(41) 

 (42) 



326 Dr. Latham on the Subjectivity of 



u^-k k'{uQ-k) * ' ' ' \ f 



with the significations (26) or (27) of a^, b^, and therefore with 

 the relations (34) (35). Observing that 



A2«=(--l)"=^2«^ ....... (40) 



we find that the formula (39), by comparing separately the real 

 and imaginary parts> in the two cases of x even and x odd, gives 

 these four others, not involving the symbol h : 



U^n^ i _, Agn . l—j __ Ban . 



Man— A: UQ—k* U2n—k UQ—k' 



Uin+i-k k{uQ—k)' U2n+i — k k[uQ—k)' 



of which the consistency with (28) is evident, and which are 

 found to agree in all other respects with conclusions otherwise 

 obtained. Thus all these different processes of calculation con- 

 duct to consistent and interpretable results, although the method 

 of the present article appears to depart even more than those of 

 former ones from the ordinary analogies of algebra. 



Observatory of T. C. D. 

 March 17, 1853. 



[To be continued.] 



LII. On the Subjectivity of certain Classes in Ethnology. 

 By R. G. Latham, M.D.* 



TO the investigator who believes in the unity of the human 

 species, whether he be a proper ethnologist, or a zoologist 

 in the more current signification of the term, the phsenomena 

 exhibited by the numerous families of mankind supply nine- 

 tenths of the data for that part of natural history which deals 

 with varieties as subordinate to, and as different from, species. 

 The history of domestic animals in comprehensiveness and com- 

 plexity yields to the history of the domesticator. Compare upon 

 this point such a work as Cuvier's on the Races of Dogs, with Dr. 

 Prichard^s Natural History of Man. The mere difference in bulk 

 of volume is a rough measure of the difference in the magnitude of 

 the subjects. Even if the dog were as ubiquitous as man, and con- 

 sequently as much exposed to the influence of latitude and altitude, 

 there would still be wanting to the evolution of canine varieties 

 the manifold and multiform influences of civilization. The name 

 of these is legion ; whilst the extent to which they rival the more 

 material agencies of climate and nutrition is getting, day by day, 



* Communicated by the Author. 



