248 



KANSAS UNIVERSITY SCIENCE BULLETIN. 



(5) 



= Kab 



and we can deduce in the same manner three other 

 equations: 



= Kac 



D' 



D 



{D' and i) are the denominators of left and right 

 side of (5), respectively.) 



= Kad 



D' 



D 



= Kae 



D' 



D 



We have four linear equations to determine x'^x'^ 

 x'sX'i, w^hich is the proper number to give us a unique 

 solution. Moreover, we have the twenty-four essential 

 parameters of our collineation, namely, the twenty co- 

 ordinates of the invariant points and the four inde- 

 pendent cross-ratios K^kK^K^^K^^. 



