibrium (in contrast with Cu-Ag alloys) is conducive to extensive coherent growth in the transient state and thus the transition lattice can be detected by the usual X ray diffraction methods. 4. Finally, the relative quantities of precipitate and depleted matrix can be varied from 0 to 100 pet* thus permitting wide freedom for the study of the effect of cornposition on coherent growth and properties. In the Cu-Ni-Fe alloys of appropriate composition, the face-centered cubic precipitate and also the depleted matrix when first formed are coherent with the parent matrix.1&apos;2 The two have the same <Jo parameter as the original matrix but they are both tetragonal; the precipitate has an axial ratio c/a < I while that of the depleted matrix is c/a > I. When coherency is lost they assume the normal face-centered cubic structure with the depleted matrix having a lattice parameter greater than the original matrix and that of the precipitate less. Such a mechanism would also be expected for CU-Ni-CO alloys because of the similarity in constitution but this had not been demonstrated. The Present investigation was conducted on a CU-Ni-CO alloy. The constitution diagram and magnetic properties of these alloys have been fairly well established, however, no previous determinations of mechanism of precipitation and no correlation of structure with properties had been made. Thus, an alloy of this system Was chosen for a comprehensive investiga-

Jan 1, 1949

By Roy McLellan

THE slags derived from the smelting of lead and copper ores are composed essentially of silicates. The problems arising from the smelting of these ores consequently involve the study of silicate fusions. In the absence of specific knowledge concerning the compounds occurring in slags, it has been the practice of metallurgists to treat them in terms of their total chemical composition. Slags have been classified as monosilicates, bisilicates, sesquisilicates, and subsilicates according to the relative amounts of oxygen in the acid and basic radicles of the hypothetical salt produced. While this has been a useful guide to metallurgists in computing the furnace charges, it falls far short of a basis for the scientific investigation of slags. In order to understand the nature of a slag as a whole it is necessary to learn the physical and chemical properties of the mineral compounds which go to make up that slag. The efficiency with which an ore is smelted in a furnace depends primarily on the physical properties of the compounds formed during the operation. When the melting points and fields of stability of each of the mineral compounds in slags have been established, it will be possible to determine the properties of any given slag by examining the nature and amounts of its mineral constituents.

Jan 1, 1930

By E. Maltby Shipp

YouR committee&apos;s secretary submits the following report, or summary, to the members of the committee, in an endeavor to lay before them a general review of the information so far received and also his own knowledge of the work as carried on at a number of plants, this being done in part to secure further information and suggestions from members and lead to a more effective means of furthering the work of the committee. It is suggested that more detailed data be compiled regarding engineering features involved, and that papers be contributed which will deal with the safeguarding of underground electrical installations. There are few operating companies which have not started a more or less systematic campaign to safeguard their employees from accidental injuries and unhealthful surroundings, but a great deal is to be gained by experience. All may welcome the advice and cooperation of those who have been actively engaged in the work and have demonstrated the results obtainable by organized effort, and it is, therefore, exceedingly gratifying to note the ready assistance and hearty cooperation rendered by the companies that may be truly termed pioneers in the movement. No solution of the safety problem is to be found in a skrict standardization of methods, rules or devices, as the various mining, milling and metallurgical practices present too many conditions differing broadly in general principles, but some standard system embodying principles already proven to be efficient should be created, which may be modified or elaborated to meet specific requirements of each individual company, or to fit working conditions as they exist in the various mining camps throughout the country. An industrial plant is primarily a business undertaking, therefore the economic side of a safety or welfare campaign is of importance. Many small operators have been deterred from undertaking the work by their belief that it involved an expense beyond their means, and one that could not be counterbalanced by greater efficiency or saving along other lines. This idea is generally due to a lack of knowledge of the actual costs of such work, and of the results secured by judicious selection of a method commensurate with the size and nature of the opera-

Jan 1, 1918

By Robert Linton

This paper deals with work that has been carried on for over three years by the management and staff of the North Butte Mining Co. in an effort to standardize mining methods, to eliminate lost motion in the operating organization, and to improve the efficiency of the individual workman. Naturally, much of this work is an adaptation of ideas suggested by other mining operations or by practice in manufacturing and other productive industries. The studies, however, have developed some features that it is believed are new. Both new and adapted features are given in detail. The normal capacity of the North Butte mines is about 2000 tons per day. Hoisting is done principally through the Granite Mountain shaft, which is 3740 ft. (1140 m.) deep and equipped with an electric hoist capable of hoisting 200 tons per hour from a depth of 4000 ft. (1219 m.). The lowest stoping level is the 3400-ft. The Granite Mountain shaft is connected with the Speculator shaft, about 850 ft. (259 m.) south, and with the Gem, about 1150 ft. (350 m.) east, which are 3000 (914.4 m.) and 2000 ft. (609.6 m.) deep, respectively. These two shafts are equipped with reversible fans for ventilation. The Speculator has a steam hoist with a capacity of 150 tons per hour from the 3000-ft. level. The Granite Mountain shaft is concrete lined from the 1600-ft. to below the 3000-ft. level and gunited with cement from the 1600-ft. level to the surface. Sections of the Speculator shaft with a total combined length of 500 ft. (152.4 m.) are also concreted. There are approximately 36 miles (58 km.) of drifts and crosscuts in the mine, in which there are 15.2 miles (24.5 km.) of track. At normal capacity, about 75 stoping faces, 20 raises, and 30 sill development faces are working. Stoping is usually by the standard square-set method. Where the size of the oreshoot and character of the walls permit, the rill (or cut-and-fill) system is employed. Scope and Limitations of Standardization Standardizing mining operations presents problems quite different from the problems of the manufacturer. Methods of a successful

