1850.] 



507 



[Frazer. 



Table I. 

 2. 



Table II. 

 2. 



Table III. 



1. 



Table IV. 

 1. 2. 



No combination in any one of these pairs of Tables can be shifted to any 

 combination in the other of the same pair (while the outside numbers re- 

 main in proper order) without lifting out of the box and transposing two 

 of the numbers ; but any combination can be shifted into any other in the 

 same table by temporarily placing one number in the outer row and shift- 

 ing the positions of the other three once, or twice. 



Tables I and II are for all cases where 1 heads the column, Table III 

 and IV are for cases when 15 heads the column. 



In the first and third methods the box is turned till the first four num- 

 bers fall on the top line, or the last four on the lower line. 



