represent the relative positions of those complementary pairs, 1 + 16, 2
+ 15, etc., which sum to 17. For example, it will be seen that the first
and second magic squares given are of Type VI., that the third square is
of Type III., and that the fourth is of Type I. Edouard Lucas indicated
these types, but he dropped exactly half of them and did not attempt the
classification.

NASIK (Type I.) . . . . . 48
SEMI-NASIK (Type II., Transpositions
of Nasik) . 48
" (Type III., Associated) 48
" (Type IV.) . . . 96
" (Type V.) . . . 96 192
___
" (Type VI.) . . . 96 384
___
SIMPLE. (Type VI.) . . . 208
" (Type VII.) . . . 56
" (Type VIII.). . . 56
" (Type IX.) . . . 56
" (Type X.) . . . 56 224
___
" (Type XI.) . . . 8
" (Type XII.) . . . 8 16 448
___ ___ ___
880
___

It is hardly necessary to say that every one of these squares will
produce seven others by mere reversals and reflections, which we do not