This paper is divided into two parts. The first part is devoted to a study of absorption in a genetic population model and the second part to introducing a new method of matrix inversion. The author begins Part I by presenting the haploid population model under consideration, a constant-size population in which mutation is absent. Using the approach or Malecot, the problem is formulated in terms of an absorbing Markov chain. A brief review or earlier work by Maleoot, Fisher, Wright, and Feller is given before proceeding to the study of the distribution or time taken for the population to consist of only one gene type. The first method used by the author to determine the probability function for first passage time requires the eigenvectors or the transition matrix. A blocking transformation is used to show that only the eigenvectors corresponding to the even eigenvalues are needed to find the distributions. It is also shown that these eigenvectors are symmetric. In order to simplify computation of the needed vectors, a transformation which triangularizes the transition matrix is presented. This transformation also leads to a simple derivation of the eigenvalues and is used to derive the distributions for populations of size two through nine. Although the general solution is not obtained, expressions for the first seven eigenvectors are listed along with general results concerning the triangularized form. Next, the author attacks the problem by developing the theory or moments or the distribution and applies this theory to determine the means and variances. These are tabulated for population sizes 2(1)9 and 10(10)50. Then, by assuming a large population size, a diffusion process continuous in space and time is used to approximate the Markov chain. Expressions for the mean and variance are derived and are tabulated for the same values as in the moment approach. A comparison of the entries of these two tables gives support to the theory that the diffusion process works as the population size becomes infinite but with the gene frequency ratio kept fixed. Also, it demonstrates that diffusion theory works better for a gene frequency ratio near one-half than for values near zero or one and further that this theory consistently over-estimates the absorption time moments. The author notes, however, that the point of primary importance is the indication that diffusion theory works even with fixed gene number, that is, even in the tails of the distribution. He also states that the percentage error decreases at a faster rate for fixed gene frequency ratio than for fixed gene number and concludes the first part by suggesting a rate of decrease of percentage error for constant gene frequency. In Part II, the author begins by noting the importance of the inverse matrix in Markov chain theory. The new inversion technique given is basically one which generates the inverse with a minimum number of determinantal operations. The method is thoroughly described and it is applied to some problems encountered in the first part of the paper. The paper ends with a comparison of the new method with well-known techniques presently in use which shows that the method proposed is especially efficient for small order matrices. / Ph. D.

In order to determine the feasibility of using the laying hen as a source of molybdenum containing eggs, a dose response experiment was conducted which involved the feeding of graded levels of molybdenum to White Rock laying hens. The feeding of 2000 ppm of molybdenum resulted in decreases in egg production and hen weight. Only egg production was decreased at 1000 ppm of molybdenum. The 500 ppm level of supplementation appeared to be most applicable to further studies in that little effect on either hen weight or egg production was noted. It was also observed that at this level the egg concentration of molybdenum plateaued at 16.4 ppm after 14 days of feeding the experimental ration. An experiment designed to assess the toxicity of the molybdenum included in the egg by the laying hen to the developing chick embryo permitted the estimation of the L.D.₁₀₀ to be about 17 ppm of molybdenum. This value agrees quite closely to the L.D.₁₀₀ of yolk sac injected molybdenum. The embryonic death response observed in this experiment did not occur during any specific period of development. Succinoxidase assays conducted to study the death response indicated that there was no difference in succinoxidase. It was further noted that there was a decline in lethal response in embryos from hens fed the molybdenum containing ration for periods in excess of three months. This decline was mediated by a decreased concentration of molybdenum in the eggs from these hens. The mode of inclusion of molybdenum in the egg, by the laying hen was studied. It appeared that the majority of the molybdenum is included during the maturation of the ova in the ovary. The high concentration of molybdenum observed in the uterus suggests that the shell be considered in future studies. A chemical fractionation of the eggs from the hens fed the molybdenum containing diet indicated that very little of the molybdenum was present in the lipid fraction. Twenty-five percent of the total egg molybdenum was found to be associated with the protein fraction. A rat assay coupled with further chemical procedures indicated that the molybdenum to protein bonding was not of a covalent nature. The observation of n growth depression in chicks which had been injected with molybdenum during their embryonic development was not corroborated by a more extensive study. Although this study was confounded by the possible existence of a copper deficiency, some evidence was obtained for the involvement of molybdenum in the copper metabolism of the chicks. It was surprising that no increase in the blood and liver molybdenum concentrations was observed when the diets containing either 500 or 1000 ppm of molybdenum were compared. The blood and liver copper concentrations were little affected by molybdenum supplementation. / Ph. D.

