A Moak type radio frequency ion source, capable of producing a pulsed beam of deuterons has been built for use with a Cockcroft-Walton accelerator. Pulsed deuterons striking a deuteron target produce neutrons in bursts thus allowing dynamic measurements of moderator and reactor core properties. Beam pulsing is accomplished by means of an einzel lens and an alternating potential applied to a pair of deflection plates. Proteins have been used exclusively in adjusting the source for optimum results since the radiation background due to the protons is much less than that due to deuterons. In actual experiments, however, when using deuterons, no modifications need to be made in the source. Beam currents have been measured at the source and at a target located at the end of the accelerator tube. Maximum currents measured are 150 microamperes and 60 microamperes respectively. Details of construction, maximum operating conditions, and oscillogram sof purse shapes are included in this report. / M.S.

C.T.G. Looney proposed a method of solving the problem of steady-state forced vibration of continuous frames. Starting with the analysis of a single span, simply supported beam, the method was extended to continuous beams and frames. An investigation of his method was undertaken comparing experimental deflection with those predicted by Looney’s method. A single span beam and a two span continuous beam was used in the experiment. A mechanical shaker was used to vibrate the beam. The experimental and nautical curves showed good agreement with the experimental values being consistently higher. Although the weight of the shaker's moving parts was less than one-tenth the weight of the beam it had considerable effect in lowing the resonant frequency and increasing amplitudes. / M.S.

The suitability of powdered starch with borax or glycerine accessories for dark cottons of three different colors and weights and with selected construction gestures was ascertained. Selected colors, weights, and construction features were evaluated by analysis of variance for their effect on the suitability of the starch and its additive. The scores recorded by a panel of competent judges supplied data on the change in color, luster, and hand of the starched fabric. The color was statistically significant in only half of the instances for which it was analyzed. The weight of the fabric was significant for one-fourth of the starched samples. Construction influenced starching only when combined with another factor, and then is only one case of a possible six. Scores indicated starching caused from moderate to considerable change for the majority of the samples. The glycerine and starch treatment was more affective than the starch and borax combination. / M.S.

This investigation was carried out primarily to study the semi-aquatic tardigrade fauna of Southwestern Virginia. Specimens were obtained from mosses and lichens and were mounted by use of a procedure employing a modification of Hoyer's medium. During the course of this study, 694 specimens were obtained and the following species were identified: Batillipes friaufi sp. n., Echiniscus (Hypechiniscus) gladiator, Echiniscus (Echiniscus) virginicus sp. n., Pseudechiniscus suillus, Macrobiotus macronyx, Macrobiotus intermedius,Macrobiotus richtersi, Macrobiotus harmsworthi, Macrobiotus hufelandi, Macrobiotus echinogenitus, Hypsibius (Isohypsibius) tuberculatus, Hypsibius (Isohypsibius) nodosus, Hypsibius (Isohypsibius) prosostomus, Hypsibius (Isohypsibius) tetradactyloides, Hypsibius (Isohypsibius) canadensis, Hypsibius (Hypsibius) convergens, Hypsibius (Hypsibius) conjungens, Hypsibius (hypsibius) oberhaeuseri, Diphascon bullatus, Diphascon angustatus, Diphascon sconticus, Diphascon belgicae, Diphascon ninguis, Diphascon nodulosus, Itaguascon bellinae and Milnesium tardigradum. Collection data, discussion of the taxonomic status and previous morphological observations were presented for each species. Recommendations were made concerning the discarding of egg morphology as a valid basis for species description and identification. The practice of using numbers for taxonomic entities in tardigrade systematics was observed to be deplorable and the abandonment of such usages was urged. Evidences for the consideration of the Tardigrada as a phylum were presented and a taxonomic hierarchy was erected for this disposition. To complete this taxonomic scheme, the Heterotardigrada and Eutardigrada were accorded class status, the Arthrotardigrada and Echiniscida (= Echiniscoidea) were raised to ordinal rank and a new order, Diplotardigrada, was included with the Eutardigrada. The following new family names, made mandatory by the rules of nomenclature, were presenteda Batillipidae (= Discopodidae), Tetrakentronidae (= Onychopodidae), Echiniscoididae (= Nudechiniscidae), Echiniscidae (= Scutechiniscidae) and Milnesiidae (= Arctiscidae). The previously suggested phylogenetic schemes for the tardigrades were reviewed and the evidences for affinities of the Tardigrada were presented. A bibliography of the recent literature on the tardigrades was compiled. / Doctor of Philosophy

