Al. a. Tchouproff 
207 
(4) The first term (of order 1/iV-) in the development of 
in powers of l/N is obtained exactly from (24). We find : 
~' /^n-i (/^ra+i f^ra+n + /^»-3+i f^r^+ri + A^'n+i M'T-i+r^ ~ H'r2+\ l^r^ f^rt 
~ f^Ti f^rs+i ^^rl ~ H-r-i f^ra ^cj + i) 
t^r-i+rs + /^/'a+i /^ri+ra + ^ra+i Mri+r2 ~ A'r-i+i A^r^ Mrs (40). 
-h[>'ir2 l^n-i M»-2-i (^ra+n f^-i + 2At,.3+, fir,+x - fJ'v, H^n f^-^^ 
+ n ''a /iri-i /^ra-i (/^rj+rj Z^-' + 2/^,.,+i /i^j+i - f^r^ /J^r, fJ-i) 
+ r-iV^ f^n-} /^r4-i (P'Tz+rs + 2/A^2^, //.^3+i — /X^j /^ra f^i) 
+ ^'2^) /^ra-i /ir3-i (H'n+r., A'-' + 2^^^+! /*r4+i " H-n fJ-r, /^g) 
+ f^r.-i /*r4-i (/^ri+ra + S/i^+i Mrj+i " /^ri /^r-^ 
- 3 [nvon fir^-i f^rs-i /^n+i Ma + r^v^ H-n- i fJ-H-i t^n+i H-Ti-i 
+ ri r., i\ fi^^_T^ /z^^+i ^2 + r„ r., /i^i+i fJ-r^-i t^r^-i l^n-i M2] 
+ '^rxr.r.,i\ /z^^.^ yu,^^_, ^,-]] + . . . 
Noting that 
^ (l-'ri - Z^n) (z'Vj - Vr.^ (v'r^ - /V.,) (f'r, - J^) 
= '^^(I'Vi -/^ri)(z^V2-Atr2)('''r3-/^r3)('''»-4-A^r4) 
+ [i^Ti - P-n) i fr.^ - IJ-r.) E {v\^ - /x^3) (rV, - ^r.) 
+ {Vri - P-n) ('Va - f^r j E {v - fJ,,J (1/^4 - f^r,) 
+ (Vri - fJ-n) - H-n) E {v\^ - ^^,) {v'r^ - IXr^) 
+ (I'ra - /^ra) (z^r-a " 1^^) E {v\^ - fj,^^) (v - [J.^,) 
+ (fra - fJ-rJ (v^ " H-n) E (v' j.^ - fX^^) {v'r^ - flr^) 
+ (I'ra - H-n) (Vft - H-rt) E (v - fJ-^) (v'r., ' H-r-^)} 
