624 PROCEEDINGS OF SECTION H. 
Hence (f()) = a G bo sino — b) | (18) 
a, b are the semi-axes of the ellipse which forms the 
centre line of the arch ring 
ry) = 
oe Jb pcosp+hbsing At ~ het sin g cos g | (19) 
ae 
gow 
Sf ou= 
E bysin p +4 be? cos p + 3 be? sin’ cos + $ he? costg | (20) 
Pic Fe, 
where e = a and observe that ds =a A.do 
a 
M a 
8 ——F er . . | 
a = f[M.b.dg (21) 
a 
ks : Les z 
—— als Ab = -1 
7 3 {A sin sin-+(e sin @) 
]—e? 
é 
+4 Bat Acos p+ log (A+ecosg) ¢ 
+ Cx E(¢9) 
— gpa®| 4b. G (gp) +} bet (Asin p + 
* sin-tesing) + at sin-1(e sing) 
— sin o( 1 — 2e? sineg)A | + the 
{ Asing cos + (1-5) F(9) 
+(1+5) E(@) \ 
where F(¢) E($) are Legendre’s Elliptic Integrals of the 
