236 Mr. H. Thompson. On Correlation of [Mar. 1 , 



3W XH XI A 



13 jyi * f\ A A w 

 X /y\ 



xm 



Diagram of exoskeleton of Palamon terratus with appendages removed. The 

 numerals refer to the numbers of the measurements. 



Out of the 1000 prawns seven had a deformed rostrum, and six 

 had a deformed telson. In several of the numerical results set out 

 below these thirteen animals have been excluded because their deform- 

 ities affected the body length to such an extent as to give a wholly 

 fictitious value to the reduced measurements of the other organs. 



The existence of a long rostrum in the prawn has proved a serious 

 hindrance, since its length in proportion to that of the body is very 

 variable, and hence those parts in which the rostrum is an element 

 present a degree of correlation which is very slight, and render im- 

 possible any real comparison with the corresponding parts in the 

 shrimp, for instance, which has scarcely any rostrum at all. 



Selection was made of the female prawn as being larger than the 

 male, and therefore more convenient for the purposes of measure- 

 ment. The largest measured 111 mm. in total body length, the 

 smallest 61*5 mm. 



All the measurements having been reduced, as above stated, to 

 fractions of the total body length, they were next arranged in order 

 of magnitude for each organ separately, and in almost every case the 

 values were found to range themselves with a fair degree of symmetry 

 around the median value, and to correspond with more or less 

 accuracy to calculated probability curves. In one case, however 

 (measurement No. VII), the curve presented features of asymmetry 

 which have been investigated by Professor Karl Pearson (' Roy. Soc. 

 Proc.,' vol. 5& p. 329). 



The next step was to determine the degree of correlation between 

 various pairs of the organs measured. The method used was that 

 originally suggested by Mr. Galton, and sufficiently explained by 

 Professor Weldon in his paper above referred to, so that it is un- 

 necessary to repeat it here. 



The following table gives the value of " Galton's function " for "'', 

 pairs of organs : 



