1892.J 



Correlated Variations in Crangon vulgaris. 



11 



carapace length which are associated with a fixed length, of the post- 

 spinous portion should be distributed about their mean with a 

 probable error of 4 , 55v / 0*34, or nearly 2*64. Therefore, when the 

 Plymouth shrimps were sorted into groups, such as those used in 

 Table I, such that the carapace length was constant in each, then the 

 post-spinous lengths in each group should have been distributed about 

 the mean given in the table with a probable error of 2 "03. The largest 

 of these groups contained only about eighty individuals, so that any 

 accurate determination of this point was out of the question; but a 

 rough estimate of the probable error was made in each group which 

 contained more than forty individuals, and the mean value obtained 

 in this way was 1*96, which is perhaps sufficiently near to 2'03. A 

 similar treatment of the groups in Table II gave 2*59 as the probable 

 error of distribution ; and this, again, is not very different from 2'64. 



The other samples show a similar rough agreement between the 

 probable error of the dependent organ in each group and that indi- 

 cated by the value Q-s/l-— r*; but the numbers employed are too 

 small to make a determination of this point worth serious discussion. 



It cannot be pretended that the results here given are either 

 sufficiently numerous or sufficiently accurate to serve as a basis for 

 generalisation ; but at the same time they seem certainly to suggest 

 a very important conclusion. For if the values of r have really the 

 degree of constancy which has been attributed to them, then by ex- 

 pressing the deviation of every organ examined from its average in 

 terms of the probable error of that organ, the deviation of any one of 

 these organs from its average can be shown to have a definite ratio 

 to the associated deviation of each of the others, which is constant 

 for all the races examined. And since both the organs measured and 

 the samples of shrimps examined were chosen, in the first instance, by 

 chance, any result which holds for all these organs through all these 

 races may be reasonably expected to prove generally true of all organs 

 through the whole species. 



That is, the results recorded lead to the hope that, by expressing 

 the deviation of every organ from its average in Mr. Galton's system 

 of units, a series of constants may be determined for any species of 

 animal which will give a numerical measure of the average condition 

 of any number of organs which is associated with a known condition 

 of any one of them. A large series of such specific constants would 

 give an altogether new kind of knowledge of the physiological con- 

 nexion between the various organs of animals ; while a study of those 

 relations which remain constant through large groups of species 

 would give an idea, attainable at present in no other way, of the 

 functional correlations between various organs which have led to the 

 establishment of the great sub-divisions of the animal kingdom. 



