THE METHOD OF MEANS. 433 



come within the sphere of vision in each half hour or 

 quarter hour, and then, assuming that the law of varia 

 tion is symmetrical, they select a moment for the passage 

 of the whole body equidistant between times of equal 

 frequency. 



The eclipses of Jupiter s satellites are not only of great 

 interest as regards the motions of the satellites themselves, 

 but used to be, and perhaps still are, of importance in de 

 termining longitudes, because they are events occurring 

 at fixed moments of absolute time, and visible in all parts 

 of the planetary system at the same time, allowance being 

 made for the interval occupied by the light in travelling. 

 But as is excellently explained by Sir John Herschel r , the 

 moment of the event is wanting in definiteness, partly 

 because the long cone of Jupiter s shadow is surrounded 

 by a penumbra, and partly because the satellite has itself 

 a sensible disc, and takes a certain time in entering the 

 shadow. Different observers using different telescopes 

 would usually select different moments for that of the 

 eclipse. But it is evident that the increase of light in 

 the emersion will proceed according to a law exactly the 

 reverse of that observed in the immersion, so that if an 

 observer notes the time of both events with the same tele 

 scope, he will be as much too soon in one observation as 

 he is too late in the other, and the mean moment of the 

 two observations will represent with considerable accuracy 

 the time when the satellite is in the middle of the shadow. 

 The personal error of judgment of the observer is thus 

 eliminated, provided that he takes care to act at the 

 emersion as he did at the immersion. 



r Outlines of Astronomy, 4th edition, 538. 



Ff 



