APPENDIX. 



THE NATURE OF SIZE FACTORS AS INDICATED BY A STUDY 



OF CORRELATION. 



BY W. E. CASTLE. 



To determine to what extent the several bone measurements studied 

 by Dr. MacDowell vary independently of each other, I asked Messrs. 

 S. Wright and H. D. Fish to form correlation tables between the more 

 important measurements taken (see tables 9-19). Their work is based 

 on the measurements of Dr. MacDowell, which he kindly put at their 

 disposal. All possible correlations were studied between the five meas- 

 urements, 0. M., Zp., H., F., and T. These include one measurement 

 of skull length, one of skull width, one of a bone of the front leg, and 

 two of bones of the hind leg. The ten correlation coefficients calculated 

 are all positive and fairly high. The lowest, 0.658, is between skull 

 width and length of tibia; the highest, 0.858, is between femur and 

 tibia, two successive bones of the hind leg, but the correlation between 

 femur and humerus is practically the same, 0.857. Skull length (0. M.) 

 is more nearly uniform in its correlation with the other measurements 

 studied than any of the other four measurements. Its coefficient varies 

 only from 0.70 to 0.76. The former coefficient is given by the femur 

 correlation, the latter by the tibia; but as femur and tibia are them- 

 selves very closely correlated, more so than any other pair of measure- 

 ments, it follows that neither correlation with the skull length can in 

 the long run be very different from the other. Hence skull length is 

 probably the best single measurement that could be taken as a basis 

 for comparing the size of individual rabbits. It happens (not without 

 reason, probably) that this particular measurement is one commonly 

 employed in systematic descriptions of rodents. A more fortunate 

 selection could apparently not have been made. 



In view of the high correlations obtaining between one skeletal 

 dimension and another (and these agree closely with those observed 

 in the case of man by Pearson and others), it follows that to a large 

 extent the factors which determine size are general factors affecting all 

 parts of the skeleton simultaneously. When the skull is long, the legs 

 are long and the skull is wide, and every other part varies in propor- 

 tion (or within 65 to 85 per cent of the same proportion). What- 

 ever special factors (if any) there are, which are concerned in limiting the 

 size of particular bones, these can play only a subordinate part in deter- 

 mining size. The chief factors are plainly general factors and control 



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