432 T. H. MORGAN. 



above (on account of the first displacement) into the one lying 

 in reality behind it. . . . The spirals when once started do not 

 run on continuously, but end after passing around the body 

 several times. The ending likewise finds its explanation in the 

 inequality of the blocks of opposite sides." I did not in this 

 preliminary paper consider a point with respect to the ending 

 of these spirals that may be spoken of here. 



If a spiral once started was dependent in order to end, on 

 another accidental displacement appearing, so that the spiral 

 is, as it were, satisfied, the chances are that most spirals would 

 reach a prodigious length before terminating. As a matter of 

 fact the spirals are generally short, the shorter the commoner. 

 This shows, I think, that the conditions, after a spiral has been 

 started, are of such a nature that the chances are the spiral will 

 soon end itself. It is easy to offer a formal explanation of 

 why this is so. The shifting of the blocks by the double union 

 established at the anterior end^ will tend to displace the block 

 behind, so that two of one side will come to correspond to one 

 of the other. 



In the preceding section of the paper there are in reality 

 two topics that have been discussed in close connection with 

 each other. The question of the shifting of the reproductive 

 openings was considered in connection with the origin of the 

 compound metaraeres and spirals. The reason for doing so 

 was based on the hope that the one relation might help in the 

 interpretation of the other. 



Moreover, in respect to the abnormal position of the open- 

 ings of the reproductive organs, we have considered first those 

 cases where, in worms with normal metaraeres, the openings 

 have shifted or doubled; and secondly, those cases where there 

 were both abnormal metameres and abnormal openings of the 

 reproductive organs in the same worm. The former of these 

 subjects has been already noticed by previous authors. Beddard 

 (5) in 1886 published some most interesting observations on 

 variations in the reproductive organs of Perionyx excavatus. 



1 It is assumed that the spiral starts at the anterior end. But it is also 

 possible that the shorter spiral arrangement involves all the segments. 



