xvi.] THE METHOD OF MEANS. 371 



Mr. Stone's arrangement of the pile might be usefully 

 employed in other delicate thermometric experiments 

 subject to considerable disturbing influences. 



Determination of Maximum Points. 



We employ the method of means in a certain number 

 of observations directed to determine the moment at which 

 a phenomenon reaches its highest point in quantity. In 

 noting the place of a fixed star at a given time there is no 

 difficulty in ascertaining the point to be observed, for a 

 star in a good telescope presents an exceedingly small disc. 

 In observing a nebulous body which from a bright centre 

 fades gradually away on all sides, it will not be possible 

 to select with certainty the middle point. In many such 

 cases the best method is not to select arbitrarily the sup- 

 posed middle point, but points of equal brightness on 

 either side, and then take the mean of the observations of 

 these two points for the centre. As a general rule, a 

 variable quantity in reaching its maximum increases at a 

 less and less rate, and after passing the highest point 

 begins to decrease by insensible degrees. The maximum 

 may indeed be defined as that point at which the increase 

 or decrease is null. Hence it will usually be the most 

 indefinite point, and if we can accurately measure the 

 phenomenon we shall best determine the place of the 

 maximum by determining points on either side at which 

 the ordinates are equal. There is 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 sym- 

 metry 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 impercep- 

 tible. 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 



B B 2 



