452 Royal Society : — 



Substituting for P in (4), (5) and (6), 



F 1 »=(l-f)^+f«-f/a"(0+/ 1 ». .... (8) 



F 2 "W=(l-f)0 1 +f0-f/,"(O+/ 2 ». .... (9) 



F a »=A-|^ 1 +^-|/ 3 "ffl+/,», ■ • • -(10) 



equations from which for a given value of x, F/'^), F 2 "(V)> F 3 "(#) 

 may be determined if </> 1 and <p 2 are known. 

 From the nature of the deflection-curve, 

 from 1 to «, 



8=^»> <») 



from « to 6, 



3-«*.»» • ■ -< ia > 



from b to 2, 



3-a»« (13 > 



.-. from 1 to a, 



^ = e F' Xar) + C ; when x = 0, F'teWO, ^ =-T ; 



dx dx 



.•.g= ei F»-T; (14) 



from a to b, 



g=«,F,'(*) + C; (15) 



making x=a in (14) and (15), and transposing, 

 C = e,F 1 '(«)-e 2 F 2 '(6)-T; 



.-. g-e 1 F 1 '(a)-«,(P,V)-F 1 '(a))-Ts (16) 



from b to 2, 



g=e,F,'(*)+C; (17) 



making x=b in (16) and (17), and transposing, 



C = e 1 F 1 '(«) + « a (F 2 '(6)-F 2 (a)) -e,F,(J) ; 

 ... J=e 1 F 1 '(«)+e 2 (F 2 '(5)-F») + e3 (F»-F 3 '6)-T; (18) 



.*. from 1 to a, 



^ — ^F^)— IX no constant; for if x = } F 1 ^' = 0, y = 0; . (19) 



from a to 6, 



y= ei F 1 '(a>+e 2 (F 2 (^)-F 2 '(«>)-T^+C; (20) 



