In farther illustration of the truth, that a custom has frequently survived the tradition of its origin, it may be here observed, that the common practice of persons who are unable to write, making their mark or cross, is derived from our Saxon ancestors, who affixed the sign of the cross, as a signature to a deed, whether they could write or not. Several charters still remain, to which kings and persons of great eminence affix “Signum Crucis manu propriá pro ignorantiá literarum.” Hence is derived the expression of signing instead of subscribing a paper. In like manner, the physician of the present day continues to prefix to his prescriptions the letter R, which is generally supposed to mean Recipe, but which, in truth, is a relict of the astrological symbol of Jupiter, formerly used as a species of superstitious invocation.
Note 54, p. [379].--Invention of the game of chess.
Alphesadi, an Arabian writer, quoted by Montucla in his Histoire des Mathematiques, expressly mentions the invention of chess as of Indian origin, and relates the following very curious Indian tradition:--Ardschir, King of the Persians, having invented the game of Tric-Trac, and being exceedingly vain of it, a certain Indian, named Sessa, the son of Daher, invented the game of chess, and presented his chess-board and chess-men to the king of the Indies. The sovereign was so much pleased, that he desired Sessa to name his reward, when this man made the apparently modest request, that he should receive as a gift so much corn as could be estimated by beginning with one grain, and doubling as many times as there were squares upon the chess-board, viz. 64. The king felt displeased at having his munificence thus slighted by a request so limited and so unworthy to be a gift from royalty; but, as Sessa remained firm, orders were given to the chief minister that he should be satisfied: when, however, the visir had by calculation ascertained the enormous quantity of corn which would be required, he waited upon the king, and with some difficulty convinced him of the fact; upon which the king sent for Sessa,--and said to him, that he admired his powers of calculation even more than the ingenuity of the game which he had presented to him, and, in respect to his promise as to the corn, he was compelled to acknowledge himself to be insolvent.
Dr. Wallis, the friend of Sir Isaac Newton, and Savilian Professor of Oxford, found that the quantity of corn would be such as to be capable of forming a pyramid, the measurement of which would be nine English miles in height, and nine similar miles for each of the four sides of the base. After this, Montucla also states some elaborate calculations made by himself, and proves, amongst other remarkable facts, that the quantity of corn in question would cover 162,000 square leagues to the depth of one foot, French measure, which would be at least three times the extent of the surface of France as it was about the year 1796, and which he estimates at 50,000 square leagues.
Note 55, p. [388].--An arithmetical trick.
This problem is to be found in Hutton’s Recreations, and is stated as follows:--
“A person having in one hand an even number of shillings, and in the other an odd, to tell in which hand he has the even number.”
“Desire the person to multiply the number in the right hand by any even number whatever, and that in the left by any odd number; then bid him to add together the two products, and if the whole sum be odd, the even number of shillings will be in the right hand, and the odd number in the left; if the sum be even, the contrary will be the case. By a similar process, a person having in one hand a piece of gold, and in the other a piece of silver, we can tell in which hand he holds the gold, and in which the silver. For this purpose, some value represented by an even number, such as 8, must be assigned to the gold, and a value represented by an odd number, such as 3, must be assigned to the silver; after which the operation is exactly the same as in the preceding example.
“To conceal the artifice better, it will be sufficient to ask whether the sum of the two products can be halved without a remainder; for, in that case, the total will be even, and in the contrary case odd.
“It will be readily seen that the pieces, instead of being in the two hands of the same person, may be supposed to be in the hands of two persons, one of whom has the even number, or piece of gold, and the other the odd number, or piece of silver. The same operations may then be performed in regard to these two persons, as are performed in regard to the two hands of the same person, calling the one, privately, the right, and the other the left.”