features of the theory of probability, with some examples in geometry and kinematics, will lead to the main work of the course, in the kinetic theory of gases, the electron theory of metals, and some aspects of the theory of radiation. Prerequisite: thorough knowledge of the Calculus. Mj. Summer, ASSISTANT PROFESSOR LUNN. [Not given in 1914-15.] 172. Partial Differential Equations of Mathematical Physics; the Conduction of Heat.-A study of certain typical linear partial differential equations occurring in the analytic representation of physical theories, and of the functional expansions of solutions satisfying given boundary conditions; with special reference to the concrete phenomena and physical analogies from which the abstract theory has been generalized. Prerequisite: courses 49 and 160. Mj. Spring, ASSISTANT PROFESSOR LUNN. [Not given in 1914-15.] 178. The Theory of Relativity.—After a brief historical introduction, on the notion of relativity of time and space in its classic or Newtonian form, the course will be devoted to a study of the recent theory initiated by Einstein and Minkowski as a geometry of space and time adapted to the representation of physical laws. Special attention will be given to the discrimination between the logical elements of the theory and the special concrete interpretations that may be used in the formulation of experimental results. Mj. ASSISTANT PROFESSOR LUNN. [Not given in 1914-15.] 181. General Seminar.-For the consideration of reports of current research and of literature, especially of a fundamental or critical nature. PROFESSOR MOORE. [Not given in 1914-15.] XVIII. THE DEPARTMENT OF ASTRONOMY AND ASTROPHYSICS OFFICERS OF INSTRUCTION EDWIN BRANT FROST, A.M., Sc.D., Professor of Astrophysics, and Director of the Yerkes Observatory. SHERBURNE WESLEY BURNHAM, A.M., Emeritus Professor of Practical Astronomy in the Yerkes Observatory. EDWARD EMERSON BARNARD, A.M., Sc.D., LL.D., Professor of Practical Astronomy, and Astronomer in the Yerkes Observatory. FOREST RAY MOULTON, PH.D., Professor of Astronomy. JOHN ADELBERT PARKHURST, S.M., Assistant Professor of Practical Astronomy at the Yerkes Observatory. STORRS BARROWS BARRETT, A.B., Assistant Professor of Astrophysics; Secretary and Librarian of the Yerkes Observatory. WILLIAM DUNCAN MACMILLAN, PH.D., Assistant Professor of Astronomy. OLIVER JUSTIN LEE, S.M., PH.D., Instructor in Practical Astronomy at the Yerkes Observatory. FELLOWS, 1914-15 JOHN WILLIAM Campbell, A.M. FRANCIS EASTON CARR, A.B. JESSIE MAY SHORT, A.B. INSTRUCTIONAL WORK The work of the Department of Astronomy and Astrophysics is divided into two parts: (1) Work at the University, comprising: (a) elementary instruction in general Astronomy, both theoretical and practical; (b) preliminary training in the principles and methods of work underlying the science of Astrophysics (given in part in the Department of Physics); (c) graduate and research work in Celestial Mechanics. (2) Graduate and research work in Practical Astronomy and Astrophysics in the Yerkes Observatory at Lake Geneva. In the work at the University, given by Professor Moulton, Associate Professor Laves, and Assistant Professor MacMillan, emphasis will be laid on the development of the mathematical principles and methods which form the basis of the physical sciences. In addition to the courses in Descriptive Astronomy, Introduction to Celestial Mechanics, and Analytic Mechanics, courses on Periodic Orbits and in the various other branches of Celestial Mechanics will be given within periods not exceeding three years. The most fundamental subjects will be arranged so as to recur at regular intervals, while other more special topics will vary from time to time. The general object of the instruction will be (1) to give experience and preliminary training in the work of observation and reduction; (2) to furnish the student an adequate mathematical basis for successful work in Celestial Mechanics; (3) to direct research work in Celestial Mechanics. FACILITIES For instruction in Practical Astronomy a students' observatory is maintained. It is equipped with a modern Warner & Swasey equatorial telescope of 6 inches aperture which is provided with a filar micrometer, a 5-inch refractor, a 3-inch Bamberg transit instrument, a Bamberg universal instrument, a Riefler sidereal clock, a chronometer, and various smaller accessories. The laboratory courses offered by the Department of Physics afford excellent preliminary