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KANSAS UNIVERSITY SCIENCE BULLETIN. 



Hi(AA')o 



Second class. 



H 3 (A) c =oc 2 Hi(AA') t . + pH 2 (A). 



HYPERBOLIC GROUPS. 



hHi(AA'). 



H 2 (AC) = ooihHi(A A') + pHi(A) . 

 hH 3 (A) = oo 2 bHi(A A') _|_ P H 2 (A). 

 H 3 (C) = oo-'hHi( A A') + oc 2 eHi( A A') + ooipHj(A) . 



ELLIPTIC GROUPS. 



eHi(AA') 



eH 3 (A) = oc 2 eHi(A A') + P H 2 (A). 

 H 3 (iC) = cx 2 eHi(AA'). 



pHi(A) . 



pH 2 (A) = ooipHg(A) . 



PARABOLIC GROUPS. 



Two points and a system 

 of double spirals. 



One point. 



Two points and a hyper- 

 bolic system of circles. 



Circle and point on it. 



One point. 



Circle. 



Two points and an elliptic 

 system of circles. 



One point. 



Imaginary circle. 



One point and a parabolic 

 system of circles. 



One point. 



