Statement of the Problem The purpose of this study was to determine the need for establishing new vocational agriculture departments in public accredited county high schools in areas of Virginia which were not offering a vocational agriculture program. Problem Analysis An analysis of the problem listed the objectives of this study as: 1. To determine each public accredited county high school in Virginia in which there was a need for establishing a new vocational agriculture department. 2. To determine the number of teachers required in each of the new vocational agriculture departments needed. 3. To determine the total number of public accredited county high schools in Virginia in which there were needs for establishing vocational agriculture departments. 4. To determine the total number of teachers required in the new vocational agriculture departments needed. / Master of Science

Ph. D.

Estimators for the individual error variance were derived in a nonreplicated two-way classification by the use of the model x_ij = μ_i + β_ij + ε_ij, i=1,2,...n; j=1,2,...,r, where x_ij = observation on the i^th treatment of the j^th block, μ_i = true mean of the i^th treatment, β_j = bias of the j^th block, ε_ij = random error, distributed normally with means zero and variance σ²_j, and E(x_ij) = μ_i + β_j. The estimator σ̂²_t, for σ²_t, t=1,2,3,...,r, was derived for n ≥ 2 and r = 3, by applying the principle of maximum likelihood to a set of (n-1)(r-1) transformed variables usually ascribed to error. Equations were derived for the maximum likelihood estimators for n ≥ 2 and r ≥ 3. A general quadratic form was used and when four reasonable assumptions were applied, estimators of the variances were obtained in for form of Q_t = [r(r-1)∑_i(x_ij-x_i.-x_.t+x_..)²-∑_i∑_j(x_ij-x_i.-x_.j+x_..)²] ÷ [(n-1)(r-1)(r-2)] where x_i., x_.j and x_.. are the means of i^th treatment, j^th block and grand mean respectively. σ̂²_t and Q_t were shown to be identical when σ²_t was being estimated for the case n ≥ 2, r = 3. It was noted that the derived estimator Q_j is equal to the estimators proposed by Grubbs [J.A.S.A., Vol. 43 (1948)] and Ehrenberd [Biometrika, Vol 37. (1950).] It was shown that Q_t/σ² = [(r-1)²x_(n-1)²-x_(n-1)(r-2)²]/[(n-1)(r-1)(r-2)], a linear difference of two independent central chi-square variates. The statistic Q/E was derived such that Q_t/E = [(((r-1)²)/(1+(r-2)F))-1]/[(n-1)(r-1)(r-2)] with F, a central F-statistic with (n-1)(r-2) and (n-1) degrees of freedom in the numerator and denominator respectively and E =∑_i∑_j(x_ij-x_i.-x_.j+x_..)². It was noted that this statistic may be used to test H_o: σ²_t = σ²against one of H_a₁: σ²_t > σ²; H_a₂: σ²_t < σ² and H_a₃: σ²_t ≠ σ² assuming σ²_j = σ², j≠t, j=1,2,...,r. A final test was of homogeneity of variances when r = 3 and was based on - 2 ln λ = (n-1)[2 ln (n-1) + ln(Q₁Q₂+Q₁Q₃+Q₂Q₃) - 2 ln E + ln 4/3], where λ is a likelihood ratio and -2 ln λ is approximately distributed as x² with 2 degrees of freedom for large n. A more general statistic for testing homogeneity of variance for r ≥ 3 was proposed and its distribution discussed in a special case. / Ph. D.

Ph. D.

