714 Prof. A. Morley on 
Applying the expansion 
a i 0*50* 61<9 6 , 13850 8 A ,„ x 
B eo^-l=j T + TT + Tr +- gT - + ...Ao.to(6), 
,, wP/,, 5tt 2 P 61tt 4 /P\ 2 , 277tt 6 /P\s _ ^ 
P 
the coefficients of the various powers of p- differing but little 
from unity. This or (5) may also be written 
M wP, 5 wV p f 1 , 61tt 2 P , 277tt* /P\* . ) /ov 
The form (8) shows in a striking manner the relation of 
the approximate method (6) to the correct method of calcu- 
lating the bending stress and the order of the error involved 
in the former ; the first two terms of (8) represent the 
maximum bending moment as estimated by method (b), and 
the coefficients of the powers of p are nearly unity; also the 
first term of (7) or (8) represents the maximum bending 
moment as estimated in the method (a). 
The equaLand opposite intensities of maximum bending 
stress in a symmetrical section are 
21 
where Z= —=■ is the modulus of section. 
a 
The maximum intensity of the compressive stress is 
and the maximum intensity of the tensile stress is 
''=*-*>= SJ( sec i\/ff - 1 ) -*> 
which may be positive or negative. 
PI 
If jj = g the error involved in calculating the bending 
stress intensities by method (a) is 20 per cent., and by method 
ib) 4, per cent.; practically the same proportions it may be 
noticed in either case that the first neglected term in the 
