124 



UNIVERSITY OF COLORADO STUDIES 



be considered as a special case of Steiner's circular series, which, in 

 general, consists of all circles tangent to two fixed circles. From these 

 circles a specml series may be selected in which one point of inter- 

 section of each pair of consecutive circles always lies on a third fixed 

 circle. These series also include the cases of Steiner's circular series 

 where each pair of consecutive circles intersect each other under a 

 a constant angle. If this angle is zero two consecutive circles are 

 always tangent to each other. If the first of the fixed circles of 

 Steiner's special circular series contracts into the centre of the second 

 fixed circle, the series arises from which Poncelet's polygons were 

 obtained by an inversion as illustrated in Fig. 9. 



§13. Circular Transformations, Conjugate Series. 



1. Representing the above configurations in a complex plane 

 it is known that a circular transformation 



cz-\-d 

 does not change properties of closure and conformity (isogonality 



