The classical method, required for its solution, the application of boundary conditions to the solution of the beam equation. Except for the case cf the beam with one concentrated load at the center, it was not considered a practical solution. The transcendental equation obtained in the solution of the unsymmetrical case, considered in part B, was found too cumbersome to handle. It was not attempted in parts C and D. The Rayleigh Method proved to be a simple, accurate and reasonably rapid method for all cases considered. The Dunkerley Equation gave very satisfactory results for parts A, B, and C. It was rapid to use, accurate and in most cases the data could be found in prepared tabulations. Results were inaccurate for the two span beam, indicating the necessity for caution in its application to multi-span beams. The Ritz Method, which is a refinement of the Rayleigh Method, proved to be exceedingly accurate when applied to the beam with the single concentrated load. However, it was found, that as the number of terms in the assumed deflection equation increased, the work became more time consuming. It was used only in parts A and B. The Influence Coefficient Method and the application of D'Alembert's Principle, which methods are quite similar, proved to be simple, accurate, and rapid. However, as the number of degrees of freedom increased, the degree of the algebraic equation increased, which complicated the solution. The Iteration Method is probably the method to be used if the number of degrees of freedom exceeds three. As the number of modes increases the number of iterations would increase, but the individual operations in themselves would remain simple. This method proved simple and accurate to use. For the cases considered, it was more time consuming to use than either the Influence Coefficient Method or the application of D'Alembert's Principle. However, for higher degree situations, it should prove to be a more practical method. / Master of Science

This investigation of design factors and operational requirements for irrigating burley tobacco was conducted on a system of irrigation control plots located on the Smithfield farm of the Virginia Agricultural Experiment Station. / Master of Science

A method has been proposed for obtaining confidence intervals for the differences between treatment means in an analysis of variance. The intervals have the following properties: (1) The probability that the interval will cover the parameter is greater than or equal to (1 - α), and (2) If the same procedure is applied simultaneously to each of the pO2 differences among p means, the probability that all confidence intervals will cover the parameters correctly is at least (1 - α) ^{p - 1}. The same properties hold if the procedure is simultaneously applied to special linear comparisons among the means as well as to differences between single means. The intervals are complex in that the limits are dependent on the values of nuisance parameters. Three alternatives for handling these nuisance parameters are discussed, and one is preferred for use in practice. / Master of Science

M.S.

Master of Science

Master of Science

The purpose of this investigation was to study the effect of the direction of flow with varying phase velocities on the overall, mass-transfer coefficient in a horizontal, unpacked, extraction tube, for the system n-butanol-water, and for the system 1,1,2-trichloroethane-sectione-water. / Master of Science

The purpose of this work is to discover an optimum sample size to be used for deciding between two methods (populations) to choose for future production. The procedure involves the formulation of a loss function, expressing the expected loss due to choosing the population with the small mean, as a function of the difference between the population means, the amount to be produced and the cost of sampling. A minimax procedure is applied to obtain the optimum sample size. Since the function does not lend itself conveniently to mathematical considerations, special cases involving the difference between the means are considered and an optimum sample size is found for these cases. In all cases, the optimum sample size is an explicit function of the amount to be produced, the cost of sampling and the standard deviation. / Master of Science

As pointed out in the “Discussion of Results”, the sub-surface stresses in a gear tooth decrease very rapidly with its depth. This result serves as a supporting evidence to the common practice of case-hardening the gear teeth. Previously this was done according to the mechanical properties of the gear materials, but without any analytical basis. Gear stress is a very complicated problem which includes in general the static, dynamic and fatigue stresses. Most of all, many uncertainties in service such as the impact load, acceleration load and work hardening are involved. These uncertainties make it difficult to get a general solution. The photoelastic method is an effective one for making a static study of gear stress, but it is understood that this method can not solve the whole problem, Since if the static stresses are considered further studies covering the notch sensitivity, friction effect, dynamic effect, and load distribution are still needed. / Master of Science

It has been found that the hodograph method can be applied with considerable ease to problems of stead, two-dimensional, irrotational, compressible fluid motion in which the bounding streamlines are made up partially of straight boundaries and partially of free streamlines. As in classical theory, these solutions can be used to determine important physical characteristics of the problem such as the equations of free streamlines and the contraction coefficient provided it is possible to carry out the mathematical operations. It must be realized that the hodograph method gives only approximate solutions. However, the hodograph solution gives a more accurate description of a fluid flow than does the classical solution since the hodograph method takes into account the effects of compressibility. It is hoped that the methods used and the solutions obtained in this thesis will aid in giving further insight into the problems of compressible fluid flow. / Master of Science