Manchester Memoirs, Vol. li. (1907), No. 16. 13 



throws, in which to make the second throw, all the dice 

 except one were gathered up from the table and thrown 

 again. In this case there is very slight correlation 

 between the two throws. To make Table II., 2 dice were 

 left down. To make Table III., 3 were left down. And 

 so on.* To make Table XII., it did not matter whether 

 the dice were stained red or not, for the second throw was 

 merely the first throw counted over again. And the 

 Table consequently shows any given number in the first 

 throw always followed by the same number in the second. 



Each of the thirteen Tables which are seen on the 

 Plate, was made by substituting for the Arabic numerals 

 in each square of Tables, to XII., a corresponding 

 number of dots, and then in erasing all the lines inside 

 the four boundary lines of the Table. 



The attempt to make the phenomenon of correlation 

 clear to an audience, previously unfamiliar with it, is in 

 my belief less likely to be successful if it is only possible 

 to show one Table such as VI., instead of a series- of 

 Tables exhibiting at a glance the gradual increase in 

 correlation as shown by the transition from a circular blur 

 to a diagonal line, as seen in the Plate. The reason for 

 this is the same as that which would make it very 

 difficult for any one to explain that the angle which 

 the two arms of a ' governor ' on an engine make to 

 one another, becomes obtuse in proportion as the speed 

 of rotation becomes great, if he lived in a world in 

 which 'governors' always travelled at a constant rate 

 such as would keep the two arms at a constant angle 

 of 90 degrees to each other. Table VI. might convey 

 nothing to the mind of anyone regarding it even after he 

 had read the first part of this paper. But a cinemato- 



* I am indebted to Mr. Charles Biddolph for making all the throws 

 except those which compose Tables 0, VI., and XII. 



