THE METHOD OF MEANS. 431 



Fahrenheit, and which represents a heating effect of the 

 direct ray of only about o*oooooi37 Fahrenheit, equiva- 

 lent to the heat which would be received from a three- 

 inch cubic vessel full of boiling water at the distance of 

 400 yards P. It is probable that Mr. Stone's arrangement 

 of the pile might be usefully employed in other delicate 

 thermometric experiments subject to considerable disturb- 

 ing 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 be- 

 gins to decrease by insensible degrees. The maximum may 

 indeed be defined as that point at which the increase or 

 decrease is insensibly small. Hence it will usually be the 

 most indefinite point in the whole course, and if we can 

 accurately measure the phenomenon we shall best deter- 

 mine the place of the maximum by determining points on 

 either side at which the ordinates are equal. There is 



P ' Proceedings of the Royal Society/ vol. xviii. p. 159 (Jan. 13, 1870). 

 'Philosophical Magazine' (4th Series), vol. xxxix. p. 376. 



