ARCHES. 629 
again since the arch ring is continuous and unbroken at*C 
Lt ees | 
ga deemed 
du, _ Su, 
dp oy 
or which are equivalent 
Vg = 0 7 
dv, dv, | ; 
yaar ig |. (28) 
Dari Lig ) 
(27) and (28) are six equations, by means of which the 
constants A, B, — of the second segment can be 
expressed in terms of those of the first. 
To determine the remaining six constants we have 
at each end of the arch 
_ ov 
ne v Sd Z 
at each end of the arch 
(29) gives six equations for the six unknown constants. ° 
The case of the circular arch in the former paper follows 
at once from the present solution by putting e — 0 
0 (29) 
CHAINS. 
Tue links are supposed elliptical and of uniform section. 
Considering half a link with ends fixed in direction at 
right angles to the applied force, and supposing radius of 
bar of which links are formed is small compared with a 
or 6, as in the paper on arches and using the same 
notation 
we have w =v so that f (~) = 0 and equation (10) (11) 
(12) become 
T=Acosy + Bsny €) 
L=Asuny— Beosy (2) 
M=—-— Ay—Bx+C (3) 