Jan 1, 1922

By W. R. Shimer, F. O. Kichline

The investigation herein described was carried out for the purpose of studying, both by chemical and metallographical means, the extent of over-oxidation of steel that can be accomplished by excessive overblowing in a Bessemer converter. 111 addition there are appended some results of basic open-hearth and crucible steels. Remarks on Chemical Methods. The test block used was hemispherical in shape, 4.5 in. in diameter and 2 in. thick. Drillings for analysis were obtained by drilling through the entire solid part of the block, carefully avoiding all cracks and blow-holes and mixing these drillings thoroughly. Drillinga were carefully examined for scale and the finest were gone over with a microscope to be sure all scale from whatever source had been removed. Oxygen was determined by the well-known method of Ledebur, modified according to Cushman,1 with, however, the removal of the preheating tube, which was found unnecessary. This method has been found to give concordant results. Blanks run from 0.0003 to 0.0006 g. Duplicate determinations varied not more than 0.001 to 0.003 per cent. It seems to be generally supposed that the hydrogen method gives only that oxygen which is combined with iron. Whether this be true or not, the content of oxygen existing as iron oxide no doubt predominates sufficiently, so that the result obtained is sufficient to indicate whether the steel is over-oxidized or not. We are well aware that the oxides of manganese and chromium, when existing alone, are not reduced by hydrogen at a red heat. To learn of their action in steel the following work was carried out: A sample of ferro-manganese and of ferro-chrome were each exposed

Jan 1, 1914

By Alexandre Mitinsky

The theory of elasticity, the science of the strength of materials, and all our calculations regarding engineering structures are based on Hooke&apos;s law, that in loaded bodies the deformations are proportional to the load producing them. Without this law it would be impossible to design intelligently engineering structures such as bridges, frames, axles, etc. This being the case, the proportional limit,l that is, the point at which deformation ceases to be proportional to load, is the most important factor in engineering design. Further, the working fiber stress should be fixed in reference to the proportional limit instead of, as is usual, in reference to the ultimate strength. The incorrect use of the ultimate strength instead of the proportional limit in setting the working fiber stress is probably due to two reasons: (1) it is a more delicate operation to measure the proportional limit; (2) it is usually assumed, though incorrectly, that the proportional limit is determined by the ultimate strength. In Germany the poin&apos;t at which permanent set first appears is often taken instead of the proportional limit. The two points will coincide if Gerstner&apos;s law, that elastic deformations are proportional to the loads producing them both before and after permanent set, is true; and the limit of proportionality and the elastic limit or point of permanent set will both be represented on a stress-strain diagram, by the point at which the line ceases to be a straight line and becomes curved or changes its inclination. It is to be further noted that the difference in definition between proportional limit and elastic limit introduces a difference in methods of determination in the testing laboratory. The German method of determining the elastic limit by alternately loading and unloading the test specimen is a lengthy process and time has in itself a very considerable influence on the results of physical tests.

Jan 1, 1916

Jan 1, 1902

By William B. Phillips

This paper was prepared at the request of Capt. A. F. Lucas, Chair man of the Institute&apos;s Committee on Petroleum and Gas; as a pre1iminary.discussion of the fuel oils which are used in the Southwest, giving their composition, uses, prices, etc. Should it afterward be found desirable, these observations may be extended over a larger area. In this connection, I suggest that samples of all kinds of fuel oils, including various tars, from all over the country, be collected and sent to some testing laboratory for examination. We would be glad to extend the facilities of the laboratory of the Bureau of Economic Geology and Technology, at the University of Texas, for this purpose, and to do the work free of all expenses. After such examinations are made and the results classified and studied, it would be possible to suggest specifications under which fuel oils should be purchased, and to arrive at some conclusions respecting the uniformity of such specifications, with due allowance for climatic and other more or less local conditions. While such specifications do not now depart from a common standard anything like as much as specifications for illuminating oils do, yet there are discrepancies which should not exist. Some of these discrepancies are of lessening importance, due to the pronounced tendency to distill every crude oil that can be distilled with profit, and to send residues into the market for fuel oil. Residues from the refineries are of a more uniform chemical composition and physical nature than many of the crude oils that go direct into the fuel market. The lower flash-point oils are disappearing from the fuel trade and in place of them we are getting oils that do not flash below 220" F., nor burn under 320" F. In the Southwest, it has not been long since we had fuel oils that flashed as low as 110" F., and the average flash point over a considerable period was 151" F. Now we are using oil that flashes at about 30" lower than the former burning point, which was 258" F. In other words, the flash point has risen, on the average, 100"; and the burning point about 75".