Previous investigations have revealed that some polymer solutions exhibit dielectric dispersion (variation of the dielectric constant with frequency) which is apparently related in some way to the molecular weight of the polymer (1) (2) (3). One of these investigations (1) was carried out on solutions to cellulose acetate in dioxane. It was found that the change in dielectric constant was so small that rather concentrated solutions had to be used in order to obtain reproducible results. The possibility of intermolecular interactions in concentrated solutions made dilute solution measurements desirable. Consequently, the object of the present investigation was to carry out such measurements with sufficient precision to define the shape of the dielectric dispersion curve over the necessary frequency range. The fundamental difficulty was that the change in dielectric constant of a solution containing less than 1% cellulose acetate was only about one part in five hundred or less in a frequency range of about three decades. The course ot such a small change is difficult to detect over such a wide band of frequencies. Capacitance bridges; which are very good for making measurements at a single frequency, particularly in the range of frequencies under investigation; were commercially available. However, bridges have certain inherent disadvantages which make difficult the coverage of such a wide band of frequencies with the necessary precision. The use of ordinary resonance methods was desirable, but they are limited by the practical sizes of the components to frequencies well above the lowest frequencies which were expected to be encountered. As a result of these limitations, a modified resonance procedure was adopted. A resistance-capacitance oscillator was substituted for the more conventional inductance-capacitance circuits. Null indications were obtained by substituting a frequency counting system of great precision for the "zero beat" method. It had been found earlier that the critical frequency was related to the weight average molecular weight of the polymer sample, the critical frequency being defined as the frequency at which the dispersion was 0.5. Based on this it seemed reasonable to assume that the dielectric dispersion curve might be related in some way to the molecular weight distribution curve in the case of a polydisperse sample. An attempt was thus made to obtain the dielectric dispersion curve in as much detail as possible, since this served the two-fold purpose of permitting conclusions to be drawn concerning the validity of the molecular weight relationship in dilute solutions and giving an indication of any influence of the molecular weight distribution on the dielectric dispersion. Apparatus was developed which gave a precision of 0.01 uuf in a total of about 250 uuf. This provided the means of measurement. Measurements were made on several fractions and three artificial blends. The results of measurements on fractions indicated that the form of the critical frequency-molecular weight relationship determined earlier (1) was correct. The dispersion curves obtained for the three blends of varying width indicated that the slope of the dispersion curve at the critical frequency decreased as the width of the blend was increased. This was the only indication of an influence of the width of the distribution on the dispersion curve. It was noted, however, that the slopes of the dispersion curves for the fractions were less than those for the narrowest blend in several cases. The most reasonable explanation of this observation seems to be that the fractions and blends have much wider distributions than was believed. It is also possible that chain flexibility might be a complicating factor. (1) Scherer, P. P., Levi, D. W., and Hawkins, M. C.: J. Polymer Sci., 24, 19 (1957) (2) Scherer, P. C., Hawkins, M.C., and Levi, D. W.: J. Polymer Sci., 31, 105 (1958) (3) Scherer, P. C., Hawkins, M. C., and Levi, D. W.: J. Polymer Sci., 37, 369 (1959) / Ph. D.

