CORRELATED VARIATIONS. 79 



spinous portion was fixed. The line drawn through 

 them indicates the ratio .81. Every point should 

 theoretically lie on it, and it will be seen that they do, 

 as a matter of fact, lie very closely around it. 



This correlation constant of .81 was obtained by 

 Professor Weldon for shrimps collected at a particular 

 locality, viz., Plymouth. Similar determinations were 

 also made for shrimps obtained from other localities, 

 with the following results : 



In Plymouth r = .81 (1000 individuals examined) 



In Southport .85 ( 800 " " ) 



In Roscoff .80 ( 500 " " ) 



In Sheerness .85 ( 380 " " ) 



InHelder .83(300 " ) 



The approach to identity between these values is very 

 striking, the differences appearing to be within the 

 probable error of each determination. There seems a 

 reasonable ground for assuming, therefore, that the 

 degree of correlation between the two particular organs 

 measured is practically constant in all the races exam- 

 ined. The correlation between other organs was also 

 estimated, but this was in each instance very much 

 slighter, and in the case of the telson and sixth abdom- 

 inal tergum, it was negative. Considering the degree 

 of independence of these organs, as shown by the small- 

 ness of their correlation constants, the similarity be- 

 tween the values for the two local races is probably as 

 close as could be expected. Hence, as both the organs 

 measured and the samples of shrimps examined were 

 chosen by chance, any result which holds for all these 

 organs through all these races may be reasonably ex- 

 pected to prove generally true of all organs through the 

 whole species. 



