WILCOX: SPERMATOGENESIS. 21 



I have used the word "reduction" without indicating the particular 

 sense in which I use it. The definition of reduction proposed by Weis- 

 mann ('92), and adopted by vom Rath, Hacker, andothers, is that wliich 

 I prefer, and according to which I have used the term. This is : " Unter 

 Reductionstheihuig verstehe ich eine jede Kerntheilung durch welche die 

 Zahl der Ide welclie im ruhenden Kern vorhanden war, flir die Tocliter- 

 kerne auf die Hiilfte herabgesetzt wird." It is not necessary to adopt 

 Weismann's terms, " ids, idants," etc., in order to use his definition. If 

 the developmental possibilities are only one half as great in the daughter 

 nucleus as in the mother nucleus, there has been a reduction in Weis- 

 mann's sense. If a nucleus contains four elements which happen to be 

 two pairs of identical elements, the formula would be 



n 



y- 



m 



Now, if the division takes place along the line xy, there is a reduction 

 in Weismann's sense ; but if the division be along the line m n, it is an 

 equation division. Either division would reduce the chromatic mass, 

 but only the first would reduce the number of different elements (ids) 

 in the daughter as compared with the mother cell. 



Since the rings, or Vierergruppen, have already been found in the 

 oogenesis and spermatogenesis of numerous species in different groups, 

 this arrangement of the chromatin just before the maturation divisions 

 is certainly very general, if not practically universal. In order, there- 

 fore, to interpret properly these two divisions, and to come to any 

 sound conclusions with regard to the reduction question, it is of funda- 

 mental importance carefully to study the formation of the Vierergruppen. 

 Hacker ('93) and vom Rath ('93) have already called attention to the 

 fact that the double longitudinal splitting of the chromatic thread, main- 

 tained by Boveri and Brauer, must bring about groups of four identical 



{ a a\ 

 elements. The formula for a Vierergruppe would then be ] a a\' 



There could not in this case be any Weismannian reduction in either 

 division, for there is only one kind of id in all the four elements of the 

 group. If the Vierergruppen always arose as Brauer describes the 

 process, — i. e. by two longitudinal splittings of the chromatic gramdes, 

 which alone, he believes, possess an individuality, — then the four com- 

 ponents of each group would be identical, and there could be no reduc- 



