314 



Lastly, on the question whether the peculiarities of structure re- 

 cognized respectively in N. Pompilius and N. umbilicatus are suffi- 

 cient to establish a difference of species, or are attributable merely to 

 variety, the author observes, that any tendency in a being to revert 

 to an original type, when such has been determined, betrays variety; 

 but this tendency is never manifested in the Nautili under conside- 

 ration by the occasional occurrence of specimens presenting charac- 

 ters which place them intermediately between N. Pompilius and 

 N. umbilicatus. Having visited the Fijii Islands since he formerly 

 wrote on N, Pompilius, he finds that the umbilicated Nautili are not 

 known to the natives, although N. Pompilius is very plentiful ; but at 

 Fatuna or Wallis's Island, where both are found, the people recog- 

 nize the difference between them depending on the presence or 

 absence of umbilical pits. On this the author remarks, that although 

 particular localities, with all attending circumstances, may favour 

 the production of varieties, yet the permanence of the distinctive 

 characters of these Nautili without symptom of amalgamation, and 

 the discovery of a female specimen of N. umbilicatus, are strong 

 arguments in support of the view that they are distinct species, 

 though very closely allied. 



Further descriptive details are given in the explanation of the 

 figures which accompany the memoir. 



III. "On a Class of Differential Equations, including those 

 which, occur in Dynamical Problems." Part II. By W. 

 F. DONKIN, M.A., F.R.S., F.R.A.S., Savilian Professor of 

 Astronomy in the University of Oxford. Received February 

 17, 1855. 



This is the second and concluding part of a paper of which the 

 first part was printed in the Philosophical Transactions for 1854. 

 In the fourth section (the first of this part) some of the most import- 

 ant results of the former part are recapitulated. 



In the fifth section the theory of the Variation of Elements is con- 

 sidered under that aspect which belongs to it in connexion with the 

 general methods of this paper ; and the facility of its application is 

 shown in two instances: (1) the expressions for the variations of 



