204 
IOWA ACADEMY OF SCIENCES. 
The double complex 
b-f-J c 
is related to points in three-fold space in the same way that the 
plane complex 
a-|-^ b 
is related to points in a plane, and in the form 
(a+i b) 
or in the general forms 
(a+^ b) (c+j d), + 
it may be treated as an ordinary algebraic quantity. 
Kansas City University. 
A REVIEW OF THE CERCOPIDigE OF NORTH AMER- 
ICA NORTH OF MEXICO. 
BY E. D. BALL. 
The family cercopidaB, 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 dn 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 
