174 



E. LANCASTER JONES 

 TABLE VI 



where 



As before, we can find a series of multipliers, namely, 



I, 3> 8, 21, 55, • • • ^r-2, /'r-l, P,' ' ' , 

 Pr = 3/''-l - Pr-2, 



pi = 3> 



pi = ^, 



(i8) 



which will eliminate all the correlates of intermediate pairs of triangles 

 down to any desired residue, e.g., 6"+ 5. For example, to eliminate from 

 S+ I to 5 + 4 inclusive, we use the series to the 5th term 55 and get 



I23WS — Ws-5 — Ws+6 = 55^5 + 2l(ds-l + ds+i) + S(ds-2 + ds+2) 



+ 3(</s-3 + ds+z) + ds-i -\- ds+i. (19) 



For cells near or at a terminus of the chain, we use the same series of 

 multipliers. 



For triangles with two second-remove cells to each first-remove 

 cell we use the multiplier series i, 3, 7; for instance, in the network of 

 figure 6a, cell o has one first-remove cell 1 1 and this has two second- 

 remove cells, 21 and 22. 



The correlate table for wo is Table VII. 



TABLE VII 



Whence, multiplying (see column p) by 7, 3, i and i respectively, 



iSmo = ydo + ^dii + ^21 + d22- (20) 



834 



