INTRODUCTION. 25 



Nebraska and Colorado, where the summer was spent at the Alpine Laboratory, except 

 for an ecologic and taxonomic excursion into the Bad Lands of Wyoming, South Dakota, 

 and Nebraska. In the meantime. Hall prosecuted studies, especially on Atriplex, in 

 the alkaline districts of Utah, Colorado, and neighboring States. In the late summer a 

 joint motor trip, with numerous stops and short sidetrips, extended across southern 

 Colorado and northern New Mexico to Arizona, Hall continuing to the borders of 

 Lower California. 



In 1921, Clements again motored from Arizona to Nebraska and the Alpine Laboratory, 

 continuing in August to the Pacific Coast. Hall spent a month in August and September 

 in the mountainous portions of Idaho, Montana, and Washington, and then joined 

 Clements for field work in eastern Oregon, western Nevada, and eastern California, 

 going as far south as Mono County. Later in the year studies were made on the Arte- 

 misias of the coastal slope of California and on the Atriplexes of the San Joaquin Valley, 

 the latter in connection with Dr. H. H. Severin, whose intimate acquaintance with these 

 plants rendered the trip especially valuable. 



Frequent short trips were made in addition to those outlined above, these being 

 mostly confined to Arizona, California, and Colorado. Short stops were also made at 

 numerous railroad stations when traveling by train. Most of these were between the 

 Pacific Coast and Colorado, but a few were on the Atlantic seaboard. Because of the 

 interest in phylogeny, an endeavor was made to reach all stations in the West where the 

 genera occurred in abundance and where information regarding variations and inter- 

 mediate forms could be obtained. Type locahties were also visited as far as possible and 

 data secured with a view to determining the degree of constancy in the characters used 

 as a basis for species and varieties previously proposed by others. It is with deep 

 regret that, because of lack of time and facilities, it has been found impossible to carry the 

 field work into Canada and the Arctic regions on the one hand and into Mexico on the 

 other. 



Results of statistical studies and experiments. — Taxonomic botany is sadly in need of 

 more exact methods of investigation. Far too many opinions have been expressed, too 

 many species proposed, and too many descriptions drawn after a casual examination of 

 only a few specimens, and sometimes without subjecting these to accurate measurements. 

 During the present studies much time and thought has been given to an attempt to 

 remedy this condition. Consequently, all criteria used have been subjected to the 

 quantitative test as far as possible. Sometimes the results are expressed in tabular form, 

 since this affords a concise method for the presentation of the evidence upon which con- 

 clusions are based, but in many cases it has been considered sufficient to preserve the 

 data only in the herbarium and thus conserve space. It has been discovered by the use 

 of these methods that many criteria heretofore supposed to be valid break down com- 

 pletely, whereas others commonly overlooked are shown to possess real merit. A notable 

 example of this latter condition is the case of relation of length of stylar appendage 

 to total length of style-branch in Chrysothamnus. By reference to table 23 it will be 

 seen that this character is too variable for use in separating most of the subspecies of 

 C. nauseosus, but, on the other hand, that two of these are set off from the others and 

 brought near to each other on the basis of this trait. The results are useful not only 

 for diagnostic purposes, but, what is of more importance, as indicating the relationships 

 of the forms involved. 



The next step in the application of the statistical method will be the expression of 

 results by the use of graphs, as is commonly done by biometricians. This seems unneces- 

 sary in the present work, since the results can be read directly from the tables with almost 

 as great ease as when expressed graphically. The importance of quantitative methods 

 and the use of graphs has been emphasized recently by MacLeod (1919). 



