362 G. H. KNIBBS. 



The combining weights for these three cases are :- 

 Case (l)...w = 1/i/S = V*H '?M?V*) + 2iMlfV)} 

 Case (ii)...to= l/r? = r/[4r 2 (U a + F J )] 



case muw^m = F7JV { ^(4 + 1 +-W 



VI Vi \h 

 Thus the most probable value of Q p is 



<?= r. _r. u ' a f : (« 



9. Algorithm of practical solution.-Statistical data of 

 all kinds are however rarely of that degree of precision 

 which would give significance to the computation p by the 

 application of (50) and the earlier equations upon which it 

 depends. Moreover it is questionable whether any curve 

 actually traced so as to represent results actually furnished 

 would conform to the fundamental expression, viz. (1), with 

 sufficient exactitude. In practice it will ordinarily suffice 

 therefore to see that the sum of the ordinates are of 

 about the same order of magnitude, and then to calculate 

 p from the geometrical mean without regard to their 

 theoretical weights, thus : 



qrv = nj5 (51) 



where rif denotes the product of r values of U/V. 



Since q has no error, the probable error of Q p immediately 

 furnishes the probable error of p. Thus writing W for U/V, 

 we have 



QP = W - P = W{\ + P fW) (52) 



whence M p=logTP/logq t Mp/W log q (53) 



M being unity orO'434 etc. according as Naperian or common 

 logarithms are used. 



When the probable errors of q p and /) are found that for 

 n can be determined, if required, from (30), that for m from 



