CONTENTS PAGE CHAPTER I. CHAITEK 11. CHAPTER IV. IINKO. SKI S R .- SSFORRI. TIOS - CHAPTER I EINSTEINS DEDUCTION OF FUNDAMENTAL RELATIONS The subject of Relative Motion is one which must have presented itself at a very early stage to investigators in Applied Xathematics, but we may regard it as being placed on a definite dynarnical basis by Newton. In fact, his first Law of Motion defines the absence of force in a manner which is independent of any uniform velocity of the frame of reference. When the ware theory of light ...
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CONTENTS PAGE CHAPTER I. CHAITEK 11. CHAPTER IV. IINKO. SKI S R .- SSFORRI. TIOS - CHAPTER I EINSTEINS DEDUCTION OF FUNDAMENTAL RELATIONS The subject of Relative Motion is one which must have presented itself at a very early stage to investigators in Applied Xathematics, but we may regard it as being placed on a definite dynarnical basis by Newton. In fact, his first Law of Motion defines the absence of force in a manner which is independent of any uniform velocity of the frame of reference. When the ware theory of light became firmly established, and when a luminiferous aether was postulated as the medium, universal in extent, which carried such waves, attention was again directed to relative motion. The questions at once arose Are we to regard the aether as being fixed Does matter, e. g. the Earth, disturb the aether in its passage through it 1 The attempts to answer such questions gave rise to numerous investigations, experimental and theoretical, on the one hand to determine the relative motion of matter and aether, and on the other to give an adequate explanation in mathematical terms of the results of such experiments. As an introduction I shall briefly describe two such experimental researches which will bring us at once to the root of the difficulty. For those who wish to pursue the historical introduction to this subject, I can refer to Professor Whittakers History of the Aether, a book the value of which can be appreciated by anyone who has ever wished to trace the somewhat tangled line of thought in these matters during the last century. I shall first refer to Eradleys A observation of the aberration of light. Let X Fig. 1 be a source of light and 0 an observer moving with avelocity represented by 0 0 v. A spherical wave of light diverges from S in all directions. Relative to 0 0-v G3 -Y I each point P of the sphere has two velocities, one equal to the velocity of light c and in the direction C. 1 ., a c, I I . . . c . . S . . . . . . 9 c 4 ., c., ., . RELATIVITY I, . ., ., . . a - 5, .. . SP, and the other equal and opposite to 0 0. The wave surface relative to the observer is thus a sphere, the radius of which is expanding at the rate c and the centre is moving at the rate v. Or again, the wave surfaces are spheres, the point S being a centre of similitude. The ray direction, or direction in which the radiant energy travels, is along the line joining S to P Fig. 2, whilst the wave velocity is along SP where SS SP c. The position of a fixed star as seen by an observer in a telescope moving with the earth 179 2 will be the centre of the sphere of the system which passes through 0, and the real position of the star can be calculated from the triangle S S 0 Fig...
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