204 IOWA ACADEMY OF SCIENCES. 



The double complex 



a+i b+./ c 

 is related to points in three-fold space in the same way that the 

 plane complex 



a+i b 

 is related to points in a plane, and in the form 



or in the general forms 



(a+i b) (c+J d), e^ + ^'^ + J^, 

 it may be treated as an ordinary algebraic quantity. 

 Kansas City University. 



A REVIEW OF THE CERCOPID^E OF NORTH AMER- 

 ICA NORTH OF MEXICO. 



BY E. D. BALL,.' 



The family cercopidse, though of world-wide distribution, 

 has comparatively few representatives within our borders, and 

 those few have been but imperfectly known, the literature on 

 the subject being scattered and fragmentary, the generic 

 references often incorrect, and the specific determinations, 

 owing to the extreme variability in color of some species, and 

 the striking similarity of color between others, rendered very 

 questionable. Scarcely one of the more common forms but 

 what has been referred to under at least four different genera 

 and several have more than that number of specific names. 



This paper recognizes twenty species as included within our 

 fauna, of which Say described six, Fitch three, Germar one, 

 Uhler four, two were introduced from Europe, and four are 

 here described as new; besides these there have been twenty 

 more described, which have been referred to the first twenty 

 as synonyms or varieties. 



Except for the isolated descriptions and a few lists, the first 

 systematic work done on the American species was Uhler's 

 article on the family in the Standard Nat. Hist. (1884). 



In 1889 Provancher, in his Hemip. du Canada, published 

 the first synopsis of the group; he divided the family into 



