432 THE PRINCIPLES OF SCIENCE. 



moreover this advantage in the method that several points 

 may be determined with the corresponding ones on the 

 other side, and the mean of the whole taken as the true 

 place of the maximum. But this method entirely depends 

 upon the existence of symmetry in the curve, so that of 

 two equal ordinates one shall be as far on one side of the 

 maximum as the other is on the other side. The method 

 fails when other laws of variation prevail. 



In tidal observations great difficulty is encountered in 

 fixing the moment of high water, because the rate at 

 which the water is then rising or falling is almost imper- 

 ceptible. Dr. Whewell proposed, therefore, to note the 

 time at which the water passes a fixed point somewhat 

 below the maximum both in rising and falling, and take 

 the mean time as that of high water. But this mode of 

 proceeding unfortunately does riot 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 pre- 

 ceding 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 con- 

 junction, that is half-way between the second day before 

 and the fifth day after 9. 



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 astro- 

 nomers 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 



i Airy 'On Tides and Waves,' Encycl. Metrop. pp. 364 



