Mr. Graves on the Porismatic Arrangement of Points, 131 



Theorem II. Let 1, 2, 3, 4, 5, \\ 2\ S\ 4\ 5' denote 10 

 points; then, if any 9 of the 10 following sets be given, the 

 remaining set will porismatically follow. (See fig. 2.). 



Any one system of 9 sets out of the preceding 10 sets may 

 be so arranged as to present the same functional form with 

 reference to its constituent symbols, and to the derivation of 

 the remaining set from it as any other system of 9 sets, e. g. 

 if, instead of placing 4' 5' 1 last, we place 2 3 4' last, we may 

 form out of the same sets the following scheme, which will be 

 functionally similar to the preceding one: 



4' 3' 4 4 5 5' 



2' r 5 1 2 r 



It may be remarked here, that if the first 5 sets in either 

 of the two last preceding schemes be called x, and the second 

 5 sets be called ?/, and if y be considered as a function fx of 

 X, we shall have f^ x — x. What is the geometrical inter- 

 pretation of this ? Observe that the functional symboiyis here 

 employed to denote similar internal changes in similarly con- 

 stituted wholes, not operations in which the functional sub- 

 jects are themselves similar constituent parts of similar for- 

 mulae. 



K2 