Jan 1, 1915

By E. C. Harder

The situation in the United States, at the present time, regarding the supply of manganese ores and alloys of manganese is one of great seriousness and is likely to become increasingly so while the European war continues. The two principal iron-manganese alloys, ferromanganese and splegel-eisen, are indispensable in steel manufacture, being used extensively in the Bessemer and open-hearth processes. Spiegeleisen, the lower alloy, contains between 15 and 25 per cent., and ferromanganese, the higher alloy, between 60 and 80 per cent., of manganese. Besides manganese the alloys contain iron and carbon. On the market ferromanganese is usually quoted on the basis of 80 per cent. manganese, and spiegeleisen on the basis of 20 per cent. manganese. The consumption of ferromanganese has been increasing during recent years at the expense of spiegeleisen, because larger quantities of the latter must be used to accomplish the same purpose with the result that the amount of carbon introduced with it into the molten metal is frequently injuriously great. Manganese ore proper, in the form of manganese dioxide, is used extensively in many chemical industries, especially for oxidizing purposes. It is also used for the manufacture of both wet and dry electric cells and in the manufacture of paints and dyes. The manganese ore used in this country has been derived hitherto from three principal sources: Southern Russia, Southern British India and East Central Brazil. The following tables show the quantity of manganese ore imported from these countries, and (for comparison) the domestic production, during 1912, 1913 and 1914. The imported manganese ore has been used largely in the manufacture of iron-manganese alloys and in addition large quantities of the alloys themselves have been imported, chiefly from Great Britain, Germany and other European countries.

Jan 1, 1917

By Bartlett W. Paulding

Since its introduction to the petroleum industry in 1949 by Clark,1 hydraulic fracturing or "hydrafracing" has developed into a widely respected and useful technique for increasing production from petroleum reservoirs. Even then, Clark described production increases of from 6 to 100 barrels of oil per day (bopd). Since that time, others have described treatments in which production increased from 12 to 456 bopd, from only a show to 40 bopd;2 from 48 to 219 bopd; 3 from 500 to 1400 bopd and from a show to 192 bopd.4 Although representative of only a few of many successful hydraulic fracturing operational6 these increases in production attest to the past and potential value of the hydrafracing technique to the petroleum industry. The technique has received a considerable amount of theoretical and experimental attention.1, 5-20 Unfortunately, however, the degree of general understanding of the mechanics of hydraulic fracturing is still inadequate to solve many recurring problems. The practicing engineer is plagued with difficulties in predicting such factors as: (1) the required pressure and viscosity of the fracturing fluid to not only induce the fracture but to control the extent of its growth, (2) the strength characteristics and amount of proppant to include in the fluid so that the fracture is held open once the fluid pressure is decreased, and (3) the volume of the reservoir influenced by the induced fractures and the resulting increase in production. A major cause of these difficulties is the uncertainty associated with determining the orientation of the hydraulically induced fractures. One&apos;s natural conclusion in considering the problem is that the orientation of the fracture would depend on several variables, as, for example, the relationship between the viscosity and injection rate of the fluid and the

Jan 1, 1968

By H. F. Perkins

CORROSION as an economic problem is growing rapidly in importance not only because it entails a replacement of corroded parts, but because it interrupts operation and causes hazards of damage and injury through failures of corroded equipment. Nearly all industries are interested in this subject. This paper, although concerned chiefly with corrosion in a complete refinery on the sea coast, discusses many of the various forms of chemical decomposition, most of which are found universally. The petroleum refining industry, in the writer&apos;s opinion, is seriously afflicted by the presence of sulfur in nearly all crude oils. The complete removal of sulfur from the crude as it enters the plant would cause such a relief from corrosion that this problem for research would seem to demand active attention. Next to sulfur the most troublesome corrosive agent is the saltmagnesium chloride, found in the water associated with crude oil, the last traces of which are so difficult to remove. This is much less serious, however, than the sulfur. Refinery corrosion can be tabulated as follows: Causes of Corrosion and Places of Attack in a Refinery CORROSIVE ELEMENTS MATERIAL ATTACKED Air: Pipe lines Moisture Tanks COQ Electric fixtures Sulfur gases Still towers Chlorine Condenser boxes Other acid-forming gases Ladders and stairs Smoke stacks Steel buildings All exposed metal Water: Alkali Fire lines and hydrants Acids Cooling water lines Air Condensers and coolers Other dissolved gases Boiler tubes Steam Steam pipes and valves Turbines Oil Sulfur compounds Tanks, pipes, valves, stills, towers MgCl2-Hydrochloric acid Condensers Air contamination

Jan 12, 1926

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.&apos;," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".&apos;"&apos;, &apos;" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"&apos; have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.&apos; The final expression presented by Starling and Ellingto&apos;n is: i&apos;. (micropoise) -- /t,, exp rX(7&apos;) p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) &apos; &apos; &apos; X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay&apos;s method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade&apos; in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965