52 pitcher: interrelations of 



47c. Developments of "ip^s. — 



AV' . = . A 9 (m . 3 . Z„ = 3 . 'i^"! = 1 . ^;^"'- = 2 . 'i)?'"' = 3). 



A?^ . =. A 9 (m . z) . L = 2 . ^l?"! = 1 . "i.^"- = 2). 



M^' . =. A a (w . =. . Z^ = 1 . ^1?"" = 1). 



Ai'' . =. A 9 (to . 3 . Z„ = 1 . ^-i = 1, 2). 



A',^^ . ^. A 9 (to . 3 . Z,„ = 1 . i^""! = 1, 2, 3). 



AJ'= . =. A 3 (to . 3 . L = 2 . i^-i = 1 . ^-"2 = 2, 3) . 



A'> . = . A 9 (to . 3 . Z„, = 2 . ^""i = ^""2 = 1, 2, 3). 



47(i. Developments of ^'^. — 



Al'^ . =. A 9 (to . 3 . /„ = 4 . i^"" = I {!)). 



Ai'* . =. A 9 (to . 3 . ?„ = 2 . ^-1 = 1 . ^l}"'^ = 2, 3). 



47e. Developments of ^'". — 



A}" . =. A 9 (to . 3 . Z„ = TO . '^'"' = I (0). 



AF . =. A 9 (to : 3 : (L = to) . (I > 2 .^ . ^"" == I) . (l ^ 2 .:d . 1^"" 



= 1, 2)). 

 Ai" . =. A 9 (??i : 3 : (/„ = ?«) . d^""" = to, ?n + 1, . . ., to + n, . . .) 



(Z < TO .3. 1^"" = 0). 

 A™. =. A 9 (to. 3. L = 1. ^^^^ = 1). 

 A?' . =. A 9 (to . 3 . Z„ = 1 . ^1^"" = 1, 2, 3, . . ., ?i, . . .). 

 AF . = . A 9 (to . 3 . ?„ = 1 . ^s"' = 2, 3, 4, . . ., n, . . .). 



Al" . =. A 9 (to . 3 . /„ = 7?l) . (to'"''' . ? . 3 . ^l.^"*' = Z + 1) 



. {771'""' . I .3. ^s"' = 0- 

 As" . = . A 9 (771 . 3 . /„ = TO.) . 



(to"'" :3 : (^""^ = 1, 2) . if""" = TO. + 1, TO + 2, . . ., 



TO. + n, . . .) . (? =1= 1, ?« . 3 . ^^'"' = Z + 1)). 



(to"'''' :3 : ('!)?'"'" = 7n, m + 1, . . ., m + n, . . .) 



. (I < TO .3. ^>' = 0). 



A5Y . =. A 9 (w . 3 . L = 1 . i^"' = 1,2). 



A?? . =. A 9 (to : 3 : (L = m) . (l < m . 3 . f^' = 1 + 1) 



. {S^rnm = ,„j _|_ ^^ .,„ + 2, . . ., TO + 71, . . .)). 



A5? . =. A 9 (tM""'"" . 3 . A"" = Aj""0 . (to"'''' . 3 . A" = A!;'"*).* 



* If m is even then stage m of aJP is the same as stage m of a"' while if m is odd stage 

 m of aJ{' is the same as stage m of aJ". 



