44 Mr Webb, The problem of three moments. [ Nov. 22, 
placed at a point P of the beam between B and C. sane cr | the - 
same notation as before we now have 
B..BC_W.PC—Mg+Moe=0 
C,. BO—W. BP + Mz— Mcp =0 
and the equations of downward deflection are 
— ES 4 =— My + B, io Oho Fe ie Hh 
steeee (vi). 
— od M+ 0, (OC — x) from P to Cc} 
On multiplymg the former of these by —(«—OB)/E, and 
integrating from B to P, treating the second of these im like 
manner with —(OC'— «)/# and using limits that correspond to P 
and B, we get the equations 
OP ORs 
BP (se) — y= Ma | fame hile (c ORR 
12 OB OB 
OP dx da , 
=P = one Gly O61) ae - 
[re 0B G + 6, = 2 Goo) 
OB 
Referring back to the first of the two equations (vi) and inte- 
grating between the limits B and P we obtain 
(54) tn e=My | S -B, | (w= OB), 
and on eliminating (2) between this and (vii) there results 
a p 
i OP(OC—x) dx ,, [°{OC~«) dx 
tan @=—Mp| ao Ga Me| ea 
OP (OC — a) (w — OB) da COGS a 
to BC E = BO ‘oO (vat) 
Now result (11) holds good here, though of course (i) is 
modified into (vii), whence, substituting in (viii) the values of B,, 
+B 
