The object of this thesis is to define special orthogonal polynomials and develop efficient methods for employing them which have the same advantages with respect to functions of the type (1.2) as do univariate orthogonal polynomials in the simple case k=1. These new polynomials may be usefully termed “multivariate orthogonal polynomials.” / Master of Science

Master of Science

The Westinghouse Induction Time Klement Overload Relay, Type CO, a relay operating on the same principle as an alternating current watt-hour meter, is considerably affected in its time of operation when non-sinusoidal waves of potential are applied. If the potential wave applied has a flat top or depressed peak or if the wave has a lagging peak, that is, its maximum instantaneous value occurs more than 90 degrees after the beginning of the cycle, the operation of the relay is accelerated. If the wave of potential applied to the relay reaches its peak more than 90 degrees and less than 180 degrees after the beginning of the cycle, the operation of the relay is retarded from what it would be with a sinusoidal potential applied. The operation of a General Electric Time Current Overload Relay, Type PAC, a plunger type relay with an air bellows time delay, is, in general, retarded in operation by the application of non-sinusoidal potential waves. The operation may be slightly accelerated, however, if the wave distortion is slight, the current setting is low, and the distortion is such that the peak of the wave is flat or lagging. The effect of the wave distortion on other relays requires more study. / Master of Science

This thesis will be concerned with the comparison of results obtained from the mathematical and experimental solution of flat plates supported by beams and columns. The experimental solution is taken from a thesis by John W. Flemer,¹ also for the degree of Master of Science in Architectural Engineering at Virginia Polytechnic Institute. Mathematical solutions of the problem with both pinned and fixed edges will be worked out and the comparison made. The method of difference equations as developed by Dr. H. Marcus,³ translated into English and explained by Joseph A. Wise,⁴ and the superposition principle as described by D.L. Holl⁵ will be used in these solutions of the problems. It is hoped that this thesis will be of use in the investigation of the problem of flat plates. This thesis is not meant to be an end in itself, but only one of the many means toward the goal of a more exact solution of flat plates to be available for the use of the designing engineer. / Master of Science

A. <u>Objectives</u>. After a careful consideration of the problems involved, the writer formulated the following objectives: (1) To determine the variation of lamp characteristics with life for various wave forms. (2) To determine the variation of lamp characteristics with voltage for various wave forms. (3) To attempt to correlate the variation of lamp characteristics to the crest factor of the voltage wave employed. B. <u>Equipment</u>. This investigation was performed on 100 watt, type A21 115-volt lamps manufactured by Sylvania Electric Products Inc. The following information obtained from the lamp manufacturer was used as a basis for all calculations. <u>Initial Lumens</u> 1635 <u>Initial Lumens Per Watt</u> 16.35 <u>Rated Average Hrs. Life</u> 750 The wave forms used were produced by means of a General Electric Sine Wave Generator, Model 15A224, consisting of a 10 horsepower, 3600 rpm, direct current motor directly coupled to five alternators. These alternators produced frequencies of 60, 120, 180, 300, and 420 cycles per second respectively. The output of the alternators were connected in series as desired by means of a specially designed switch board. The alternator fields were excited directly from the output of a 3 phase, half wave, 250 volt, 75 ampere, ignitron manufactured by the Westinghouse Electric Corporation. The value of the lamp intensity in foot-candles were read by means of a Western photronic cell. The photronic cell used was equipped with a visual-correction filter so that its response is closely similar to the visibility curve of the human eye. / Master of Science

