46 pitcher: interrelations of 



(2) Ti'' . 3 . m-\ 



(3) $nj^.3.5m = a)j'-93? = [0]. 



(4) A.m' .z>. 3n\ 



(5)* A . 9[)J = [0] . 3 . 90^'. 



(6) A . m'^'""^ . 3 . w-. 



(7) A . 9JJ . 3 . 9JJ^=. 



(8) A : 3 : 9JJ^''". ~ . fO?'^'". 



(9) A . 9JJ + [0] . 3 . W". 



(10) A . 9[«"^ . 3 . m"'-. 



(11) A . 9:)r^' . 3 . 9J^^^ 



(12) A . m^"' . 3 . m'"'*""-. 



(13) A . 5m^' + [0] . 3 . TO^"'^'^. 



(14) A . m'"-"'. 3 . 2}J^'-^'"-. 



(15) A . 9[r? + [0] . 3 . 93?^"' . - . m"" . - . m''"'. 



42. t Propositions relative to ^^"^ or ^'. 



(1) A . m"''''"''''- + [0] . 3 . m'""-. 



(2) A . g)?-^^="^----^'=- . 3 . W""". 



(3) A . g()j^^-=-A-i.-^-=. . 3 . gor-^'''-. 



* This proposition is of general reference, i. e., it holds for $ general. 

 t We add certain suggestions as to the proofs of these propositions. (1) follows from 

 §27.10, 11 and the proposition: 



5(5"s = 1, 2 . d--fr«'i . gjli's :3 : (m .3. Ml = m) ■ 9Ji*"- 



(2) is a corollary of (1). (3) is a corollary of (1) and § 27.10, 13. (4) and (5) are proved 

 through the propositions: 



5P"2 . A-''i . Hi^-A'i .3. Wi = 33J"!; 



(6) follows through a detailed consideration of admissible classes 31i^ and the proposition: 

 ^u, . gji = 31o (1, J;) . A; + 1, . m^ .3. Ai",^ 



where 2to is a subclass of 21. (7) is a corollary of (6) and § 20a3. (8,) follows through the 

 propositions: 



WU.A.m-i>^'i .3. ACi; 



^^"2. A . 9Ji"-0A'2.3. A-fi. 



