372 THE PRINCIPLES OP SCIENCE. [CHAP. 



time as that of high water. But this mode of proceeding 

 unfortunately does not give a correct result, because the 

 tide follows different laws in rising and in falling. There 

 is a difficulty again in selecting the highest spring tide, 

 another object of much importance in tidology. Laplace 

 discovered that the tide of the second day preceding the 

 conjunction of the sun and moon is nearly equal to that of 

 the fifth day following; and, believing that the increase 

 and decrease of the tides proceeded in a nearly symmetrical 

 manner, he decided that the highest tide would occur about 

 thirty-six hours after the conjunction, that is half-way 

 between the second day before and the fifth day after. 1 



This method is also employed in determining the time 

 of passage of the middle or densest point of a stream of 

 meteors. The earth takes two or three days in passing 

 completely through the November stream ; but astronomers 

 need for their calculations to have some definite point fixed 

 within a few minutes if possible. When near to the 

 middle they observe the numbers of meteors which come 

 within the sphere of vision in each half hour, or quarter 

 hour, and then, assuming that the law of variation is 

 symmetrical, they select a moment for the passage of the 

 centre 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 were, and perhaps still are, of use in determining 

 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 explained by Herschel, 2 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 

 time in entering the shadow. Different observers using 

 different telescopes would usually select different moments 

 for that of the eclipse. But the increase of light in the 

 emersion will proceed according to a law the reverse of 

 that observed in the immersion, so that if an observer notes 



1 Airy On Tides and Waves, Encycl. Metrop. pp. 364* 366*. 

 * Outlines of Astronomy, 4th edition, 538 



