Mr. C. J. Woodward on a new Form of Wave-apparatus 

 Chance of the king being in check. 



229 



For ordinary 

 chessboard 

 For chessboards of n 2 squares (n even), of 64 squares. 



Safe. Simple. Safe. 



knight 



Bishop 



Rook 



Queen 



Two bishops. 



Two rooks... 



Simple. 



8Q-2) 



n?(n + l) 



2?i-l 



n(n + 1) 



2 



71+1 



5n-l 



3 n(n + l) 

 - (n— l)(2w— l) 

 I' n(?i 2 -2) 

 2(2n 2 -2n-l) 



(n + l)(w 8 -2) 



8(n-2) 

 n\n + l) 

 (w-2)(2w-3) 



n 2 (n + 1) 

 2Q-2) 

 n(n + V) 

 (w-2)(5w-3) 



\n + l) 



1 



1 



12 



12 



5 



13 



36 



144 



2 



1 



9 



6 



13 



37 



36 



144 



35 



1 9/1 





37 





93 





We may conclude by remarking that the relative values of 

 the knight, bishop, rook, and queen are, according as we mea- 

 sure them by the chance of simple check or of safe check, on 

 the ordinary chessboard in the ratio of 3, 5, 8, 13, or 12, 13, 

 24, 37 respectively ; while the values of the pieces in the 

 same order, as given by Staunton in the 'Chess-Player's 

 Handbook,' are 3'05, 3-50, 5'48, and 9-94, the value of the 

 pawn being taken as unity. 



N.B. — fiie value of a pawn depends so much on the fact 

 that it is possible to convert it into a queen, that this method 

 does not appear applicable to it. 



XXVIII. On a neiv Form of Wave-apparatus suitable for the 

 Lecture-room. By C. J. Woodwakd, B.Sc* 



THE apparatus about to be described illustrates the motion 

 of the air-particles when a sound-wave is propagated, 

 and also the motion of the sether molecules in a wave of plane- 

 polarized light. 



Wave motion consists in the repetition by a number of par- 

 ticles of some prescribed motion which is given to the first of 

 the particles and taken up successively by the others, a certain 



* Communicated by the Physical Society. 