We consider a multivariate situation with means µ₁,...,µ_p and covariance matrix Σ. We wish to derive sequential procedures for testing the hypothesis: H₀: (µ̲ - µ̲ₒ)Σ⁻¹(µ̲ - μ̲₀)’= λ₀²( usually zero) against the alternative: μ̲₀ H₁: (µ̲ - µ̲ₒ)Σ⁻¹µ̲ - μ̲₀)’=λ₁² both for the case where Σ is known (the sequential X²-test) and where Σ is unknown and must be estimated from the sample (the sequential T²-test). These sequential procedures should guarantee that the probability of accepting H₁ when H₀ is true is equal to a and the probability of accepting H₀ when H₁ is true is equal to β. For the case where Σ is known, λ₀² = 0 and λ₁² = λ², the test procedure is as follows: for a sample of n observations form the probability ratio: P_1n/P_0n = e^-nλ²₀F₁(p/2;nλ²X_n²/4) where p denotes the number of variables, _nx[with horizontal bars above and below the x] denotes the vector of the sample means based on n observations, X²_n = n(_nx[with horizontal bars above and below the x] - μ̲₀) Σ⁻¹(_nx[with horizontal bars above and below the x] - μ̲₀)’ and ₀F₁ (c;x) is a type of generalized hypergeometric function. a. If P_1n/P_0n ≤ β/(1-α), accept H₀; b. If P_1n/P_0n ≥ (1- β)/α, accept H₁; c. If β/(1-α) < P_1n/P_0n < (1-β)/α, continue sampling. For the case where Σ is unknown, the procedure is exactly the same except that the probability ratio is now: P_1n/P_0n = e⁻^-nλ²/2 ₁F₁[n/2,p/2;nλ²T_n²/2(n-1+T_n²)] where T_n² = n(_nx[with horizontal bars above and below the x] - μ̲₀)S<sub>n</n>⁻¹(_nx[with horizontal bars above and below the x] - μ̲₀)' , S_ndenotes the sample covariance matrix based on n observations and ₁F₁(a,c;x) is a confluent hypergeometric function. Procedures are also given for the case λ²₀ ≠ 0. Similar procedures are given to test the hypothesis: H₀ = (μ̲₁ - μ̲₂- δ ̲)Σ⁻¹(μ̲₁ - μ̲₂ - δ̲)’ = λ₀² (usually zero) against the alternative: H₁ = (μ̲₁ - μ̲₂- δ ̲)Σ⁻¹(μ̲₁ - μ̲₂ - δ̲)’ = λ₁² It is shown that these sequential procedures all exist in the sense that the risks of accepting H₀ when H₁ is true and of accepting H₁ when H₀ is true are approximately α and β respectively and that these sequential procedures terminate with probability unity. Some of these situation have been generalized to give simultaneous tests and the means and covariance matrix of a sample. No expressions yet exist for the OC or ASN functions although some conjectured values have been determined for the latter and suggest, in comparison with their corresponding fixed-sample tests, substantial reductions in the sample sizes required when either H₀ or H₁ is true. The general problem of tolerances is discussed and then some of these procedures are demonstrated with a numerical example drawn from the field of ballistic missiles. The determination of P_1n/P_0n is quite laborious for both the sequential X² - and T²-tests since it requires the evaluation of a hypergeometric function each time an observation is made. It would be better for each value of n, given p, α, β and λ² under H₁, to compute the values of X²_n or T²_n which would correspond to the boundaries of the tests indicated by β/(1-α) and (1-β)/α. Tables to facilitate both the sequential X²- and T²-tests are given for p = 2,3,...,9; λ² = 0.5, l.0, 2.0; α = β = 0.05 for n ranging from the minimum value necessary to reach a decision to 30, 45 and 60 for λ² = 0.5, 1.0, 2.0 respectively. These tables were prepared on the IBM 650 computer using the Newton-Raphson iterative procedure. Finally, a discussion is given for the hypergeometric function ₀F₁ (c;x) and a table given of this function for c = .5(.5)5.0 and x = .1(.1)1(1) 10(10)100(50)1000. / Doctor of Philosophy

