September 30, 1921] 



SCIENCE 



301 



preliminary remarks, which are, in part, as 

 follows : 



The preponderant role of the theory of groups 

 in mathematics has been unsuspected for a long 

 time. Eighty years ago even the name of group 

 was unknown. It was Galois who first had a clear 

 notion of it, but it is only since the works of 

 Klein, and especially of Lie, that one has begun 

 to see that there is almost no mathematical theory 

 in which this notion does not occupy an important 

 place. ... It is necessary to give the same name 

 to different things, but on condition that these 

 things are different as to matter but not as to 

 form. What is the cause of the mathematical 

 phenomenon so often constant! And, on the other 

 hand, of what consists the community of form 

 which subsists under the diversity of matter? It 

 is due to this that every mathematical theory is, 

 in the last analysis, the study of properties of a 

 group of operations, that is to say, of a system 

 formed by certain fundamental operations and of 

 all the combinations which can be made therefrom. 



If, in another theory, one studies other opera- 

 tions which combine according to the same laws 

 one will naturally see a set of theorems, having a 

 one to one correspondence to those of the first 

 theory, unfold themselves, and the two theories 

 may be developed with a perfect parallelism; an 

 artifice of language like those of which we just 

 spoke, suflBces to make this parallelism manifest 

 and to give almost the impression of a complete 

 identity. One says then that the two groups of 

 operation are isomorphic, or that they have the 

 same structure. If then one divests the mathe- 

 matical theory of this which appertains to it only 

 by accident, that is to say, its matter, there will 

 remain only the essential, that is to say, the form ; 

 and this form, which constitutes, so to say, the 

 solid skeleton of the theory, will be the structure 

 of the group. 



G. A. Miller 



University of Illinois 



GALL EVOLUTION: A NEW INTERPRETATION 



Practically all gall students to date have 

 regarded cecidia as responses to specific stimuli 

 relating specific differences causally to the 

 plant bearing the gall. 



Basing his ideas on Kiister's logical classifi- 

 cation of galls (structurally considered) into 

 " kataplasmas " (galls of indefinite character; 

 ex. oak knot gall, Andricus punctatus Bass.) 



and " prosoplasmas " (galls of definite charac- 

 ter; ex. oak apple, Amphibolips inanis O. S.) 

 together with Cook's recognition of the influ- 

 ence of the animal in gall formation, the 

 writer has developed a new theory of gall evo- 

 lution. 



The new interpretation holds that phylo- 

 genetically prosoplasmas have been derived 

 from kataplasmas. Further, kataplasmic evo- 

 lution involves progressive inhibition of the 

 normal differentiation of the plant part until 

 homogeneity is reached. iN'ot until kataplas- 

 mic evolution has been completed is it possible 

 for prosoplasmic evolution to begin its course 

 in which fundamentally new tissue orienta- 

 tions and forms are produced. Thus from the 

 standpoint of the plant's differentiation we 

 have first a regressive movement (kataplasmic) 

 and then a progressive one (prosoplasmic) but 

 from the standpoint of the animal the series 

 should be regarded as progressive throughout. 



A corollary of the above interpretation is 

 the striking situation that an animal may not 

 only inhibit the expression of a plant's char- 

 acters but may introduce new ones, or in other 

 words the evolution of the animal induced 

 galls (zoocecidia) is primarily or fundamen- 

 tally related to the animal. The initiating 

 changes producing the different gall types 

 probably occur in the germ plasm of the ani- 

 mal. This means that the evolution process 

 carried out in the animal comes to expression 

 in the plant, an interesting situation to say 

 the least. 



The evidence for the above theory drawn 

 from the fields of comparative morphology and 

 embryology appears to the writer to be over- 

 whelming. 



The writer has presented this thesis at 

 greater length in the May, 1921, number of the 

 Botanical Gazette. 



B. W. Wells 



North Carolina State College 



ON SOUNDS ACCOMPANYING AURORAL DIS- 

 PLAYS 



To the Editor of Science: The existence 

 of sounds in connection with manifestations 

 of the aurora is regarded by many as still a 



