98 KANSA*; llNlVERSITY QUARTERLV. 



If we eliminate x,, yj, Zj from these two sets of equations, we are 

 able to express the co-ordinates of P^ in terms of those of P. 

 Setting XA'=A,, the elimination gives 



y„ y z„ 2 ^2 ^ 



~=A, — ; — =A.-a_; ^=xa-l_. 



Xo X y2 y z, z 



This shows that the two transformation T and Tj are together 



equivalent to T^: another transformation of the same group which 



transforms P directly to Pg. 



This analytical expression for a one-termed group G.^ is in fact 



identical with Lie's expression in homogeneous co-ordinates. 



[ Tc? be Continued. ] 



