FLUCTUATING VARIATIONS 79 



The value of precise measurements of even trivial variations 

 is great. The curves show at a glance the range of variability, 

 the amount of a character that occurs with greatest frequency, 

 and it is easy to deduce by various methods an index or 

 measure of variability. Moreover the curves, especially if 

 made year after year, may show the direction in which the 

 species is moving, perhaps the way in which selection is 

 working, perhaps even that the soecies is splitting up into two 

 subspecies. 



As we have said, these individual or fluctuating variations 

 can usually be registered on the normal curve of frequency, such 

 as is exhibited when results depend on a complexity of con- 

 ditions. They are often called fortuitous or chance variations, 

 but as this phrase always misleads the careless mind, it may 

 be profitably dispensed with. Individual or fluctuating varia- 

 tions are often termed continuous, which means that any case 

 differs but slightly from its parents, that the whole of them 

 taken together form a continuous series, that one generation 

 differs from another as the state of an embryo on one day differs 

 from that of the next day. 



Registration of Variations. — " The modem methods of statis- 

 tics deal comprehensively with entire species, and with entire 

 groups of influences, just as if they were single entities, and 

 express the relations between them in an equally compendious 

 manner. They commence by marshalling the values in order 

 of magnitude from the smallest up to the largest, thereby con- 

 verting a mob into an ordeiiy array, which, like a regiment, 

 thenceforth becomes a tactical unit. Those to whom these 

 considerations are new, will grasp the results more easily by 

 thinking of the array in its simplest, though not necessarily in 

 its most convenient form for mathematical treatment. Let 

 them conceive each value to be represented by an extremely 

 slender rod of proportionate length, and the rods to be erected 

 side by side, touching one another, upon a horizontal base. 



