ARCHES. 631 
Hence D = 0 and 
Aut ® sin -te 2} 
where c is the radius of the bar of which the link is 
formed and / is the length of a quadrant of the ellipse 
but since c is supposed small compared with a and 6 we 
may neglect c? compared with 4* and ab and we have 
C= 
W ab 
Se Oe, b2 aks -1 i 
Al ; +— sin-‘e (5) 
The constants are now all known and we have 
i ud cos W 
L= us sin ~ (6) 
W W ab it 
=== =e wens 2 aly 
5 Y + a {0 = gin +7 é } 
The following table gives the bending moment at A 
and B for 2 or 3 cases :— 
b My, Mp 
a Wa Wa 
l oe) ea eek 
k Few 8-075 
} 120. | — “047 
cae Ef, x é 
fF, = Fy 
i =7.FRh¢ 