Many experimental problems in the natural sciences result in data which can best be represented by linear combinations of exponentials of the form f(t) = ∑[with p above and k=1 below] α_k e^-λ_kt. Among such problems are those dealing with growth, decay, ion concentration, and survival and mortality. Also, in general, the solution to any problem which may be represented by linear differential equations with constant coefficients is a linear combination of exponentials. In most problems like those which have been mentioned, the parameters α_k and λ_k have biological or physical significance. Therefore, in fitting the. function f(t) to the data it is not only necessary that the function approximate the data closely, but it is also necessary that the parameters α_k and λ_k be accurately estimated. Furthermore, a measure of the accuracy of the estimation of the parameters is required. A new estimation procedure for linear combinations of exponentials is developed in this paper. Unlike the iterative maximum likelihood and least-squares methods for estimating the parameters for such a model, the new procedure is noniterative and can be easily applied. Also, in contrast to other non-iterative methods, error estimates are available for the parameter estimates yielded by the new procedure. In the model for the new procedure the points t_i at which observations are taken are assumed to be equally spaced and the number of such points is specified to be an integral multiple of the number of parameters to be estimated. Moreover, each observation is specified to have expectation f (t_i), where f is the function mentioned earlier. The coefficients α_k are assumed to be non-zero and the exponents λ_k are assumed to be distinct and positive. Then in the derivation of new procedure, the observations are reduced to as many sums as there are parameters to be estimated. Each of these sums is equated to its expected value and the resultant equations are solved for estimators of the parameters. The estimators from the new procedure are shown to be asymptotically normally distributed as either the number of points at which observations are taken or the number of observations made at each such point approaches infinity. The asymptotic variances obtained are used to form approximate confidence limits for the α_k and λ_k. The statistical properties of the estimators are also studied. It is found that they are consistent, but not in general unbiased or efficient. Asymptotic efficiencies are calculated tor a few sets of parameter values and a bias approximation is obtained for two special cases. The new method is also shown to be optimum relative to certain similar methods and necessary conditions for the new procedure to lead to admissible estimates are studied. In the last portion of the thesis a sampling study is reported for observations generated with a model containing only one exponential term and with errors which are normally distributed. The small sample biases and variances for the estimates computed from these observations are given and the effects of changes in the parameters in the model are investigated. Then some actual experimental data are fitted using both the new procedure and some alternative methods. The final chapter in the body of the thesis contains a critical evaluation of the new procedure relative to other estimation methods. / Ph. D.

Through the years, many millions of people have been living in poverty with lack of economic opportunity. These people live in the underdeveloped areas of the world. Until recent years, they accepted their poverty as a part of life, but the two world wars and the spread of industrial civilization have changed their lives. They now realize their misery is unnecessary and a better standard of living is possible. These people need the hand of fellowship with all free nations to give them guidance and help in their endeavor to bring about a better life for their masses. The United States and the rest of the free world can no longer live in isolation from the two-thirds of the human race that are poor and hungry. Most Americans are now realizing our importance in helping to raise the standard of living throughout the world. The United States has adopted the Point Four Technical Assistance Program to provide help to these underdeveloped areas in order that they may realize their aspirations for a better life. This aid is provided only to those countries that ask for help; it is not forced upon those countries that are reluctant. The objective of Point Four is to help the people of those countries, through their own efforts to produce more food, more clothing, more materials for housing, and more mechanical power to lighten their burdens. India is an underdeveloped country that has put forth a. great effort to improve its economic condition. After becoming independent in 1947, India tried out many experiments in rural betterment. These experiments proved to be so successful that India drew up a Five-Year Plan and a Community Development Program to help relieve the tremendous poverty in India. The development programs are to arouse the Indian people to an understanding of what they can accomplish through their own group efforts. These millions of people, who have lived so long in poverty, will benefit from modern scientific knowledge. The United States immediately made Point Four Technical Assistance available to India upon the signing of the Indo-American Agreement in January 1952. This assistance was to be used in assisting the Indian Government in its program of economic development. The first major task undertaken under tho economic development programs was to improve agricultural production. Other goals to be worked toward were better education, improved health, housing, and developing of natural resources. These goals will have to be carried out over a long period of time to obtain maximum economic development, but minimum development goals were hoped to be reached by 1956. India is receiving Point Four Technical Assistance from the United States, the United Nations, and other countries of the world in order that its people may be lifted out of poverty into a better standard of living. This cannot be done overnight, but with continued help India’s people will be able to realize their hopes of a self-sufficient country and a better life. / Master of Science

