704 



SCIENCE. 



[N. S. Vol. XX. No. 517. 



hydroids does not occur in the absence of 

 potassium. We know, likewise, that iron 

 is necessary to the formation of the chro- 

 matin of the nucleus. 



The physical conditions have likewise an 

 influence in morphogenesis. The rate of 

 development is controlled within limits by 

 temperature. The number and position of 

 stomata and of leaves by light and moist- 

 ure; the number and form of plant hairs 

 by moisture; the position of branches and 

 leaves on a stem by gravity; the formation 

 of a hydranth in a hydroid stock by light. 

 So evident is this dependence of morpho- 

 genesis upon physical agents that two in- 

 dividuals of the same family develop alike 

 only under the same conditions of en- 

 vironment. 



There remain to be considered the rela- 

 tions of morphology to the queen of the 

 sciences— to mathematics. Until recent 

 years little relation has been recognized, 

 and this I attribute to the fact that few 

 naturalists have a type of mind that at- 

 tracts them to mathematics. They have 

 usually been led to their science through a 

 love of nature— a passion that belongs 

 rather to the poetic type of mind than to 

 the severely precise mathematical. And 

 so I find that, even to-day when the bear- 

 ing of mathematics on morphological prob- 

 lems can not be overlooked, few morpholo- 

 gists take an interest in the subject of 

 biometry by which the two sciences are 

 connected. 



The fact that few morphologists have 

 little taste for mathematics can not stay 

 the inevitable trend of the science toward 

 greater precision of expression and toward 

 mathematical analysis. Until recent years 

 characteristics have been described only in 

 the crude language of adjectives and ad- 

 verbs—where greater precision is necessary 

 quantitative expression is inevitable. So 

 we have seen during the past ten years the 

 rise of biometrj^ and its application to 



many morphological problems. Biometry 

 had its beginning in the suggestive investi- 

 gation of Galton; its great development in 

 the last ten years has been due, above all, 

 to the tremendous activity of Karl Pearson 

 and the workers he has gathered about him. 

 By the aid of efficient methods of analysis 

 we are able to state quantitatively not only 

 the mean value of any measurable charac- 

 teristic, but also the degree of its variability 

 and the closeness of associated variability 

 of two interdependent organs. Moreover, 

 it is possible to study the nature of the 

 variability exhibited by any characteristic 

 in any homogeneous lot of individuals and 

 to draw an inference from the nature of 

 this variability — as exhibited in the varia- 

 tion polygon — concerning the condition of 

 the characteristic in question in the given 

 race. A person of experience can tell from 

 a glance at the variation polygon whether 

 the race is in a condition of equilibrium 

 so far as this characteristic goes, or whether 

 it is breaking up into several forms or is, 

 perhaps, evolving into some other condi- 

 tion. The quantitative expression gives a 

 means of measuring change of the mode 

 from epoch to epoch which Weldon used 

 in studying the crabs at Plymouth and 

 which enabled him to demonstrate a pro- 

 gressive change in form. It gives also a 

 means of measuring the alteration of an 

 organ in different environments and so of 

 estimating the effects of changed external 

 conditions. Thus it has been shown that 

 the modal number of ray flowers in the 

 ox-eye daisy depends upon the conditions 

 of nutrition in the soil; the chela of the 

 male crab, Eupagurus, is relatively smaller 

 in deep water; the mud snails, Nassa, of 

 irackish water are depauperate. 



Again, mathematical methods have given 

 us a measure of the correlation between 

 organs, so that the exact relation between 

 human stature and the length of a long 

 bone being known, the stature of extinct 



