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



Hence 



l {^g G (r, )} = -5 + siity (r -1-2 cos 2 <) 



+ S ~ "*' (1 - 

 o * 



{log G (r, )} - ~ cos^ (2-1+2 si 



cos 



(2s + 3) <f>] l(cxlix.), 

 J 



. . . (cl.), 



ilr dv 



{log G (r, )} = siu < cos <^ (2 cos 2 ^. - r) 



- S - - 



2 2s+2 cos &+3 <^ sin (2* + 3) A 1 . . . (cli.). 



J 



These allow of the fairly rapid calculation of 33) a it , a. H . The values of the 

 standard deviations of the errors, and of the error correlations, can then all be 

 calculated from the determinant 



A =: a,,, ,,, 13 . ((,4, 



and its minors.""' 



Let b pp , = - a pjl ; and let A' = A, then if B A/ be the minor corresponding to 



'/& fv 



l> n ,, in A', we must work out for any special numerical case 



n A 



~ n A' : 

 R B 



ail /fO. TJ V 



V (Bii B 22 ) 



I ^S. 

 n A" 



7 A 7 ' 



BIS 



T? ^ 



^"- v/(B M B 1( y 



v/(Bs3B 44 y 



* As in the former case, these were all developed, but the extreme length of the resulting formulae 

 gives them no advantage over working in any special case with the numerical determinants. 



