Alloys in and near the ε single phase region found by Morral In the iron-aluminum-carbon system were prepared and their ferromagnetic and structural properties determined„ The ε phase has been described as chiefly Fe₃Al plus 15 atomic percent carbon with the possibility of varying the Fe:Al ratio from approximately 2 to 3.5. The face-centred cubic ε phase was found to be highly ordered with iron at the face centre positions, aluminum at the cube corners and carbon in the body-centred position. The lattice parameter varies with carbon content from 3.73 to 3.76 A°. Keeping the amount of carbon constant at 14.6 atomic percent the alloys with the Fe:Al ratio less than 3 have their saturation magnetization increasing with increasing iron by an amount corresponding to the estimated increase of 5.4 Bohr magnetons per iron atom. However, for values of the ratio greater than 3 the magnetization is decreased with increasing iron. The amount of this decrease is not certain but it is thought to be of the order of 8 Bohr magnetons per iron atom in excess of that required to give Fe:Al equal to 3. Increasing the carbon content with the Fe:Al ratio kept at 2.9 ± .1 also decreases the magnetization by an amount corresponding to an estimated 8.5 Bohr magnetons per carbon atom. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

Standard techniques of radio-frequency nuclear resonance spectroscopy have been applied to further studies of the interaction between atomic nuclei in crystals and the crystalline electric' field gradients at the nuclear sites. Observations have been made on the nuclear magnetic resonance spectra of Al²⁷, Li⁶, Li⁷ and Si²⁹ in single crystals of LiAl(Si0₃)₂ (spodumene) in strong magnetic fields. Results from the Al²⁷ spectrum provided improved values of the field gradient constants of spodumene and a check on the adequacy of second and third order perturbation theory in describing the electrostatic perturbation of the magnetic energy levels; these results also provided an experimental check on a proposed new method of nuclear spin determination. The Li⁶ and Li⁷ measurements provided a more accurate value of the quadrupole moment ratio for this pair of isotopes. Observations on the Si²⁹ spectrum support; existing evidence that the spin of Si²⁹ is 1/2. A super-regenerative spectrometer has been built for the detection of nuclear magnetic resonances and nuclear electric quadrupole resonances. Preliminary tests indicate that it will detect resonances in solids at low frequencies which could not be detected with the continuous-wave type of spectrometer. A pure quadrupole resonance in Na₂B₄O₇.4H₂O (kernite) has been detected at 1.27 Mc./sec. using this super-regenerative spectrometer. This represents a pure quadrupole resonance of the lowest frequency reported to date. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The Lubzinski.spectrograph has been accurately focussed and its performance as a high dispersion vacuum ultraviolet instrument has been studied. Light sources have been designed for the excitation of the hydrogen Lyman series. The α line of this series has been obtained using exposure times ranging from twenty minutes to seven hours. A spectrogram of the hydrogen-deuterium isotope structure obtained in the fifth grating order at a dispersion of 1 A°/mm. has been obtained permitting positive identification of the hydrogen Lyman α line. Light sources for the excitation of the first-spark spectra of copper have, been constructed and experimentally studied. This spectrum contains a large number of standard wavelengths, in the vacuum ultraviolet; however, because of low grating intensity we were unable to observe these lines. An existent discrepancy between calculated and measured, values for the ionization potential of Helium-like atoms has been resolved by a generalized Lamb electromagnetic shift. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Binary alloys of manganese and boron and ternary alloys of manganese and boron with aluminum, zinc, tin and indium were prepared. Their structures were determined from x-ray powder photographs, and their ferromagnetic properties were measured with a Sucksmith rinf balance, using a powerful electromagnet. The orthorhombic phase MnB had a ferromagnetic Bohr magneton number of 1.73 per molecule and a Curie point of 309°C. Most of the ternary alloys were slightly ferromagnetic, but no strongly ferromagnetic single phase regions were found. Paramagnetic measurements on Heusler alloys showed that they followed the Curie-Weiss law for the restricted range of temperature in which measurements could be made. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

Thirteen specified water soluble dyes are permitted for use in edible products consumed in Canada and the United States. The official chemical-physical method of analysis is not very successful when small amounts of one dye are present with larger amounts of others, or even in the analysis of a single dye if present in small quantities. The spectrophotometer has been shown to be very useful in identifying the thirteen permitted dyes individually, and by its means many previously unresolvable binary mixtures have been readily analyzed. Further investigation of the possibilities of this method of analysis is proceeding. / Science, Faculty of / Chemistry, Department of / Graduate

