A study was made cf the cost per pound of magnesium sulfate monohydrate produced by a "Krystal" crystallizer at recirculation rates from 20 to 40 gallons per minute and operating temperatures from 150 to 180 °F. From these tests, the optimum operating conditions within the range of these variables were derived. The problem was studied by operating the equipment at all sixteen combinations of these variables in unit steps of ten. The crystallizer was operated at each set of conditions, the product collected, and the cost per pound determined. The operating conditions were found to affect power and steam costs greatly, varying from 1.689 mills/lb at 50 gallons per minute and 170 °F to 0.737 mills/lb at 20 gallons per minute and 180 °F, representing a decrease. cf 0.952 mills per pound upon correct choice of operating temperature and recirculation rate. / Master of Science

A series of eight compounds with bis-diamine cores were prepared and their electrochemical behavior was explored polarographically. The behavior of the compounds was studied at the dropping mercury electrode and the rotating platinum electrode. Trans-dinitro-bis-(ethylenediamine) cobalt (III) nitrate shows reversible behavior in well-buffered solutions at the dropping mercury electrode, The mechanism for the reduction is proposed as; rapid, reversible election transfer; decomposition of the reduced species; and, in solutions sufficiently alkaline, the formation of tris-(ethylenediamine) cobalt (II), thereby accounting for the observed second wave. The reduction of cis dithiocyanato-bis-(ethylenediamine) cobalt (III) thiocyanate and oxalato-bis-(ethylenediamine) cobalt (III) chloride both give irreversible waves, thereby complicating any proposal of a mechanism. The observed second reduction wave, though, appears to be caused by the formation of tris-(ethylenediamine) cobalt (II), as in the case of the dinitro compound. A proposal of the mechanism for the other five compounds was not possible as they either reduced at too positive a potential, aquated too rapidly, or both. / Master of Science

The primary purpose of the study was to obtain estimates of heritabilities of the important economic characters in Columbia and Columbia X Southdale sheep at weaning and yearling ages as well as the phenotypic and genetic correlations among these traits. Information was acquired concerning the effects of year of birth, age of dam, type of birth and rearing, sex, breed, and station on the weanling and yearling traits considered. Data were available on 2442 lambs from 1707 ewes for weaning weight analysis. The lambs were predominantly of the Columbia X Southdale strain. The Columbia X Southdale lambs were raised at Middlebury, Vermont, and Beltsville, Maryland, while the Columbias were reared at the Vermont Station only. Numbers of records for the other traits were not as large, many of the lambs having been culled before yearling age. Three weanling traits and six yearling traits were considered on each individual. The traits were scored or measured at about 140 days of age for the weanling. Yearling measurements were made when the sheep were approximately 13 months old. The nine traits evaluated were: weaning weight, weaning type, weaning condition, yearling body weight, yearling type, yearling condition, yearling fleece weight, yearling fleece character, and yearling staple length. The traits most influenced by the environmental effects were weaning weight, weaning type, weaning condition, yearling body weight, and yearling fleece weight. The year of birth was the most consistent cause of environmental differences of any of the effects studied. Heritabilities of weaning weight, weaning type, weaning condition, and yearling body weight were found to be 0.14, 0.14, 0.15, and 0.13 respectively. Heritability values for yearling type, condition, fleece weight, fleece character, and staple length were 0.32, 0.45, 0.69, 0.66, and 0.73 respectively. The estimates were obtained by paternal half-sib analysis. The 36 phenotypic correlations were all of a positive nature with the exception of four and only one of these negative relationships, between yearling fleece weight and fleece character, was statistically significant. Correlations of the greatest magnitude were found among the weanling body traits. The yearling traits were not highly correlated with the exception of type and condition (0.68). The genetic correlations revealed genetic antagonisms which might impede genetic progress if ignored in selection procedures. Negative genetic correlations were found between yearling how weight and weaning type, yearling fleece character, and yearling staple length. Yearling fleece weight was negatively correlated with yearling condition, yearling type, and yearling fleece character. Staple length was negatively correlated with yearling condition and fleece character. The majority of all traits were positively correlated and weaning weight showed a positive relationship with every other trait. The comparison between the Columbia and Columbia X Southdale sheep showed the Columbias to rank heavier in weaning weight, yearling weight, yearling fleece weight, and longer in yearling staple length. The Columbia X Southdale ranked higher in weaning type, condition, yearling type, condition, and fleece character scores. The estimates of genetic parameters obtained in the study form important guidelines for the development of future selection procedures, thus making possible more rapid progress in the improvement of the flocks studied. / Ph. D.

This thesis is the study of the effects of several commercial admixtures on the properties of concrete in the plastic and the hardened state. The project is divided into two parts. Part I deals with the laboratory investigation and Part II takes into account the theoretical study of Part I. Three standard concrete mixtures at different water-cement ratios and approximately at constant slump were designed without the addition of admixtures to serve as a parameter for the test mixtures. Eighteen different test mixtures were made with local aggregates. Three test mixtures for each individual admixture and combination admixtures were used for comparison purposes. From the results obtained in the laboratory study, it was found that all the admixture used, separately and in combination, the test mixtures with an air entraining agent produced the greatest improvement in the plastic state as compared with their standard. In the hardened state, the cement dispersing agent (normal set) and the accelerator produced the greatest increase in the compressive strengths at all ages of testing as compared with their standard. It is further revealed that the accelerator imparted the greatest influence when used in rich mixture. In the theoretical study, by making alterations in the water-cement ratio so as to obtain a desired slump of four inches, the theoretical test mixtures so designed predicted a further increase in the compressive strengths, except in the case of the accelerator. It is noteworthy that the accelerator produced the same magnitude of compressive strength as was produced by the cement dispersing agent (normal set) at 28 days in the rich mixture, but in the case of the poor mixture, the latter was more effective. / Master of Science

