This **permutation** by a transposition of two numbers, say a, 13, becomes 0, a, 7, ...

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.

By this **permutation**, Aleph, the first letter of the alphabet, becomes Lamed, the twelfth letter; Beth becomes Mem, and so on.

V, and by successively transposing pairs of letters the **permutation** can be reduced to the form I, 2, 3, ..

-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by **permutation** of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

V is some **permutation** of these n numbers.