Let k such transpositions be necessary; then the expression X(kal aa2 N a 3.
A and 13 are transposed, and it is clear that the number of transpositions necessary to convert the permutation say...v of the second suffixes to the natural order is changed by unity.
Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all permutations, the number of transpositions necessary determining the sign to be affixed to the member.
These transpositions are purely arithmetical.
But of late years an increasing desire has been manifested, especially in Germany and America, to manipulate the fourth Gospel on grounds of internal evidence, at first only in the way of particular transpositions of more or less attractiveness, but latterly also by schemes of thorough-going rearrangement.