i894. NOTES AND COMMENTS. 83 



shown "(i) that the observed deviations from the average size of every 

 organ measured are grouped symmetrically about the average, and 

 occur with a frequency corresponding closely to that indicated by the 

 probability integral; and (2) that the 'degree of correlation' between 

 a given pair of organs is approximately the same in each of five local 

 races of the species." {Proc. Roy. Soc, vol. xlvii., p. 445 ; and vol. li., 

 p. 2). He has now measured specimens of the shore crab in two lots, 

 one from Naples and the other from Plymouth, and after an elaborate 

 comparison of the correlated variations between different organs, 

 he shows that, though variation may differ, yet the amount of 

 covyelation is the same for both groups. 



The method followed by Professor Weldon in determining the 

 degree of correlation between two organs was that proposed by Mr. 

 Francis Galton in his paper on Family Likeness in Stature [Proc. 

 Roy. Soc, vol. xL, pp. 42-63), and it appears that the results obtained by 

 that ingenious anthropometer are fully confirmed b}* the study of so 

 remote a group as the Arthropoda. The suggestion has recently been 

 made that " the method of composite portraiture, as developed by 

 Mr. Francis Galton and others, might be employed with advantage 

 to discover a type or standard from which degrees of variation within 

 the limits of a species might be measured in positive or negative 

 terms " (Bather, " Crinoidea of Gotland," p. 5). This, perhaps, is 

 often impracticable, but the construction of a diagram from the 

 average of numerous measurements would serve a similar purpose. 

 Such a diagram of the carapace of the crabs in question is actually 

 given by Professor Weldon. The diagram is drawn to scale, the 

 right half representing a perfectly average Plymouth crab and the 

 left an average crab from Naples. 



Professor Pearson's contribution to the subject is a mathematical 

 analysis of certain curves that may be constructed from a series of 

 measurements of a number of objects of the same type. Such curves, 

 which he terms frequency curves, are often abnormal, especially in 

 biological measurements, such as those of Professor Weldon, or the 

 similar ones of Thompson for prawns, and Bateson for earwigs. 

 Although abnormal, however, they are subject to certain laws, and 

 from a consideration of these Professor Pearson believes it possible to 

 detect whether the individuals measured represent a mixture of two 

 heterogeneous groups, or whether they represent one homogeneous 

 species gradually being evolved into two differentiated species. Thus 

 he finds that the Naples crabs are all of one species, but that they are 

 breaking up into two varieties owing to evolution in their foreheads. 

 Mr. Thompson's prawns, on the other hand, either have a small per- 

 centage of individuals deformed in the carapace, or else have a small 

 but unstable giant population mixed with the normal population. 



These modern mathematical investigations differ widely from the 

 fine-drawn and metaphysical "pro-morphology," as Geddes calls it, of 

 the old German nature-philosophers. As to their value, hear Pro- 



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