350 Mr. John Imray on the [May 21 



mediate step, with three classes only of the Arthropods the Myriopods, 

 Spiders, and Insects, i. e. the Tracheata. From the primitive condition of 

 the tracheaB in lulus, and the many relations between Peripatus and Scolo- 

 pendra, it would seem that the Myriopods may be most nearly allied to 

 Peripatus, and form a distinct branch arising from it and not passing 

 through Insects. The early- three-legged stage may turn out as of not 

 so much significance as supposed. If these speculations be correct, the 

 Crustacea have a different origin from the Tracheata. Peripatus itself 

 may well be placed amongst Professor HackeFs Protracheata ; Grube's 

 term Onychophora becomes no more significant than De Blainville's Mala- 

 copoda. Some notions of the actual history of the origin of Peripatus 

 itself may be gathered from its development. 



In conclusion I would beg indulgence for the many defects in this 

 paper, due to the hurry with which it was written (all available time, almost 

 up to the last moment of our sailing for the Antarctic regions, having 

 been consumed in actual examination of the structure of Peripatus), and 

 due, further, to the impossibility of referring to origioal papers in any 

 scientific library. At all events it is hoped that Peripatus has been shown 

 to be of very great zoological interest, as lying near one of the main stems 

 of the great zoological family tree, and that further examination of the 

 most minute character into the structure of this animal will be well 

 repaid. 



H.M.S. ' Challenger,' Simon's Bay, Cape of Good Hope, 

 December 17, 1873. 



II. " The Uniform Wave of Oscillation/' By JOHN IMRAY, M.A., 

 Memb.Inst.C.E. Communicated by W. FROUDE, M. A., F.R.S. 

 Received April 11, 1874. 



(Abstract.) 



The results of the investigation worked out in this paper correspond 

 with those previously deduced by other analysts, particularly by Mr. 

 W. Froude, F.R.S. The paper is therefore presented, not because it 

 discloses any novel result, but rather as an example of a method which 

 the author has found useful in the discussion of other dynamical problems. 



The object of the paper is to trace the conditions under which the 

 separate molecules of a liquid such as water move, when a body of that 

 liquid is in a state of oscillatory wave-movement. It is assumed that the 

 wave-movement is established in a channel of uniform width and of 

 length and depth so great that the conditions of motion are not affected 

 by the interference of fixed ends or a fixed bottom. 



The wave treated of has as its characteristics permanence of form and 

 uniformity of apparent velocity. 



In order that these conditions may be fulfilled, it is asramed, as being 





