Miss Wrinch, On the exponentiation of well-ordered sei'ies 229 



*-41. t- : . Hp *-203 . p\Tp^-A y\ = A . i2 e C'P'? . 



7? [ (VPQ'X = PQ'\.D. RP'i V : D : g^S' . ,S' e X . .S'pv V 

 Dem. 

 [*17G-19] h:Hp.D.-(rra'PQ'\ = PQ'A,): 



[*176-19] D H : Hp . D . 32 , 5 6 (J'PQ'X . V [Q'z 



= (PQ'X) ['Q'z . (PQ'X'z) P ( V'z) 

 [*-4] h . Hp . D . a^S' . <S6\ . SP^V 



*-42. |-:.P, QeO.X-eOul.xC C'P'^' . p'(Tp^A Y\ : 



D:p = C'P'i nR[R\ a'PQ'X = PQ'X] .D.pC p'P'"'X . 



pcpQ"p c s'P''\ [*r3.r-H] 



r43. \-:¥AQ^'X.D.s'X'Q^'X^el.s'fp'X'Q^'Xel [*r0r02] 

 r431. \-:Tp(lA.{Tp\^(lA 



Deni. 

 |-.r43. Dh: fiTpX.D.ij,CX.^^X (1) 



|-.(1).*201-18. Dh.Prop 



*-432. h : Hp *203 . D . "I^i (P«)'X C /j'CTp*^ )'X 



[*-21 7] h :. Hp . P e /ci . yLt e (^V*.! )'X . /x {xl (T'p, \)| v . 



P ~ 6 z/ : D : g! z^ . D . a*S' . >SP^'P :. 

 DI-:.Hp.Peyit.yL6e (rp*J.)'\ . P mill (P'O X : 



D : /x [^ (Tp, X)]v.'^\v.D.R€ V (1 ) 



[r431] t-:Hp.Pe/i.i;{^(Tp,X.)j/i.D.Pei; (2) 



h . (1) . (2) . D h :. Hp . D . P e i"^ P^'X : D : /^ e {Tp^Ayx . 



^M.Pe/^ (3) 

 h . (3) . D h . Prop 



*-433. h : Hp *-42 . p = C'P^^ nR(R[ a'PQ'X = PQ'X) . 



D.'^(P<0'/3 = tl(P'^)*X 

 Dem. 



h :: Hpr42 . D :. SeC'P'^' : D : S[a'PQ'X = PQ'X . 



y.'^z.ze a'PQ'X . ^ ['Q'z = PQ'X [ Q'z . 

 (S'z)P{PQ'X'z) . V . (PQ'X'z)P(S'z) :. 



