During his life, then, the efforts of Galileo to determine the velocity of light remained uncrowned with success. But the subsequent history of the measurement of the velocity of light is intimately associated with his name, for with the telescope which he constructed he discovered the four satellites of Jupiter, and these furnished the next occasion for the determination of the velocity of light. The terrestrial spaces were too small for Galileo's experiment. The measurement was first executed when the spaces of the planetary system were employed. Olaf Römer, (born at Aarhuus in 1644, died at Copenhagen in 1710) accomplished the feat (1675-1676), while watching with Cassini at the observatory of Paris the revolutions of Jupiter's moons. [Illustration: Fig. 14.] Let _AB_ (Fig. 14) be Jupiter's orbit. Let _S_ stand for the sun, _E_ for the earth, _J_ for Jupiter, and _T_ for Jupiter's first satellite. When the earth is at _E₁_ we see the satellite enter regularly into Jupiter's shadow, and by watching the time between two successive eclipses, can calculate its time of revolution. The time which Römer noted was forty-two hours, twenty-eight minutes, and thirty-five seconds. Now, as the earth passes along in its orbit towards E₂, the revolutions of the satellite grow apparently longer and longer: the eclipses take place later and later. The greatest retardation of the eclipse, which occurs when the earth is at _E₂_, amounts to sixteen minutes and twenty-six seconds. As the earth passes back again to _E₁_, the revolutions grow apparently shorter, and they occur in exactly the time that they first did when the earth arrives at _E₁_. It is to be remarked that Jupiter changes only very slightly its position during one revolution of the earth. Römer guessed at once that these periodical changes of the time of revolution of Jupiter's satellite were not actual, but apparent changes, which were in some way connected with the velocity of light. Let us make this matter clear to ourselves by a simile. We receive regularly by the post, news of the political status at our capital. However far away we may be from the capital, we hear the news of every event, later it is true, but of all equally late. The events reach us in the same succession of time as that in which they took place. But if we are travelling away from the capital, every successive post will have a greater distance to pass over, and the events will reach us more slowly than they took place. The reverse will be the case if we are approaching the capital. At rest, we hear a piece of music played in the same _tempo_ at all distances. But the _tempo_ will be seemingly accelerated if we are carried rapidly towards the band, or retarded if we are carried rapidly away from it.[14] [Illustration: Fig. 15.]