LECTUEES ON THEOBETICAL PHYSICS DELIVERED AT THE UNIVERSITY OF LEIDEN BY H. A. LORENTZ AUTHORISED TRANSLATION BY L SILBERSTEIN, Pir. I., AND A. P. Jl. TKIVKLLl VOLUME I AETHER THEORIES AND AETHER MODELS EDITED UY II. BREMEKAMP, Pn. I. KINETICAL PROBLEMS EDITED JBY E. D. BRUINS, Pu. D., AND J. REUDLER, Pii. D. Osmania University HYO - i. MACMILLAN AND CO., LIMITED ST. MARTINS STREET, LONDON 1927 COPYRIGHT PRINTED IN GREAT BRITAIN BY It. K. CLARK, LIMITED, EDINBURGH PREFACE TO THE ENGLISH TRANSLATION A SERIES of admirably clear and instructive courses of lectures, covering essentially almost the whole field of Theoretical Physics, were delivered by Professor Lorenf z at the University of Leiden. Seven of these courses, bearing on subjects of fundamental importance, were, up to 1922, edited by Lorentzs pupils and published in the Dutch language. During Professor Lorentzs visit in the United States in 1922 the plan was conceived to make these courses of lectures accessible to. English readers. After some delay necessitated by circumstances the present Volume I. is being issued. It contains the English version of two of these courses of lectures, viz. Aether Theories and Aether Models, edited in the Dutch language by Prof. H. Bremekamp, and Kinetical Problems, edited by Dr. E. D. Bruins and Dr. J. Heudler. To preserve the peculiar charm of Lorentzs own style and exposition the translation of these lectures has been made as literal as was compatible with the nature of the English language. Only a very few changes or explanatory additions were made in the text. The latter are placed in square brackets. Volumes II. and III., now in preparation, will contain the remaining five lecture courses, namely, Thermodynamics, Entropy and Probability, Theory of Radiation, Theory of Quanta, and The Principle of Relativity for Uniform Translations Special Theory of Relativity. Recently, 1925, one more course of lectures, on Maxwells Theory, was brought out at Leiden, and arrangements will be made to include its English version into this publication. L. S. A. P. H. T. ROCHESTER, N. Y., July 1926. CONTENTS AETHER THEORIES AND AETHER MODELS I. ABERRATION OF LIGHT PACK 1. Stokes 1 Theory The Earth drags the Surrounding Aether . . 3 2. Velocity Potential in an Incompressible Aether ... 6 3. Plancks Theory. Compressible Aether .... 7 4. Fresnels Theory. Fixed Aether ..... 12 5. Dragging Coefficient ....... 13 6. Theory of Aberration ....... 14 7. Michelsons Experiment . . . . . . .19 8. Contraction in the Direction of Motion ..... 23 II. MECHANICAL AETHER THEORIES 9. Maxwells Equations ....... 24 10. The Magnetic Force as Velocity. Neumanns Theory of Light . 26 11. The Electric Force as Velocity. Fresnels Theory of Light . . 29 12. Theory of Elasticity. McCullaghs Aether .... 30 13. Quasi-rigid Aether 31 14. Quasi-labile Aether ....... 35 15. Graetzs Theory ........ 36 16. The Charging of a Conductor according to the Elastic Aether Theories ......... 37 III. KELVINS MODEL OF THE AETHER 17. Kelvins Model of the Quasi-rigid Aether .... 40 18. Solid Gyrostat 44 19. Liquid Gyrostat ........ 48 20. Liquid in Turbulent Motion as Aether Model .... 52 IV. ATTRACTION AND REPULSION OF PULSATING SPHERES 21. Nature of the Problem 58 22. A Single Moving Sphere ....... 59 23. A Sphere at Rest in a Liquid with a given Motion ... 60 24. n Spheres ......... 61 25. Two Spheres ........ 62 26. Treatment of the Problem by means of Lagranges Equations . 65 27. Pearsons Theory ........ 67 SOURCES AND REFERENCES ...... 70 vii viii CONTENTS KINETICAL PROBLEMS PAOR INTRODUCTION ......... 75 CHAPTER I INNER FRICTION AND SLIDING, TREATED HYDRODYNAMICALLY 1. Hydrodynamical Equations of an Incompressible Viscous Liquid . 77 2. Effect of Sliding upon a Liquid flowing in a Tube ... 80 3. The Dragging of a Liquid by a Moving Plate .... 81 4. Effect of Sliding in the Case of Translational Motion of a Sphere in a Liquid ......... 83 5...