44 
Proceedings of the Boycd Society 
Hence the values are represented by the following scheme — 
0 10....* 
0 1110 
0 1 2 3 2 1 0 
0 13 6 7 6 3 10 
&c. y &c. 
Thus the value of P x , y in this case is the coefficient of a x in 
Hence the number of different modes in which the game may 
finish, when one of the players is x u up,” and there remains y “ to 
/ l\y 
play” is, calling R#, the coefficient of a x in I a + 1 + - J , 
C( D + d)( 1 + DD'-l) + 
while the number of different ways of finishing if the whole y holes 
are played out is 3 y . 
There are many very curious properties of the numbers we have 
denoted by P#, y , A*, y , Qx, y . Thus, for instance, it is easy to 
see that 
Ql, 2 = Q2, 2 - 1 Qo, 2 = Q3, 2 + 1 
Qi, 3 = Q2, 3 + l Qo, 3 = Q3, 3 - l 
all of which are included in 
Qx,y = Q 3-x,y + (-i f+V . 
2. Laboratory Notes. By Professor Tait. 
1. On the Stiffness of Wires. 
The following are the results of some experiments made for 
me by Mr W. M. Ogilvie with Amontons’ apparatus; chiefly with 
the view of testing the accuracy with which it can be applied, but 
incidentally, with the view of obtaining an idea of the relation be- 
tween tension and stiffness in the same wire or cord. 
