a7 
) NEWSON: PROJECTIVE TRANSFORMATIONS. 69 
This completes the list of thirteen types. The invariant figures 
characterizing the last six cases are all seen to be self dualistic. 
There is in every case an identical transformation along at least 
reader may verify that this list is complete by assuming in turn an 
: one invariant line and in one invariant pencil of planes. The 
| extra invariant point on each of the invariant lines of the first five 
N 
types. No new self dualistic figure will be found. 
There are thirteen types of projective transformations in space; each 
type ts characterized by one of the self dualistic figures of Fig. 2. 
The determination of these thirteen types of transformations is 
preliminary to the more extensive problem to determine all the 
continuous groups of projective transformations in space and to 
| classify them according to these thirteen types. The writer has 
completed the investigation of this problem for a majority of the 
o¢ 
thirteen types and will soon begin publishing the results. 
