1886.] Mr Webb, The problem of three moments. 45 
C,, and using (iii) as a guide to the form of the result of this sub- 
stitution we get 
oc( 2 oc 
a (OC —a2) da i (OC — x) (2 —OB) dx 
tanB=—Mp| aE IR —Mg 
OB BC 13: 
oP (OC — 2) (% — OB) Loe Be a") = 
Whence by means of (11) and (ix) we now obtain 
0B (OB — x) (w— OA) da i —«) (« — OB) dx 
M4 OA AB’ E tite BC’ 1) 
ss OA AB K OB IOP H 
sd OP (OC — x) (a — OB) e [oe a) = 
= W | Pe i BOE + BP BC (Ei 
The corresponding equation for the moments Mz, Mg, Mp will 
of course be 
0¢C (OC — x) (« —OB) da i (OD — x) (a— OC) dx 
Mp a of + Mp CD? Te 
ODay te | [I OUb= ay Z| 
= e| ag OD ae 2 fy) HOP ae 
ms OP (Oe Ses 0¢ (OC —2x)(a—OB) dx] ,. 
=w|Pe on BC? FE nee ae | os 
and in all other cases the equation is simply that given in (iv). 
At present little further need be added other than the remark 
that the principle of superposition, or rather addition, enables us 
to build up from this case any other, no matter how complicated. 