Though some of the discrete distributions, for example the binomial, hypergeometric, Poisson, are well tabulated, often statisticians use the percentage points of approximating continuous distributions when analysing discrete data. In this thesis, the exact relationships between certain discrete and continuous distributions are established, and these relationships are used for setting confidence limits and significance testing of hypotheses. In Chapter 1, statements of all distributions and mathematical functions used in this thesis are made, and also some approximations are mentioned without proofs. In Chapter 2, exact relationships between discrete distributions (the binomial, negative-binomial, and Poisson) and continuous distributions (the F and χ²) are proved. In Chapter 3, use is made of the approximate and exact relationships between discrete and continuous distributions, for setting confidence limits on the parameters of the discrete distributions. Chapter 4 consists of the approximate and exact significance testing of hypotheses by using the approximate and exact relationships, given in Chapter 2. In Chapter 5, two-sample, exact and approximate, significance tests of hypotheses on the Poisson distribution are performed, in the case of fixed number of events experimentation and fixed time experimentation. / M.S.

A kinetic study of the oxidation of arsenic(III) by chromium(VI) was made in acetic acid-acetate buffers at ionic strengths 1.5M and 3.0M. The reaction rate showed a first order dependence on the arsenic(III), total chromium(VI), and acetic acid concentrations. Two possible mechanisms for the reaction have been suggested. One possibility is the formation of an arsenic-chromium adduct in which either the acid chromate or dichromate ion is involved. A second possible mechanism postulates adduct formation involving only the acid chromate ion, followed by a CrO₄= catalyzed decomposition of the adduct. In either suggested mechanism, the acetate and hydroxide ion catalyzes the decomposition of the adduct. The rate dependence on total chromium(VI) concentration is contrary to previous reports which postulate an adduct or ester mechanism. Induced reaction studies show the initial step involves the oxidation of one arsenic(III) species by chromium(VI) with the formation of tetravalent chromium as-a reactive intermediate. The stoichiometry or the overall reaction was found to be 3 As(III) + 2 Cr(VI) = 3 Aa(V) + 2 Cr(III). / M.S.

A preliminary experiment was conducted during the horn fly season at Blacksburg, Virginia from May through September, 1959, to determine the relationship of weather conditions to horn fly populations on 3 breeds of dairy heifers. Daily records of the fly populations on 10 animals selected at random from a mixed herd of Holstein, Guernsey, and Jersey yearling heifers were made. In addition, the daily minimum and maximum macrotemperatures and relative humidities, the approximate wind direction, and the amount of sunlight or cloud coverage were recorded. Usually there was a significant difference between the number of horn flies on Holstein and that on Guernsey and Jersey heifers. Horn flies generally preferred the dark colored areas of bicolored cattle during the hours of daylight, and they preferred the black of the Holstein rather than the tan of the Guernsey. When the macrotemperature was above 85°F, many of the flies were found on the white skin of the belly and udder area of a heifer. During inclement weather the flies were observed on both the white and dark colored areas of all the heifers. Macrotemperature and relative humidity influenced the horn fly populations within the biocenose. Light rain and winds of less than 20 miles per hour were found to have a negligible effect on the number of flies in the populations; however, significant population decreases were attributed to heavy rain, wind in excess of 20 miles per hour. Often, when the macrotemperature was below 55°F, light rain or wind of low velocity influenced movement of the flies to more sheltered areas on the host. The apparently preferred macroclimate for horn flies was: temperature of 73 to 80°F; relative macrohumidity of 65 to 90%; scattered light showers; and no wind. During the horn fly season of 1960, a second experiment was conducted to correlate the effect of the macro-environment on the micro-environment within the ½ inch mantle of the animal, and also to correlate the locations of horn flies within this mantle with various factors of the micro-environment. (Daily macro-environmental data, including air temperature, relative humidity, wind direction and velocity, amount of cloud coverage, and precipitation, were recorded as in the preliminary experiment of 1959.) Methods for measuring the micro-environment were devised, and the data obtained were analysed statistically and interpreted. Accordingly, the effects on horn fly populations of dark skin color, low temperature, and low humidity were highly significant at the 1% level; the effects on horn fly populations of high humidity and precipitation were significant at the 5% level; and the effect of high temperature on horn flies was not significant at the 5% level. According to the results of the second experiment, the horn flies apparently sought certain micro-environmental conditions which were most commonly observed on Holstein heifers. Within the mantle of micro-environment, horn flies appeared to prefer an air temperature of about 85°F, a skin temperature of about 97°F, and a relative humidity of about 65%. When such conditions were not available to the horn flies on the sides and backs of Holstein heifers, the flies usually found near optimum conditions along the belly midline for each of the 3 breeds of heifers. / Ph. D.

