390 THE GRAMMAR OF SCIENCE 



falls under the mathematical theory of chance, and it is the 

 duty of the mathematician to find the best types of curves, 

 by means of which a concise description can be given of 

 the frequency polygons for different characters. Such 

 curves are termed frequency curves, and their discussion and 

 fitting to observations is the starting-point of the mathe- 

 matical theory of evolution. By means of them we again 

 replace the discrete polygon by a continuous frequency 

 distribution, and endeavour to allow for and describe 

 various types of frequency, e.g. those in which equal devia- 

 tions in excess and defect of the mode are not equally 

 probable, or skezv variation ; frequency of two modes due 

 to heterogeneous material, etc. But to enter into such 

 details would carry us far beyond the scope of this chapter 

 and book. 



So far we have been dealing with cojttinuous variation, 

 under which heading we include even discrete variation, 

 if the numbers which measure the character form a 

 continuous series. But if the reader examines several 

 hundred individuals with regard to ojie character, he is 

 almost sure to come across some in which that character 

 cannot be numbered or measured in the classification 

 adopted for the rest of the series, Such an individual 

 forms an abnormal variation. If the reader will turn to 

 our poppy capsule distribution, he will find it continuous 

 from I to 1 6. If a poppy were found with i8 

 stigmatic bands, must it be treated as an abnormal 

 variation ? Certainly not, for there is little doubt that if 

 30,000 capsules had been examined we might have found 

 one with this number of bands ; it is only a very 

 infrequent normal variation. For example, there are no 

 i6-banded capsules in the poppies from the top of the 

 Chilterns, and we might equally well have argued that a 

 i6-banded capsule was abnormal in the wild poppy. 

 This distinction between very infrequent normal varia- 

 tions and abnormal variations is a most important one, 

 but one too often disregarded. 



It might very likely be that no single capsule with 20 

 stigmatic bands existed in a given summer on the whole 



