(438 ) 



And as 



dB 



'~dx 



dA 



dx 



B (K-b^a 



A c 



-1 = 



an 



B 



\A 



dA dx 

 dx 



dA 



(1 =27 pier, it appears that and so 



/;'-' dx 



dB , . dpjcr , . . a a, <Li 



also - nave the same sign as — . bo if — >- - or «/>«!, then — 



dx dx /'," 'V ''■'' 



and is positive, and vice versa. The line which divides the angle 



dx 



between the axes into two equal pans in fig. 36 or joins point 0' 

 with point in fig. 37, gives the division between b % -^b 1 . For 



dph 



ill 



- "> 0, Pkr 2 ^> Phi or ]> ' and *-.4>?v This is the case for i 



dx /'..' b x s 



points lying right of this line ;\\x\ the other way about. For the 



dpic, dA 



points of this line themselves s, = s , or — =0. But then also 



dx dx 



dB x 1 



and — =0 and so — = , or what is the same thing 

 dx 1— •• a 



1—x V a,~~ nV H ->•. 



But, as we already observed above, this requires that the value / 2 



r ! + ' r ' 

 be greater than J in the formula I 3 n 2 (1 -\- Ej) 3 = w -) — e t 



l + » s 



or /w(l -\-£ x ) = ft *-,. then we have: 



1 + n- 

 1 + -—— g. 

 2rc 



or 



/- 1 



1 +«, 



(n - \y- 



2n(l + ei ) l 



Now for the area OPQ, under the parabola we have 



(1 +n)\/e l gn—l 

 'n — V 



and so g, can become equal to ( — 1 as highest value, and hence 



\n + 1/ 



l)mai=- — 7— — • For not very high value of n, I — 1 is only 



4n(w 2 4 1) " ^ 



