( 256 ) 



l>) The other liniitiiiji,' ease is (t = 0. The expressions (9) and (Or/.) 

 hike tlien the form 



'crT\ 1 Arr 



cPT\ 1 rdT 



d.ir' ).. q, \ dx' 



or 



d''T\ _ 1 /'dT\ 



dx^J, q\dx), 



d'T\ _ 1 /dT\ 



{q-^'^\) 



('7x-47\)-2(<7,-7.) 



(./=()),(! 3) 



('A+4Ï^)- '- ('Zi + -i'^\)-2('?:-7.) 



where according to (8) the limit oftiie i)roi)or(ioii - ) i'^ represented \)} 





(14) 



We see from these exi)ressions, tliat even \\ ith {i' = a [)oiiil of 

 inflection at ,v = (and so also before it) is possible for the tino 

 curves T=f{.r) and T=zf{y). For liiis it is required for Ihe 

 curve 7' = /(,i'), «liat 



' 'x\ q-Vl\ 1 



or 



Vo ('/i-4ï\)-2((?i-g,) ^ o gi— ga 



ï:-47'. 



'1 '■-^ 1 





iod I 1 — 2 -—- 



If 2 — ^ — ~- is not large, we mav write for it bv appro 

 7i-47; 



ximalion : 



(li—1-z 



1\1\^ ' '^ Vl\-q, 



We see that in anv case —}, ^ must be jfositive. 



^^ i — qi 

 The condition may no^v be written as follows : 



qx — <l-2 (47\— 7i)(^i — ^'2) 



']-z 



47\ 7' 



-*)(*- 1^ 



or 



hence 



7.~2; 4 7' A 7; / 



