158 ANATOMY OF THE GYMNOSPERMS 



different forms of distribution may be regarded as forming a 

 second series similarly valued. Any primitive or other character 

 which has become obliterated through development may be held 

 to retain its original value with respect to the general course of 

 such development, and it is always indicated by . Vestigial 

 structures occurring sporadically are designated by i, and to 

 them one half the value of the fully developed character is 

 assigned. All normal features are designated by x, which 

 becomes x + when they show development toward the next 

 higher form, or x when they show a definite tendency to degen- 

 eration. Sporadic characters which are obviously in the line of 

 development are indicated by o, but they are assigned only 

 half values. On this basis it is possible to arrange a sequence of 

 genera and species in such a manner as to exhibit a progressive 

 development from the simple Dammara, with a minimum of char- 

 acteristics, to the complex Pinus, in which the greatest number 

 of anatomical features is involved. Furthermore through such a 

 series it is possible to determine the relative position of the vari- 

 ous genera by percentage values, and it gives the most valuable 

 insight into the approximate relations of the various members 

 within the general line of descent. Such relations are determined 

 not only for each anatomical character but also for the collective 

 characters. Reducing these facts to a graphic form, the accom- 

 panying curves will assist in making the relations more clear, 

 especially in emphasizing the general course of development, and, 

 in their final form, they are best expressed by a biological tree. A 

 figure of this sort is difficult to construct, and there is no agree- 

 ment among investigators as to the particular form it should take. 

 While the figures in common use indicate a certain relationship 

 in descent, they completely fail to convey any impression of the 

 way in which the succession arises, and they furnish no indica- 

 tion of possible gaps. They therefore constitute a very poor 

 working basis. 



In teaching I have long been accustomed to compare the 

 various lines of descent among plants with the branchings of 

 a deliquescent tree, since it has always seemed reasonable to 



