real or absolute time existed, but only the local times, different for different observers. He showed that absolute simultaneity and absolute location in space are inextricably bound together, and the denial of the latter carries with it the denial of the former. By realising that an observer in the moving system would measure all velocities in terms of the local space and time of that system, Einstein removed the last discrepancies from Lorentz's transformation.
The relation between the space and time coordinates in two systems in relative motion was now obtained immediately from the principles of space and time-measurement. It must hold for all phenomena provided they do not postulate a medium which can serve as a standard for absolute location and simultaneity. The previous deduction of these formulae by lengthy transformation of the electromagnetic equations now appears as a particular case; it shows that electromagnetic phenomena have no reference to a medium with such properties.
The combination of the local spaces and times of Einstein into an absolute space-time of four dimensions is the work of Minkowski (1908). Chapter iii is largely based on his researches. Much progress was made in the four-dimensional vector-analysis of the world; but the whole problem was greatly simplified when Einstein and Grossmann introduced for this purpose the more powerful mathematical calculus of Riemann, Ricci, and Levi-Civita.
In 1911, Einstein put forward the Principle of Equivalence, thus turning the subject towards gravitation for the first time. By postulating that not only mechanical but optical and electrical phenomena in a field of gravitation and in a field produced by acceleration of the observer were equivalent, he deduced the displacement of the spectral lines on the sun and the displacement of a star during a total eclipse. In the latter case, however, he predicted only the half-deflection, since he was still working with Newton's law of gravitation. Freundlich at once examined plates obtained at previous eclipses, but failed to find sufficient data; he also prepared to observe the eclipse of 1914 in Russia with this object, but was stopped by the outbreak of war. Another attempt was made by the Lick Observatory at the not very favourable eclipse of 1918. Only preliminary
