Methods of Investigation. 



525 



of opportunity of convincing myself of its general ap- 

 plicability in the vegetable kingdom.^ 



When it is once proved that the form of the emi)irical 

 curve of fluctuations in plants coincides with that (jf the 

 theoretical curve of probability, so far as unavoidable 

 errors in observation permit, the properties of the latter 

 may evidently be ascribed to the former. 



The most important property of the curve for our 

 purposes is that it may be definitely descril^ccl by two 

 magnitudes, (I) the mean value of the character in ques- 

 tion and (II) the amplitude or extent of variation. The 

 mean value used by Galton is that magnitude which half 

 of the individuals exceed, but which the other half do not 

 attain. This he calls the median. It need not be a mag- 

 nitude which actually exists, but is found by interpola- 

 tion on the assumption that variation is unbroken and 

 continuous. 



Galton 's median can be determined more easily than 

 the ordinary mean, which is obtained by dividing the sum 

 of all values by the number of observations. It has 

 exactly the same justification and in symmetrical curves 

 the two necessarily coincide. 



The second factor is the amplitude of variation which 

 finds its simplest expression in the remoteness of the ex- 

 treme variants, provided that the number of individuals 

 is not too small. But the raritv of these extremes makes 

 the determination of these limits by their simple observa- 

 tion largely a matter of chance. Galton therefore uses 

 another value borrowed from the theory of prol)ability, 

 as a measure of the amplitude. This is the magnitude of 

 the deviation from the mean which is exceeded by a 



^ See Ber. d. d. Bot. Gcsellsch., Bd. XTT. 1894. p. 197. wlicrc lie 

 previous literature is cited. 



