118 
u = 
MR L. N. G. FILON ON AN APPROXIMATE SOLUTION FOR BENDING A 
+ 
V = 
CO 
x 
1 
w 
1 
711 
a 
CO 
1 
W 
1 
At 
a 
CO 
V 
1 
1 
771 
a 
OO 
V 
1 
YY 
w 
1 
At 
a 
TfWx 
2aE 
CO 
V 
1 
W 
1 
m 
a 
CD 
1 
W 
1 
At 
a 
CO 
V 
1 
W 
1 
771 
a 
CO 
2 
1 
W 
1 
At 
a 
cos ml 
I 
^ sinh mh -^ mi 
cosh mi\ 
sinh 2mi + 2mh 
' *1 
- II sinh mij sm m.r 
i 
- cosh mh - mi sinh mb 
/A__ 
sinh 2mh — 2mh 
- y cosh my cos mx 
A- cosh my sin mx 
sinh my cos mx 
cos ml 
iAx' + a^ At 
) (94). 
1 \ 1 ] 
sinh mi - mi cosh mi ^ 
fj. I 
sinh 2mi + 2mi 
y cosh my cos mx 
sinh my cos mx 
sm 
ml ihAutii 
1 \ 1 . 
+ — I cosh mh H- mi sinh mb 
/A / At 
sinh 2iah — 2'nih 
y sinh my sin mx 
cosh my sin mx 
\Yy 
2aE 
+ Acc. 
J 
P = - 
Q 
2W 
a 
2W 
a 
2W 
a 
2 \V 
a 
\X 
' 2a ' 
COS 
2 COS 
, sinh mb — mb cosh mi •, 
ml - ■ , , , -— COS mx cosh my 
sinh 2mh + 2mi 
, my sinh mh . ^ 
ml -— , , cos mx sinh my 
2 sin 
2 sin 
a 
ml 
sinh 2riih + 2mi 
cosh mh — mi sinh mi 
sin mx sinh my 
sinh 2mh — 2mi 
, my cosh mh . . 
WAA . ,' , -sm mx cosh my. 
sinh 2mh — 2mb 
“ , sinh mh + mi cosh mb , 
2 COS ml -- ^ , - -r- — cos mx cosli my 
1 sinh 2mh + 2mb 
+ 
a 
a 
2W 
a 
, my sinh mi . , 
ml - ^ , cos mx sinh my 
2AV ^ 
_|_ > OOR fitjt, 
1 sinh 2inh + 2mi 
2 sin 
1 
CO 
2 sin 
, cosh mi + mb sinh mi . . , 
ml -— ^—;— sm mx siiili my 
sinh 2mh — 2mb 
my cosh vii 
sinh 27nh — 2mb 
^ 7ny cosh mh . , 
ml . y ^ ^ , sm mx cosh my. 
(95). 
