252 PROFESSOR K. PEARSON AND MB. L. N. G. FILON 



Here the signs of the terms in the last six rows have been changed from minus to 

 plus.* Now multiply the first four rows by R 12 /R and add them to the fifth row, the 

 first four rows by Ri 3 /R and add them to the sixth row, the first four rows bv R U /R 

 and add them to the seventh row, and so on. Then, remembering that 



/H.A 2R U R 12 1 <jBy 



13 \ B / " R s R dr a ' 



R- ' R dr a ' 



2R 3t R,, _1_ dEn 



and, further, that li jv does not contain r,,, so that <7(R w ,)/dr,,, = 0, we have, taking 

 a factor 1/R out of each row, 



A= (_=4)^l 2R M , 0, 0, 0, R,,, R 1:) , R I4 , 0, 0, 0, 



0, 2R,,, 0, 0, R,,, 0, 0, R M , R,,, 0, 



0, 0, 2R 38 , 0, 0, J1 13 , 0, R,,, 0, R 34 , 



0, 0, 0, 2R 44 , 0, 0, R 14 , 0, R 24; R 34 , 



0, 0, > - -' 1 - ! - > - ) - > 



ar n ar K ar a ,. dr } , ar a dr v dr n 



'/RSS dE H (lEu dE 13 dE lt dE n dE 



u > :7T~ ' u > TET ' ^7~ ' ~TT ' j ' ' ~7~: 



dr ls dr u dr 13 dr a 

 dR.,, dE. a dE K dR a 



r/K.,., rllty r/K )2 dR a dE u dE.,.. 



0, > ^ --- ' (), -- - > > - 



ar u ar u ar lt dr u dr lt dr lt 



> 0, 0, ~ > > : > I - - J - j; 



o, P> o, 



J J 



lr^ dr., t dr.^ dr* t 

 - > > 0, 0, ~ " > ~ '" > ~ > -'- > > > (xxxin.). 



The form of A is now clear for the case of any number of correlated organs."!" 

 (10) Case (i). Let us evaluate A and its minors for the case of three correlated 

 organs. 



* The factor ( l)to(-i) must be introduced if we deal with p organs. 



f We may reduce this determinant as follows to one of the 6th order. Divide the 1st, 2nd, 3rd, 4th, 

 5th, 6th 7th, 8tb, 9th, 10th columns by 2B n , 2R 2! , -21^, 2R, B IS , B,,, B J4 , RU, B M , B M respectively. 

 After this division, subtract the first column from the 5th, 6th, and 7th. The determinant reduces to 

 one of the 9th order ; subtract the first column of this new determinant from its 4th, 7th, and 8th 



