PROCEEDINGS OF SECTION H, 353 
In the case of an arch in which the abutments and direction 
of the arch ring at the abutments are fixed, we have, calling 
a> + asinacosa— 2sin?a=T 
and a — sinacosa =A, 
g pa’ . - ane 
Ax" _ (2 @ cos a — a Sin a — Sin” a cos a) —- 2C a cos 4 
4K 
+2D sina + F (a + sina cos a) 
E x P=!" (acosa- sina)? +C(sinza—acos?a)-Da-Fsina (7) 
where 
C ei x A=y pa(b—-0b’) { cos a(2—cos a+) —cosB—(a +B) sin s 
+ W { F(sin2 a- sin28)—(a+8)+2 cosa cos pt 
D aks x A=gpa(b-D’) {2 a (sina + sin 8) — 2 cos a (I—cos a+) 
—a(a+) cosB+8 cosa sin a+ Bt + W { a (sin a + sin B)? 
— sin 2.a-+a4 B costa — 2 cos a cos + cos asin 8 cos a+r 
4 RUF -Ceosa)=gpa(b-0') | (a +8) (2+c08a+ B)— 3 sin (a+) 
+W { (a+ 8) (2sin 8 ~ sina) +2(cosB ~ cosa) — sing sin(a +p) | (8) 
If there is no partial load, b’=6 and W =0; hence, C = D=F =o, 
and we have 
— gpa 2a° cos a—a sina—sin-a cos a 
4K a> +asinacosa—2sin?a 
Bo! pa (a cos a—sin a)? 
4K at+asinacosa—2 sin? a (9) 
The bending moment is known, from (4) or (5), at all points, 
for a given value of 6 the maximum bending moment can be at 
once determined by differentiation. 
6.—GRAPHICAL CHRONOLOGY OF ARCHITECTURE. 
By ANKETELL Henperson, M.C.E., F.R.V.I,A. 
[Abstract and Diagram. | 
THE object of the paper was to bring under the notice of the 
members the advantages of graphical chronology in dealing 
with architectural history and the analysis of styles and their 
mutual influence and reaction on each other. The principal 
example was a diagram showing the evolution of architectural 
styles from the earliest periods down to the Northern and 
ye 
