Page:Notes and Queries - Series 12 - Volume 5.djvu/98

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NOTES AND QUERIES. [is s. v. A,

" VESTIS ADRIATICA." (See 11 S. viii. 270.) At the above reference L. L. K. quoted the following passage from St. Alexius' s life in the ' Legenda Aurea ' of Jacobus de Voragine, and asked for an explanation of " vestis adriatica," which, as he observed, " French and other Continental writers translate as ' vesture de deuil,' ' raiments of sorrow, mourning,' or ' black dress '":*.

" Sponsa vero eius induta veste adriatica cucurrit plorans."

It was natural to conjecture that the text might be corrupt, an obvious too obvious emendation being atrata. An examination of the saint's life in the Bollandist ' Acta Sanctorum ' threw no light on the difficulty. In the ' Sancti Alexii Viri Dei Vita ' given from Simeon Metaphrastes in the abridgment of Aloysius Lipomanus's ' Vitse Sanctorum,' 1573, pt. ii. p. 339, the words used are " Sponsa vero lugubri veste induta currens," &c. I have not examined the original Greek of the Metaphrast, but am now strongly inclined to believe that adriatica is a cor- ruption of Atrabatica. See Du Cange's account of " Atrabaticre Vestes " ; and ' Atrebates ' and ' Atrabaticus ' in the ' Thesaurus Linguae Latinae,' vol. ii. col. 1094. It appears from the ' Thesaurus ' that, although of course the adjective " Atraba- ticus," when applied to clothing, means that it was manufactured by the Atrebates, the Gallic tribe whose chief town was the modern Arras, yet Johannes Lydus and Suidas, misled by the resemblance to atriim, sup- posed the name to refer to the colour. Prof. Postgate has pointed out to me that certain MSS. haveAdrebas instead of Atrebas in Csesar, 'E.G.,' iv. 35, 1. This helps to show that the corruption of " Atrabatica " or " Atrebatica " to "Adriatica" is easy and natural. EDWARD BENSLY.

CHESS : THE KNIGHT'S TOUR. The well- known problem, or puzzle, of the Knight's tour consists in the discovery of a series of moves by which the Knight, starting from a given square, may visit successively, but only once, every square of the chessboard. The problem has been solved in many different ways, but I doubt whether it has hitherto been shown that the tour may start from any square that all the squares of the board will serve the Knight's purpose equally well.

Let the reader take, or make for himself, any solution of the puzzle. In the tour that lies mapped out before me, which I will call A, square 1, from which the Knight starts,

TOUR A.

28

11 '

42

49

30

9

32

45

41

48

29

10

43

46

19

8

12

27

50

47

18

31

44

33

51

40

17

64

61

58

7

20 ;

26

13

52

59

16

63

34

57

39

2

15

62

53

60

21

6

14

25

54

37

4

23

56

35

1

38

3

24

55

36

5

22

is Queen's Rook's square ; and square 64., at which he ends, is Queen's 5th. Now for certain inferences. In the first place, the tour may be reversed may start from 64 as well as from 1. Next, a Knight standing at 64 commands, in the tour before me^ squares 63, 53, 15, 13, 27, 29, 43, and 31. It follows, therefore, that, besides 64 r squares 54, 16, 14, 28, 30, 44, and 32 are squares from which other tours can be made~ For instance, the tour beginning, say, at square 16, proceeds from 16 forwards to 64,. and then, as 15 is a Knight's move from 64* from 15 backwards to 1. Let us call this tour B, and record it on a plan or diagram: of a blank chessboard, marking 16 as 1, 17 as 2; 64 as 49, 15 as 0, 14 as 51, 13 as 52, and so on. Again, a Knight at square 1 of the A tour commands, besides 2, square 54. It follows that a fresh tour may be made backwards from 53 to 1, and then, as the Knight commands 54, forwards from 54 to 64. We infer, then, from our first tour A* that squares 1, 64, 54, 16, 14, 28, cO, 44, 32, and 53 ten in all are possible starting- points. Tour B should be treated in the same manner for the discovery of other squares from which the Knight may start. Record the results on a blank diagram of 64 squares, and make as many more tours,, each of them strictly derived or deduced from its predecessor, as may be necessary to- cover the w T hole board with possible starting- points. I have found six tours necessary ,. some of them, as it happened, yielding very scanty new results.

But this is not all. As the board has four sides, and can be turned in fcur different directions, every square is one of a set oi