This thesis presents two alternative procedures for comparing standard and quick tests of a null hypothesis H_o. This comparison is usually made by plotting the power curves of each test for a fixed Type I error. However, the power curves give only an indication of the individual performances of each test and not of the extent to which they agree when applied to the same problem. The procedures discussed in this paper deal with determining this degree of agreement. The first method determines the probability, P, that the quick test leads to a significant result at a level α given that the standard test is just significant at level α. If the standard and quick tests are based on the statistics u₁ and u₂ , respectively, the second approach determines the level of significance corresponding to the expected value of u₂ given that u₁ is just significant at level α. This level of significance is termed the "equivalent Type I error" of the quick test and denoted by γ. Both methods are applied to compare tests of location, dispersion, and the paired t-test with the sign test, all in samples taken from a normal population. In the first two cases, values of P and γ are given for different sample sizes, and in the third case only the “equivalent Type I error" of the sign test is given, P being rather difficult to evaluate. / Master of Science

The Organization tor European Economic Co-operation(O.E.E.C.) was a result of Marshall Plan pressure for co-operation among the states receiving American aid. The cooperative spirit engendered by O.E.E.C. prompted the formation of the Council of Europe, where the international problems of the members were debated. Conclusions of the Council were addressed to the states, but were not binding. A. closer association was sought by men such as Paul-Henri Spaak, Robert Schuman, and Jean Monnet. The Schuman Plan launched the European Coal and Steel Community, whereby six states - France, Germany, Italy, Belgium, Luxembourg, and the Netherlands - pooled their coal and steel industries, and relinquished national control over them. This was followed by an abortive attempt to form a common European army and a common political community. The effort failed in the French National Assembly in 1954. The following year brought the “new drive for European union” led by MM. Schuman and Monnet. The result was the establishment of the European Economic Community (Common Market) and the European Atomic Energy Community (Euratom) in January of 1958. Complications in the relations between the Community and the other western European states - particularly the United Kingdom - have yet to be resolved, but negotiations are currently being conducted. The effectiveness, even the very existence, of the Common Market and the unity movement may well depend on the result of these negotiations. / Master of Science

A one-tenth scale model of a skewed reinforced concrete rigid frame bridge was constructed and tested both within the elastic range and to ultimate load. The model was fabricated of reinforced concrete using a 1: 3.8 : 0 mix and 1/8 inch deformed reinforcing bars. A total of 57 SR-4 type AR-7 rosette gages were used to measure the strains on the surface of the concrete at selected positions. An additional 108 SR-4 type AR-7 and AR-7-4 strain gages were fastened to the steel reinforcing. Deflections were measured at 11 points of the deck and supporting reactions determined by suitable dynamometers. The vast amount of strain data was presented in tables. Part of it was converted into stresses and these integrated to find the internal reactive forces and moments at selected sections. However, the unknown behavior of concrete in biaxial tension and difficulty in establishing the precise position of the neutral surface prevented as close a check of static equilibrium as would have been desirable. / Master of Science

In order to solve a highly indeterminate rigid frame structure by the method of slope deflection a high order stiffness matrix needs to be inverted. Existing computer programs for the IBM Type 650 Computer are entirely too time consuming when the matrix coefficients and program instructions exceed the storage capacity of the computer drum. The method described in this paper involves the solution of the problem by the inversion of a partitioned matrix originally described by Duncan, Prazer, and Collar. Machine time was reduced by 91% using the new method. The program retains accuracy of six significant figures for a matrix normally twice as large as a machine can handle at one time, and four plus significant figures if the matrix is four times as large as the computer can handle in one storage operation. The method can be applied to digital computers of any size, thus increasing their apparent storage capacity or decreasing their operating time for a matrix inversion. The method is applicable to symmetrical as well as unsymmetrical matrices. / Master of Science