[ 350 ] 



XXXVI. Note on the Calculation of Correlation hetween 

 Organs. By Professor F. Y. Edgewoeth, M.A., D.C.L.* 



IN a former paper f I have shown how to calculate the 

 coefficients of the qnantic which expresses the correla- 

 tion between a set of organs, say, 



p Y x* +P2X2 2 +^ 3 ^3 2 + &c. + 2q 12 x 1 x 2 + 2q n ,v l Xz + &c, 



where aa u x 2 , 3s Zi &c. are the deviations of the organs from 

 their respective means. Form the determinant : — 



h 



Pl2> 



Pro 



P12, 



h 



P-23 



Pn, 



P23 



1, 



where p i2 , pis, P22? & c - are the coefficients termed by Mr. 

 Galton r t pertaining to each pair of organs. Call the 

 above-written determinant T A ; and call the determinant 

 which forms the discriminant of the above-written quantic A, 

 The first step of the calculation is to equate each minor of 

 X A to a corresponding coefficient (of the required quantic) 

 x A. To proceed from these proportionate values of the 

 coefficients to the absolute values I before employed § the 

 proposition A==p 1 =p 2 = & c - But it has occurred to me 

 that this second step can be effected more easily by the 



proposition -r = A' ; which may be thus proved. If each of 



the constituents of a A be multiplied by A, the determinant so 

 formed is the reciprocal of A ||. But the reciprocal of 



A = A*- J . Therefore A^ Xl A = A 51 " 1 ; X A = ^. This propo- 

 sition enables us with great ease to proceed from the propor- 

 tional to the actual values of the sought coefficients. For 

 example, let there be three variables, and let 



Pu= '8 ? Pn — '9, £> 23 = "8; 



* Communicated by the Author. 



t See " Correlated Averages," Phil. Mag. 1892, xxxiv. p. 190. 



t Proc. Royal Soc. 1888. 



§ Phil. Mag. 1892, xxxiv. p. 197, 



Ibid. p. 201 