The following conclusions were drawn from this activity study with one subject: 1. The Kofranyi-Michaelis apparatus may be successfully used with children if it is worn on the back of an adult beside the child. 2. More than one test should be used to establish the energy value for a particular activity with one child. 3. Basal metabolism tests should be made near the time that activity studies are to be made. 4. The actual protein content of the diet should be known and used in the Weir formula for accurate energy determinations. 5. Energy expenditure studies are expensive in terms of time, equipment, techniques to be mastered, and the number of personnel required. The conclusions that were drawn in developing the methods used for this study are: 1. It is desirable to have the stand designed for the Haldane-Henderson glassware from Arthur H. Thomas Company to permit proper alignment and closer readings from the carbon dioxide absorber. 2. That enough sampling bottles be available to hold duplicate samples from bladders made in two different activities it the Haldane-Henderson method or gas analysis is used. / Master of Science

Laboratory studies and field observations were conducted to ascertain the development of the female sex organs of the alfalfa weevil during aestivation, to study the role of this aestivation on sexual development, and to investigate the factors responsible for this interaction. Measurements of female sex organs were made in dissected weevils at monthly intervals to observe each of the developmental stages of sexual maturation. Results of this sexual development as it progressed after adult emergence, were presented by means of tables, graphs, and a series of photographs. The importance of not confusing old and new weevils was recognized in this work, since their behavioral patters differ in many respects. The nature and physiology of the aestivation of this weevil was discussed and evidence was presented to support the author's suggestion that this aestivation is a "true diapause." It was demonstrated in this paper that diapause synchronized the sexual growth of the alfalfa weevil to the seasonal changes of the year for species adaptation and survival. / Master of Science

The desirability of finding approximation formulas for IÎ (p,q)is obviously not decreased by the author's difficulty in fitting the function over a larger area. This thesis, other than the area fitted, has pointed out some of the problems that must be solved before adequate approximations over a large range can be developed. / Master of Science

Soil clays relatively high in montmorillonite were examined and compared to the reference material. / Master of Science

The following paragraphs contain the conclusions drawn from this investigation. 1. The rate of attack on the bare metal increases with increasing temperature; particularly in the pickling of black stovepipes steel in 18.3 percent sulfuric acid solution where the rate of attack on the bare metal at 75°F is 0.097 milligrams per square inch per minute, while at 142°F the rate of attack is 0.51 milligrams per square inch per minute. 2. The time required to remove the surface oxide from the sample decreases with increasing temperature. 3. The 18.75 percent phosphoric acid solution removed the most surface oxide in the least amount of time at 165 and 177 °F. 4. The effect of Rodine 50 inhibitor on 20.5 percent hydrochloric acid pickling solution cannot be studied because the rate of attack on the bare metal of uninhibited pickling solution was too small, at 80 °F. 5. The addition of Rodine 82-A inhibitor to a pickling bath containing 18.5 percent sulfuric acid decreased the rate of attack on the bare metal from 0.0858 milligrams per square inch per minute to 0.0286, without appreciably affecting the time required to remove this scale, at 78 °F. 6 No valid conclusions can be made concerning the life of the Rodine 82-A inhibitor because of the erratic nature of the results. / M.S.