46 Gmiihif/ Percent of Indian Cottons 



From these tiguivs the . j)artial correlation eucfHcieiits may be 

 ealciilated. These have been determined as follows': 



r,,.4+-8392 r,2.34+-!l7W) 



r,3.4+-1992 (-,3.24+ -9198 



r23.,--3260 ru 23 -■9282 



(■,2.3+ -8285 )-23.i4- -925.5 



/•U-3--2898 r24.,3+-92fif. 



rs4.3+-2566 r3,.,..+ -9316 



n3.2+-3952 

 In. 2- -^909 

 1-34.2+ -5540 

 '•23.1 -•■4449 

 (-24.1 + -4577 

 r34.i + -5406 



From a consideiaticjii of these coefficients it is clear that the tonr 

 characters concerned form a closely interrelated gi'onp in which variation 

 in any one character is very fully accounted for by variation in one or 

 other of the other three. Further, of the three characters by which the 

 ginning percent may be affected, one only, namely the number of fibres 

 per seed, has any marked effect on the value of the ginning percent. 



Certain other conclusions may be drawn from the above figures of 

 which one or two may be mentioned here. In the first place the high 

 negative correlation (r = — '9282) between the ginning percent and the 

 volume of the seed indicates the validity of the conclusion, based above 

 (p. 42) on a priori considerations, that the ginning percent, other 

 factors being constant, will increase as the volume diminishes. Secondly, 

 the high negative correlation between the number of fibres per seed and 

 the weight of 1000 fibres (r = — •9255) seems to indicate that the area 

 in which the fibre can develop is limited as a result of which any 

 increase in the number must be accompanied by a diminution in the 

 space occupied by each individual fibre. This conclusion has already 

 been foreshadowed above. 



Lastly, while variation in the number of fibres per seed will produce 

 a marked direct effect on the value of the ginning percent, variation in 

 either the fibre weight and the volume of the seed can produce but a 

 small effect in that the correlation between these and the iiund^er of 

 fibres per seed is low (»-23= — -2285 and ?-,4 = — •0966). 



The main and all-important conclusion, however, to be drawn from 

 these results lies in the fact that there is here definite proof that the 

 ginning percent is a complex character, the variation found in which can 

 be almost completely accounted for by the variation found in the three 



' Cf. Yule, An introduction to the Theory of Statistics. 2nd edition, p. 241 et seq. 