Webster describes education as ….. “a science dealing with the principles and practice of teaching and learning". Vocational Agricultural Education endeavors to train present and prospective famers for proficiency in farming. The end of World War II found this country faced with the problem of readjusting to civilian life many millions of men and women who so ably served their country in the armed forces. The Servicemen’s Readjustment Act of 1944., Public Lew 346, and The Act Providing for Vocational Rehabilitation of Disabled Veterans, Public law 16, commonly called the G. I. Bill of Rights, was formulated by the 78th Congress of the United States with the expressed idea in mind of rehabilitating and re-establishing veterans of World War II into a more permanent and satisfactory way of life. The application of the provisions of these laws, as amended by Public law 377, 80th Congress, makes specific provisions for training; veterans who elected to pursue a course of Institutional on-farm training. The responsibility for training those veterans who had returned to the fam to live, finally rested with the Virginia State Department of Education. Much work had been done in connection with this program. Supervisors and instructors have spent many hours of concentrated work and study in carrying out a program designed to meet the requirements of the law, with specific emphasis placed on the needs of the individual veteran. The purpose of this study was to show some of the conditions and practice: being; followed in carrying out the institutional on-farm training; program, and any evidence of success that the program may show. / Master of Science

Form is the manifestation of a process. Since our senses are our only means of perception, then a process to be manifest must necessarily assume a state that our senses can perceive. This state or expression which we can perceive is its form. “Every process has its necessary form which always results in functional forms. They follow the law of the shortest distance between points; cooling occurs only on surfaces exposed to cooling; pressure only on points of pressure; tension on lines of tension; motion creates for itself forms of movement for each energy there is a form of energy.” The functional form of anything is the way in which it acts or functions. Everything has many functional forms and these are perpetually changing. They are constantly being influenced to manifest themselves in different ways by processes which are in perpetual change; and these in turn are influenced by other processes in perpetual change. Functional form at any time is the form in which processes manifest themselves and is the result of all of the changes that have occurred up to that time. / Master of Science

The multiplier phototube thickness indicator developed in this research detects the varying thickness of the carbon ink coating on a moving web of paper. The absolute effect of the density variations of any of the particular types of tissue tested on those measurements has not been fully determined as yet, but it is believed that if a given type of tissue is used the density of variations of the paper can be neglected or compensated for. Changing the type of tissue when coating would necessitate recalibration of the multiplier phototube thickness indicator every time a different type of tissue was used. The multiplier phototube detects changes in density in a moving web of paper. This property can be useful in monitoring the thickness of tissue paper as it is being manufactured and in monitoring and compensating for changes to the density of different types of tissue fed into the ink coating machine. / Master of Science

The determination of the heat transfer through a flat wall of which one surface is isothermal at a temperature of t_a and the other surface is isothermal at a temperature t_b is the simple problem of heat transfer. The equation: Q= (kA(t_a - t_b))/L Permits an easy solution of the problem where Q is the heat transfer, k is the thermal conductivity, A is the area through which the heat is transferred, and L is the distance between the two surfaces. The equation is only applicable where the area A is constant. This equation may be used without appreciable error for insulated enclosures such as furnaces where the insulation thickness is very small in comparison with the dimensions of the enclosure. Shape factors have been applied to this basic equation so the equation may be used in the determination of heat transfer where the area A is not constant and the effect of corners can not be neglected. The equation then becomes Q= (fkA((t_a - t_b))/L Where f is the shape factor. In 1947, T. S. Nickerson for a Master’s thesis at V.P.I. determined the values of the shape factor where the above equation is applied to cylindrical enclosures having flat ends and relatively thick walls of uniform thickness. Mr. Nickerson solved this problem analytically by the relaxation method. His solution depended upon the inside and outside surfaces of the insulation about the enclosure being isothermal surfaces. The values were calculated for combinations of ratios of insulation thickness to length of enclosure and length of enclosure to diameter of enclosure. This investigation is an experimental determination of these values using gypsum plaster cylinders of different combinations of ratios of length to diameter. However, before tests could be conducted on the cylindrical enclosures, the conductivity of gypsum plaster, the insulation about the cylindrical enclosure, had to be found. The method of determination of the conductivity and the values are given in Appendix A. / Master of Science

THIS THESIS HAS THREE OBJECTIVES: FIRST, to present the findings of an investigation made to determine typical family living habits and possessions as they affect the housing requirements of present-day families. SECOND, to employ these findings in an organized study of the specific requirements for a residence to be designed for Doctor and Mrs. James McDonald Grayson, and to be located in Blacksburg, Virginia. THIRD, to present a detailed design of the residence which shall be designated, “A Design For Family Living”. / Master of Science