training for the work in Astrophysics. In the work at the Yerkes Observatory, the advanced student is made familiar with modern methods of research in various branches of Practical Astronomy and Astrophysics. The rapid development of the latter science within the last two decades has been fully recognized in the equipment of the Observatory; the special laboratory facilities make many investigations possible which cannot be carried on where the equipment is less complete. In general, the work in progress during the year 1914-15 will include: Researches in solar physics with the spectroscope, spectroheliograph, and photoheliograph; micrometric observations of double stars, planets, satellites, nebulae, and comets; photographic studies of stellar spectra and determinations of motions in the line of sight; photography of stars, comets, nebulae, etc.; photographic investigations of stellar parallax; research in visual and photographic photometry; special astrophysical researches. The opportunity of taking part in these investigations is deemed of more advantage to the qualified student than set courses of instruction; but regular programs of work, with courses of collateral reading, will be laid out as conditions may require. ADMISSION TO YERKES OBSERVATORY The Yerkes Observatory is open only to graduate students who have completed the necessary preliminary studies and have had the requisite experience in practical laboratory and observatory work. Students wishing to work at the Observatory should first consult the Director of the Yerkes Observatory, Williams Bay, Wis., and obtain his approval. DEGREES The Master's degree. Students working for a Master's degree in Astronomy are advised to choose three majors of graduate work in the Department of either Mathematics or Physics and six majors in the Department of Astronomy, from courses numbered 5 to 10, 22, and 23. The degree of Doctor of Philosophy.-The courses prescribed for the Master's degree together with three other graduate courses will meet the requirement for the Doctor's degree, where Astronomy is the minor subject. Candidates for the Doctor's degree, with Astronomy as major subject, are expected to make their secondary subject either Mathematics or Physics. Students intending to specialize in the lines of Astrophysics will be required to take the work in Theoretical Physics, Advanced Experimental Physics, Sound and Light, and Physical Manipulation. The courses in Astronomy which will be required depend on the phase of the subject which the candidate elects for his special work, and will be arranged for each candidate during the progress of his work. Students specializing in Celestial Mechanics are expected to spend six months at the Yerkes Observatory, and those working there in Practical Astronomy and Astrophysics are expected to spend six months at the University. CLUB The Departmental Club meets fortnightly for the review of memoirs and books, and for the presentation of results of research. The club is conducted by the members of the Faculties of Mathematics and Mathematical Astronomy. Graduate students of Mathematical Astronomy are expected to attend regularly and, so far as possible, to participate actively in the meetings of the club. SEQUENCE OF EARLY COURSES Undergraduate students who desire to specialize in Astronomy are recommended to take course 19 and its antecedents in Mathematics, and courses 3, 5, 6, 10, 22, and 23 in Astronomy, as a basis for further work. COURSES OF INSTRUCTION AT THE YERKES OBSERVATORY Advanced students in Astronomy may register for work at the Yerkes Observatory, spending their entire time at Williams Bay (see p. 450). The Observatory will be open throughout the summer. Instruction will be offered by the various members of the staff. I. JUNIOR COLLEGE COURSES 1. Descriptive Astronomy (Shorter Course).-An elementary course, dealing with fundamental facts, principles, and methods. Frequent access to the Observatory. Mj. Summer, PROFESSOR MOULTON; Spring, PROFESSOR MOULTON AND ASSISTANT PROFESSOR MACMILLAN. 2. Spherical Trigonometry with Applications to Astronomy.-Prerequisite: Plane Trigonometry. Mj. Winter, ASSOCIATE PROFESSOR LAVES. 3A and 3B. Descriptive Astronomy.-A two-quarter course dealing with the fundamental facts and principles of Astronomy. Modern as well as Classical methods and results are brought into full discussion. The observational side of the subject also is emphasized. Prerequisite: Plane Trigonometry. Mj. Autumn, PROFESSOR MOULTON; Winter, ASSISTANT PROFESSOR MACMILLAN. 