Writings of Charles S. Peirce: A Chronological Edition, Volume 6. Charles S. Peirce

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      Fig. 9

⊙	An instant of time. Joined by barbed line to a later instant. The length of the interval is roughly represented by that of the barbed line. Instants are joined by plain lines to the events that take place about that time.
•	A person or firm. Goods. ⊚ A sum of money.
	A bill. Amount due and goods joined by plain lines. Party making out bill joined by wavy line . Party to whom made out joined by line .
	A verbal contract. Negotiators joined by lines . The contract is for the sale of goods joined by plain line, for each payment of sum joined by plain line. Goods to be delivered by party joined by dotted line to party joined by broken line .
	Order for goods joined by plain line. Order delivered by party joined by line . Goods to be sent by party joined by dotted line to party joined by broken line . Price to be sum joined by plain line, to be paid as usual at end of month.
	Act of delivery by party joined by dotted line of object joined by plain line, to party joined by broken line .
	Receipt by party joined by scraggly line, , of bill joined by plain line.
	Disappearance of party joined by plain line.
	Quarrel between parties joined by plain lines.

      [Card Games]

      Take a pack of cards, select from it the spades and the hearts, rejecting only the kings. Arrange each of these suits in sequence,—ace, 2, 3, … 9, 10, Knave, Queen,—the ace being at the back, the queen at the front. Put the hearts on the table in a pile, backs up. Deal off the spades one by one into two piles, turning each card over and laying it down, face up. The cards in this dealing are, of course, alternately placed on the left hand and the right hand piles. But when you come to the last card, which will be the queen, instead of putting it down on the pile where it would regularly go, you put it down on the table, face up, to form the first card of a new pile. In the place where the queen would have gone had you proceeded regularly, now put instead the top card of the pile of hearts, which is the ace, turning it face up. Now cover the pile upon which you have just laid this card, with the other pile of six spades, and take up the combined pile into your hand, faces down. Repeat this operation: that is, deal out the cards you hold in your hands into two piles, until you come to the last card which will be the knave, which you place on the queen, as the second card of that pile, and in place of the knave you put on the second pile, the top card of the pile of hearts, which will be the two. You then cover this pile with the other pile of six, and take up the combined pile, as before. Do this over and over until you have done it twelve times in all, when you will hold all the hearts in your hand, and all the spades will lie in a pile on the table. Now I say that there is a singular relation between the arrangement of the spades and that of the hearts, so that when you have once remarked the secret of it, by examining the spades which you hold in your hand, you can readily tell off the hearts in the order in which they lie on the table. What I ask you to do is, preserving their order, to spread out the spades and the hearts on the table, and try if you can see what this relation between the two orders is.

      Take a pack of cards, and arrange them in sequence, proceeding from back to face, as follows:—Spades: ace, 2, 3, … 10, Knave, Queen, King. Diamonds: ace, 2, 3, … 10, Knave, Queen, King. Clubs: ace, 2, … Queen, King. Hearts: ace, 2, … Knave, Queen, King. Thus, the ace of spades will be at the back, and the king of hearts at the face of the pack. Take the pack in your hand, face down, and deal the cards out singly, into five piles, in regular rotation, turning each card face up as you lay it down. Take up the third pile and lay it face up on the first, so as to make one pile of the two. Place this combined pile on the last pile but one, so as to make one pile of them. Take up this still larger pile and lay it on the first pile, so as to combine these. Take up this pile and lay it on the last of the original piles, so as to unite the whole pack. Take up the pack into your hand, faces down, and deal the cards out one by one into six piles in regular rotation, turning them up as you lay them down. Place the fifth pile on the fourth, this united pile on the third, this pile on the second, this on the first, and this again on the last, so as to reunite the whole pack, spread the cards out in four rows, of thirteen in a row, as follows, where the numbers show the places of the cards in the pack before they are spread out.

      1 2 3 4 5 6 7 8 9 10 11 12 13

      14 15 16 17 18 19 20 21 22 23 24 25 26

      27 28 29 30 31 32 33 34 35 36 37 38 39

      40 41 42 43 44 45 46 47 48 49 50 51 52

      You will now find a singular relation between a card and a certain other, in respect to their suits and numbers in the suits, their rows and places in the rows. Try to discover that relation.

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