2GO 

 or 



PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



1:! . 



- .... (xxxvm.). 



The percentage probable error in a partial coefficient of regression is accordingly 



67-449 



Before discussing the significance of these quantitative results for three organs, it 

 seems desirable to complete the general case by investigating the con-elation between 

 the errors made in the correlation coefficient* of a first pair of organs and a second 

 different pair of organs. 



(11.) Case (ii.). Case of Four or more Organs. In the case of four or more organs 

 the only new probable error will be that of a partial regression coefficient, but this 

 can theoretically always be found by the method of the preceding paragraph, provided 

 we know all the error correlations. The only novel correlation among the errors 

 will be that of r^r^ and this we shall now proceed to investigate. The discovery of 

 an error correlation coefficient of this type completes the theory of the errors of 

 normal frequency constants. 



Instead of evaluating A of (xxxiii.), which in the case of four organs appears to be 

 very laborious, we may proceed as follows : 



If A be written in the form 



and M denote the minor of the corresponding a in A, we have by a well known 

 property of the determinant, 



Divide by A, 



a M ('-. a . -i) 4. a Miriam 4. a MiDiLD.) + . . + a ,. M(r ' 2 ' rsi) = 0. 



"^"i A ' "<f-i A ' "?* A 



