A Card Trick

The explanation of the card trick from the 'Scientific American' given on p. 15 of Vol. V of the Journal, is as follows:

(Diamonds) 1 2 3 4 5 6 7 8 9 10

(Hearts) 10 1 2 3 4 5 6 7 8 9

(Spades) 9 10 1 2 3 4 5 6 7 8

(Clubs) 8 9 10 1 2 3 4 5 6 7

Denote the position of any card in the above arrangement by (x, y) where x, y are the orders of the column and row to which it belongs counting from the left-hand column and top row respectively.