The problem discussed in this paper is the estimation of a single missing observation, two missing observations and several missing observations in a Group Visible (Singular) for Shirley balanced incomplete blocks design with two associate classes. Subsequently the analysis of variance, of the data augmented by the estimates of the missing observations, is derived. The method, first employed by Yates (1933), was followed to minimize the error sum of squares. Explicit formulae were developed, for the estimates of one missing observation, two missing observations occurring in various configurations and general formulae for z (= n) missing observations for certain particular configurations. Analysis of the data augmented by the estimates of the missing observations lead to positive bias in the case of treatment sum of squares, a method of analysis was discussed to eliminate this bias. A numerical example of illustrating the technique of estimating missing observations in a GDS P.B.I.B. design was given. The approximate and exact tests were performed, for the null hypothesis of no treatment differences, using the intra-block error mean square. / Master of Science

The general solution was obtained for the free flexural vibrations in the plane of a thin circular ring containing a point mass. As a degenerate case of the general solution, the solution for a uniform ring alone was derived from the general solution by taking the point mass to be zero. Numerical calculations of the frequencies and mode shapes of the first and second flexural modes were made for values of the point mass in the range from zero to infinity. The results are presented in graphical form. The predominant feature of the investigation was the difference in frequency and mode shape found in the symmetrical and antisymmetrical modes, and the particular orientation of the nodes with respect to the point mass. It was noted that similar phenomena were observed experimentally for vibrations of imperfect bodies of revolution. In conclusion, it was brought out that a ring with a point mass offers a convenient mathematical model for a preliminary theoretical investigation of the vibrations of imperfect bodies of revolution. / Master of Science

Early in the thirteenth century, Leonardo de Pisa, or, Fibonacci, introduced his famous rabbit problem, which may be stated simply as follows: assume that rabbits reproduce at a rate such that one pair is born each month from each pair of adults not less than two months old. If one pair is present initially, and if none die, how many pairs will be present after one year? The solution to the problem gives rise to a sequence {U_n} known as the Classical Fibonacci Sequence. {U_n} is defined by the recurrence relation U_n = U_n-1 + U_n-2, n ≥ 2, U₀ = 0, U₁ = 1 Many properties of this sequence have been derived. A generalized sequence {F_n} can be obtained by retaining the law of recurrence and redefining the first two terms as F₁ = p', F₂ = p' + q' for arbitrary real numbers p' and q'. Moreover, by defining H₁ = p+iq, H₂ = r+is, p,q,r and s real, a complex sequence is determined. Hence, all the properties of the classical sequence can be extended to the complex case. By reducing the classical sequence by a modulus m, many properties of the repeating sequence that results can be derived. The Fibonacci sequence and associated golden ratio occur in communication theory, chemistry, and in nature. / Master of Science

The stress concentration factors for rectangular slots with semicircular ends with their major axes inclined to the direction of a uniaxial tension field were investigated by photoelastic methods. A major portion of this thesis deals with the problem of loading a circular disk such as to create an approximately uniform tension field. This circular disk was used to investigate the stress concentration factors of the slots which were compared to the known results of a slot perpendicular to a tension field in a rectangular plate. The maximum value for the stress concentration factor occured when the slot was perpendicular to the direction of the tension field. A method of determining the stress concentration was developed which required only the recording of the load at which each fringe appeared on the edge of the slot. This method gave results with 6% of accepted values. / Master of Science

Early weaning onto pasture, separate grazing for ewes and lambs on pasture, and weaned and nonweaned lambs in a drylot were compared with control groups of ewes and lambs grazed together at Blacksburg and Glade Spring in 1960 and 1961. Data were available on 457 lambs for average daily gain and slaughter grade and on 311 lambs for carcass grade and yield. The data were adjusted for the effects of breed of sire, breed of dam, age of dam, sex, and type of birth and rearing. Comparing the pasture treatments at both Blacksburg and Glade Spring in 1960 and 1961, in a two-way classification, in the analysis of variance there was a highly significant interaction between years and treatments. There was no significant difference between the high and low roughage ration that was fed to weaned and nonweaned lambs at both stations. The weaned lambs on the low roughage ration at Blacksburg performed significantly better at the 5 percent level than the pasture groups, for average daily gain. The means were higher for the other three traits, though not significantly so. At Glade Spring the drylot lambs that were weaned had a significantly higher mean at the 5 per cent level for yield over the control group, and the means were higher for the other three traits. / Master of Science

The purpose of this investigation were to use chromatographic methods to study the effects of pH, time of equilibration, and the effect of anions themselves in the anion retention in an acid red soil. It was found that chloride was held much less tightly than sulfate by soils. It was also noted that more sulfate was retained at higher concentration. A time factor was also noted in this investigation. It took a longer period to reach true equilibrium when sulfate was used. Results showed a positive correlation between sulfate retention and time to reach true equilibrium. The disappearance of aluminum from the solution added to soil suggested that the continuing hydrolysis of aluminum being the main cause of the time effect. Such hydrolysis produces hydrogen ions which can neutralize the hydroxyl ions exchanged by anions and kept the pH of the system from going up and continuing the reaction. The non-symmetrical elution patterns indicated the retention of anions• The longer the tail of the elution patterns, the more tightly the anions are retained. Distribution coefficients (Kd) for Cl⁻, NO₃⁻, and SO₄ showed approximately linear relationships between pH 3 and 6. Chloride and NO₃⁻ exhibited similar Kd values at similar pH values. It also indicated that SO₄⁻ was held much more tightly at low pH values. / Master of Science