The first objective of this problem - thorough literature review - was conducted on all available references concerning humidity measurement, and visits were made to the American Instrument Company in Silver Springs, Maryland, and the National Bureau of Standards. The survey evaluated the instruments in use today and also explored many of the ideas and concepts that have been suggested in past years as possible means for humidity measurement. A summation of the survey indicated that the electric hygrometer with a ceramic element was a good basic theory for a humidity instrument, but still required development before it,would be of any practical use. The second objective - development of a useful hygrometer - was directed towards the development of the electric hygrometer using a ceramic element. The study that resulted included the evaluation of two methods for determining the change of resistance of the ceramic element, as well as a preliminary investigation of the characteristics of a ceramic element when employed as the sensing element for an electric hygrometer. The element intended for the initial tests, a porous ceramic containing mostly aluminum oxide, was the only material tested, but the tests included elements of the pure ceramic material and the same material after it was soaked in a saturated solution of lithium chloride. With the instruments used, the indications were that both elements were suited for determining the high humidities. The pure element had a lower limit of 50 percent relative humidity, and the coated element a lower limit of 20 percent. Two instruments were used for indicating the change of relative humidity. A vacuum tube voltmeter type instrument was tested, but found unsatisfactory due to variations of readings under the same conditions, drifting of the zero set, and excessive fluctuations of the indicating meter. The other instrument or method used was to apply an A-C voltage across the element, and to measure the resulting current flow. Because the current was maintained above 1 milliampere, heating of the element was caused, resulting in a change of element resistance. However, results with this instrument were sufficient to establish a calibration curve for the apparatus. A comparison of this device and a psychrometer indicated the usefulness of such an instrument, but confirmed that the development was not complete. The overall result of the research indicates that the selection of the ceramic sensing element for an electric hygrometer has merit, but more development is necessary. Two phases of any future work on the problem should be the development of the indicating instrument, and the selection and design of the sensing element. The need for a satisfactory instrument still exists, and the successful development of the type instrument described herein, would undoubtedly meet the requirements. / Master of Science

Manganese is a metal of strategic importance which is vital to the steel industry. In the production of steel, the two main uses of manganese are as a deoxidizer and as an alloying constituent. Approximately 13 pounds of manganese are used for each ton of steel, and for this use alone, the requirement of the United States in 1956 will approach two million tons of ferromanganese ore. In 1954, the United States imported over 90 percent of its manganese requirements and if these sources become unavailable, this nation will be dependent to a great extent upon abundant low-grade ores. A sample of the head ore from the Betty Baker Mine, Great Gossan Lead, Carroll County, Virginia, analyzed 0.82 percent acid soluble manganese. An analysis of the tailings from flotation of this complex sulfide ore revealed a total manganese content of approximately three percent of which two-thirds is acid soluble. The remaining one percent is in the form of a silicate-aluminate gangue which is acid insoluble. Mechanical methods such as froth flotation, sink float, and magnetic separation have not been too effective in upgrading the ore from Carroll County. Chemical procedures, such as roasting, leaching, and electrodeposition, were thought to offer a better means for the recovery of manganese from the beneficiated ore or tailings. It was the purpose of this investigation to evaluate procedures for chemically converting the manganese compounds in the tailings, from bulk sulfide flotation of the Carroll County ore, to soluble salts from which the manganese could be recovered electrolytically. / Master of Science

Master of Science

For all those sports enthusiasts within the Blacksburg area; for all members of the student body interested in intercollegiate, intramural, or individual sports competition; for all members of the administration interested in school prestige; and for all members of the athletic plant staff; a new building to house intercollegiate sports activities is a very vital and realistic problem - vital because of the present inadequacy and inflexibility of the War Memorial Hall, and realistic because of actual plans now in progress to expand the athletic facilities of Virginia Polytechnic Institute. This thesis deals with the design of a building that will meet the needs of adequacy and flexibility. / Master of Science