The beta and gamma spectra of Fe⁵⁹ have been examined in a thin lens beta ray spectrometer. Gamma rays with energies of 1.10 Mev and 1.29 Mev were detected using the photoelectric technique with a Uranium radiator. Using a thin foil as a source, beta groups with maximum energies of 1.77 Mev and 0.45 Mev were found. There was no evidence of a 0.26 Mev group as reported by other workers. Tentative decay schemes are presented. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The purpose of the present study was that of presenting the fundamental theorems and techniques of Thurstone's Multiple-Factor Analysis in a manner that would be understandable to the non-mathematically trained student of psychology. The work was introduced by a discussion of Spearman's "Theory of Two Factors" which is so-called since the method analyses each test into a general factor "g" and a specific factor. It was found that such a factorization could be performed if the correlation matrix exhibited hierarchical order. The tetrad difference equation and a standard error formula were next discussed as tests of this order. Finally, mention was made of a few of the problems which investigators have attempted to solve by means of the method. Upon turning attention to the multiple-factor theory, an initial chapter was devoted to the presentation of the relationship between such theory and scientific method in general. This facilitated a discussion of some of the major limitations and values of the technique. It was found that the methods could best be designated as classificatory. Furthermore, it was discovered that factor analysis was not only applicable to a diversity of problems in psychology but also to those of other sciences. Following this more general discussion, consideration was given to the derivation of the fundamental equations. It was proven that if the original scores are converted to standard form the sum of the squares of the factor loadings for any test is equal to unity. It was also shown that each factor loading for statistically independent factors is the square root of the variance that is attributable to that factor. The fundamental theorem of factor analysis, which proves that any reduced correlation matrix can be factorized, was then discussed since it is basic to the entire theory. The centroid method of factoring a reduced correlation matrix was next developed. A method was thus obtained by which the correlation matrix could be analysed into a common factor matrix. However, since Thurstone does not consider these to be psychologically meaningful factors it was found that a rotation of reference frame must then be carried out. Consideration was given to the problem of rotating axes and a method examined which enables one to rotate axes in a two-dimensional plot. This method was found to be such that it could be generalized to an r dimensional factor pattern. It had the advantage of furnishing a graphic record of the relationships among the tests. However, it had a disadvantage in that many diagrams must be plotted if the number of dimensions is large. Upon examining the problem of attaching psychological meaning to the factors, it was noted that subjectivity must play a large part and so no rote rules could be furnished as a solution to this problem. For this reason several examples of interpretations were presented in order to enable the reader to obtain a clearer insight into the logical steps employed. Finally, the limitations of this study were considered and a brief discussion of the possible future development of factor analysis was presented. / Arts, Faculty of / Psychology, Department of / Graduate

Jazz composers and scholars have praised American pianist Bill (William John) Evans as a superior improviser. But oddly, considering the renown gained by Evans, his music is only recently being analyzed in any theoretical detail. An essential aspect of Evans' style, in my opinion, is his ability to satisfy the harmonic obligations of the theme and, at the same time, establish a maximum degree of rhythmic contrast with the metrical pattern of the original harmonic succession. This paper examines the rhythmic relationship of Evans' melodies to the chord changes over various timespans of the theme and its variations. A method of accent analysis is developed to describe this relation and is applied to excerpts firm two of his solos with a distinct bebop character. According to the provided criteria, this analytical method defines the strongest melodic accents ("points of emphasis") in the melodic accent pattern in relation to the different chordal accents generated by the theme's harmonic progressions and to a lesser extent by the interpolated substitutes that together constitute the hypermetrical accent pattern. In comparing these accent patterns and the accent processes of "coincidence", "synchronization", "cross-accent", and "convergence" they articulate we determine some of the techniques Evans uses to create rhythmic contrast between the theme and its variations. On the grounds of this study, one may conclude that the rhythmic structures of melody shown to be in "Peri's Scope" and "Beautiful Love" are characteristic of Evans' improvisations, especially in the early stages of his career. Hence, one may use this type of analysis to investigate the improvisational styles of Evans' predecessors: innovators such as Charlie Parker and Bud Powell, and those of some of his contemporaries, such as the pianist Red Garland. Finally, the original concepts, terms, and processes identified by this method of accent analysis may help the jazz student to recognize the possible relations of melodic pitches to underlying chords during the course of performance. It seems likely, then, that this type of analysis can form the basis for a pedagogical method that has a distinctly rhythmic-harmonic aspect, an aspect that deserves more attention in jazz education. / Arts, Faculty of / Music, School of / Graduate

This thesis is broadly concerned with two problems: obtaining the mathematical model of the specific infinite self-similar graph, and investigating the connectedness of the tree-like graph in order to show its relation to the associated hyperbolic space. Our main result concerning the former problem is that, in a variety of situations, the self-similar infinite structure obtained by using our method as the graph product of a disconnected finite graph and regular rooted tree can be connected (i.e. have the hyperbolic metric space associated to it). This addresses a question about the existence of the optimal depth for the breadth-first search algorithm and also has possible applications to the recent research topics in Psychological and Brain Sciences. We approach the connectedness problem by showing the similarity of obtained geometric structures to well known algebraic structures such as groupoid and pseudogroup. One of our main results is that, under the assumption that the emerged geometric self-similar structure is connected, it is naturally associated to the hyperbolic metric space. Thus, the variety of well known methods can be applied in further study. We also show that the connectedness of our structure can be reached in the finite number of steps or can not be reached at all. This gives the grounds for the optimal application of the breadth-first search algorithm.

No abstract included. / Science, Faculty of / Mathematics, Department of / Graduate