170 E. LANCASTER JONES 
correlates. The corner rectangle oo has two first removes and one 
common second remove, and the correlate equations are 
4Mo0 — Moi — Mio = doo, 
— Moo + 4mMo1 ee (23 0 tem (21)) = do, 
— Moo + 4m — my — M2 = do, 
— M1 — Myo + 4m — Mi — Me = di. 
Multiplying the equations by 7, 2, 2 and 1 respectively and adding, 
we eliminate m1, #19 and my and obtain 
2400 — 2(mo2+m29) oe (mi2+m21) = 7do9+ 2(do1 +410) +d, (12) 
= 24D, say, 
and moo = Doo gives a good approximation to moo, which can be con- 
tinued by writing 
, 4 att 
Moo = Moo + Moo + Moo +--- , 
where 
fap / y / 7 
24Mo0 = 2(mo2 + moo) + M2! + Mar ) 
TY, iad yt 
24Moo” = 2(Mo2"’ + Moy’) + mig’? + Moi", 
and these mo’, mo’, :- - are approximations similarly obtained. The 
rectangles such as o1, 02,--- , 10, 20,---, which are on the boun- 
dary but not in corners, have each three first-remove and two common 
second-remove rectangles. Two of the first removes are on the boun- 
dary and one is in the interior; this third interior rectangle touches 
both the common second removes. 
For o1, for instance, the correlate equations are expressed as 
shown in Table IV, by means of the coefficients only, all applicable to 
any one m being in the same column while all applicable to any one 
rectangle are in the same row as its excess d. 










TABLE IV 
d mo} Moo my Mo? Myo M12 Residues 
oI 4 —I —I —I 
00 —I 4 —I 
Il —I 4 —1 —I — mM t 
02 —I hy 4 I — moa 
yes as aL aL 4 — Moo 
m sit | 3 | 4 —™M13— Moo 


