( 257 ) 



2\ o'. 



(15) 



If e.g. 7;=ii()(), 7', = IHM), 7i = 2200, 7, = 11)!S0, the (ii-sl 

 Dienihci' is ^'^, Üie second uiomher -^ — , so also ^' 



Tlie (enn 



1/ 



2 7— niidei' the An/-sii>-ii is liere 



q,—VJ\ ■' '^ 2200 



Ev^eii with 1^' = O a point of inllcelion can vevy well occur 



somewhere in the cui-ve 7' 1= ƒ'(,/■). The corresponding condition for 



the occurrence of a point of inlleclion at ,(' = in the curve 



7' = f (,/;') becomes : 



7x + 42\ 1 



or 



'7o 7. + 47\-2(<7,-^,) ^_2JiZ:7^ 



%x + 47\ 



^ri_lV-/./l-2^i^ 

 for which we may write for small values of 7, — (/.^ 



This is onlv possible when <ji^ <[.,■ Again we may write: 



' 11, 



7, 4777; V "^-i7\yv7\ 



or 



1. e. 





(15u) 



If e.g. 7; = 1100, 7; = 900, 7, = 2200, ./.^ = 1650, the tirst 



■'/ —11/ 

 member is again \'.^, and also the second member is -^^^-^ -^ =\/s- 



7,-7, 1100 1 



The term 2 ^' /.;, is now = — 



7,-f47\ (3(300 (3 



Also in the curve T^ f(.r) a point of inllection may occur even 



with if = 0. 



And now we have gi\en a coni[)lete answer lo the question 



