Methods of Investigation. 527 



number of groups in the tables. This is sufficiently evi- 

 dent where we are dealing with continuous variations 

 such as length. For here the unit chosen is quite an arbi- 

 trary one. For example, if I had measured the fruits of 

 Oenothera accurately to tzvo millimeters only {or if I 

 had measured them in English inches), I should have 

 had fewer ordinates; but if I had measured them to half 

 a millimeter, I should have had twice as many. And in 

 dealing with ray-florets we may consider units or pairs 

 or larger groups. In fact the data may be grouped in 

 any desired way, to suit our purposes. 



The number of units to be used in the construction of 

 a curve depends in principle on the number of individuals. 

 If this is small, they must be made correspondingly few. 

 In order to do this the two or three groups of figures, in 

 the midst of which the interpolated value of M lies, are 

 united to form a single ordinate; this forms the apex of 

 the curve. We then deal with the groups to the right and 

 to the left of it in the same way. This is the only way in 

 which the peaks and valleys, in the curve, resulting from 

 an insufficient number of observations can be smooth.ed 

 away. 



Finally, if the various curves are to be compared with 

 one another, the empirical data must of course be reduced 

 to percentages. 



