August 30, 1901.] 



SCIENCE. 



335 



cies. A like revision has never appeared in English, 

 and not in any language since 1853, during which 

 time many new facts have been brought out. The 

 classification differs slightly from that of previous 

 workers, in view of recently discovered facts of hy- 

 bridization. An attempt is made to arrange the 

 types as nearly as possible in their evolutionary 

 relationships. Twelve species, representing all the 

 natural groups from all parts of the world, and a 

 number of hybrids and varieties, have been studied 

 carefully in cultivation in the Botanic Garden of the 

 University. Others also have been studied in the col- 

 lection of the Henry A. Dreer Company, at Riverton, 

 N. J., and elsewhere. Each description takes up : 



1. Diagnostic characters. 



2. Literature and synonymy. 



3. Minute morphological, physiological and, in 

 some critical cases, histological descriptions of flower, 

 leaf, stem and root, and the development from seeds 

 and tubers. 



4. Habitat. 



5. Eemarks, historical and critical. 



6. Varieties similarly described. 



The results of a number of observations on the 

 times of daily opening and closing of the flowers are 

 incorporated in the descriptions ; these, and the devel- 

 opmental histories of species are, for the most part, 

 entirely new records. The paper is illustrated with 

 photographs and line drawings. 



Mr. Conard is unanimously recommended to the 

 Faculty of Philosophy by Group Committee XV. for 

 the degree of Doctor of Philosophy. 



Professor Craicley, Presentor. 

 Burton Scott Easton was born in Hartford, Conn., 

 December 4, 1877. He received his early education 

 at the Hamilton School, Philadelphia, and with pri- 

 vate tutors in Germany. He entered the University 

 of Pennsylvania as a freshman in 1894, receiving the 

 degree of Bachelor of Science in 1898. During the 

 year 1898-99 he was instructor in mathematics and 

 astronomy in the State University of Iowa, and pur- 

 sued graduate work in the same institution. He 

 entered the Department of Philosophy of the Uni- 

 versity of Pennsylvania, September 27, 1899, electing 

 his major in mathematics, one minor in mathematics, 

 and the other minor in astronomy. He was appoint- 

 ed Harrison Fellow at Large in Mathematics for the 

 year 1900-01, and was transferred to the regular fel- 

 lowship in mathematics and astronomy January 11, 

 1901. He has received credit for the following work : 

 (1) For graduate work in mathematics pursued before 

 receiving his Bachelor's degree, and not credited 

 toward that degree, four standard courses ; (2) for 

 graduate work in mathematics at the State University 



of Iowa, six courses ; (3) for graduate work in this 

 University since 1899, sixteen courses, a total of twenty- 

 six standard courses. He has satisfactorily passed 

 written examinations on March 30, April 4 and May 

 16, 1901, in mathematics with Professor Crawley, 

 Assistant Professors Fisher and Schwatt and Dr. 

 Hallett ; on March 16, 1901, in astronomy with pro- 

 fessor Doolittle and Mr. Eric Doolittle. He has 

 presented a thesis entitled ' Substitutions and Sub- 

 stitution Groups.' He has deposited with the Dean- 

 a copy of this thesis and the monej' necessary to print 

 it. The thesis will appear in the spring of 1902. A 

 brief outline of its contents is as follows : 



The group theory is one of the most recent devel- 

 opments of mathematics. It is far-reaching in its 

 applications and is a most prolific field of research at 

 the present day. The literature of the subject is, 

 however, principally to be found scattered through, 

 the pages of the mathematical and scientific journals, 

 and is therefore disjointed and fragmentary not only 

 in form but also in the manner of its presentation. 

 Moreover, much of importance is almost useless from 

 the difficulty of finding it when wanted. 



The primary object of the dissertation is to present 

 the results of the most recent investigations in this 

 subject in such a manner as to give a coherent view 

 of what has been done. The way in which this has 

 been accomplished by the candidate shows good 

 mathematical judgment, and a thorough appreciation 

 of the philosophy of recent mathematics. Only a 

 portion of what has actually been accomplished in 

 carrying out this work is embodied in the disserta- 

 tion, which is devoted in the main to a careful con- 

 sideration of transitive and intransitive groups, 

 primitive and imprimitive groups, and the isomor- 

 phism of one group with another. The limits of 

 transitivity have received special attention. A certain 

 looseness has been found to exist in the use of some 

 terms, notably in the expression ' permutable groups.' 

 Mr. Easton has given precise definitions in all these 

 cases, and the necessary modifications in the subse- 

 quent developments have been introduced. 



Mr. Easton is unanimously recommended to the 

 Faculty of Philosophy by Group Committee XL for 

 the degree of Doctor of Philosophy. 



Professor Doolittle, Presentor. 

 Henry Brown Evans was born in Dayton, Ohio, 

 July 2, 1871. He was educated in the public schools 

 of his native town, graduating from the High School 

 in 1889. He entered the Freshman Class of Lehigh 

 University the same year, and received the degree of 

 Mechanical Engineer in 1893. He was instructor in 

 mathematics and astronomy at Lehigh, 1894-95, and 

 has been instructor in astronomy in this University 