4. Introduction to Surveying (Mathematics 1).-Mj. Spring, ASSOCIATE PROFESSOR LAVES. II. SENIOR COLLEGE COURSES 5. Analytic Mechanics, I.-An introductory course. Prerequisite: Mathematics 18, 19. Mj. Autumn, ASSOCIATE PROFESSOR LAVES. 6. Analytic Mechanics, II.—Prerequisite: Astronomy 5. Mj. Winter, AssoCIATE PROFESSOR LAVES. 7. Spherical and Practical Astronomy.-Time, latitude, and longitude determination. Prerequisite: Astronomy 1 and Mathematics 3. Mj. Spring and Summer, ASSOCIATE PROFESSOR LAVES. 8. Practical Astronomy, I.-Observations of binary stars and determination of their orbits. Mj. Autumn, ASSOCIATE PROFESSOR LAVES. [Not given in 1914-15.] 9. Practical Astronomy, II.-Observations of planets and satellites and determinations of satellite orbits. Mj. AsSOCIATE PROFESSOR LAVES. [Not given in 1914-15.] 10. Spectroscopy and Astrophysics (Physics 24).-A non-technical treatment of the growth of Spectroscopy, with applications to solar and stellar phenomena. Mj. Spring, AssOCIATE PROFESSOR GALE. 20. Analytic Mechanics.-Mj. Summer, AssOCIATE PROFESSOR LAVES. III. GRADUATE COURSES 22. Introduction to Celestial Mechanics, I.-Prerequisite: Astronomy 5. Properties of conic section motion, determination of orbits from three or more observations. Mj. Winter, ASSISTANT PROFESSOR MACMILLAN. 23. Introduction to Celestial Mechanics, II.-Special cases of the problems of three bodies: the Lunar theory geometrically considered; variation of the elements and absolute perturbations. Mj. Spring, ASSISTANT PROFESSOR MACMILLAN. 31-36. Research Courses at the Observatory.-Prerequisites: See "Admission to Yerkes Observatory," p. 246. DMj. each Quarter, PROFESSORS AND INSTRUCTORS resident at Yerkes Observatory. 51, 52. Modern Theories of Analytic Differential Equations with Applications to Celestial Mechanics and Periodic Orbits, I, II.-Prerequisite: Astronomy 50. Properties of the solution of a general system of differential equations of the nth order as functions of the independent variable, of the parameters, of the initial values of the dependent variables. Solutions developed as power series in the independent variable, in the parameters, in the initial values of the dependent variables, by the Cauchy-Lipschitz process, by the Picard approximation process, by continued variation of parameters. Applications to elliptic and hyperelliptic functions and to periodic solutions of the problem of three bodies. Linear equations with applications to hypergeometric functions. Linear equations with periodic coefficients. Winter and Spring, PROFESSOR MOULTON. 60. Periodic Solutions of the Problem of Three Bodies.-Autumn, PROFESSOR MOULTON. 80. The Problem of Three Bodies.-Mj. Summer, PROFESSOR MOULTON. XIX. THE DEPARTMENT OF PHYSICS OFFICERS OF INSTRUCTION ALBERT ABRAHAM MICHELSON, PH.D., Sc.D., LL.D., F.R.S., Professor and ROBERT ANDREWS MILLIKAN, PH.D., Sc.D., Professor of Physics. HERMAN GUSTAVUS HEIL, PH.B., Assistant in Physics. SUMMER, 1914 EDWIN SHERWOOD BISHOP, Instructor in Physics, University High School. GEORGE WINCHESTER, Professor of Physics, Washington and Jefferson University, Washington, Pa. NEWLAND FARNSWORTH SMITH, PH.D., Professor of Physics, Central University of Kentucky. ALBERT E. HENNINGS, Assistant Professor of Physics, University of Saskatchewan. The instructional work in Physics is directed toward the following ends: (1) The training of original investigators in physics; (2) the training of men competent to fill college and university positions as teachers of physics; (3) the training of teachers of physics for secondary schools; (4) the training of preengineering and pre-medical students for later professional work; (5) the training of the general student in scientific methods of work, and in the understanding of the place of physical science in the modern world. From the most elementary to the most advanced courses, the laboratory and the problem method of instruction are emphasized. FACILITIES The Ryerson Physical Laboratory has been enlarged and remodeled with especial reference to offering the best facilities for research work. The entire lower floor and basement are given up to private research rooms. A wellequipped shop, with skilled instrument-makers, furnishes opportunity for the construction of special pieces of research apparatus. The equipment has been selected with reference to the needs of research, and includes spectroscopic |