352 Trowbridge and McRae—Elasticity of Ice. 
the centre of the curve. Then taking the moments about any 
section between one of the weights and the nearest support the 
ay 
dax* 
BPM) (b -n)rn(l -) C-) 
=-¥(5 2) -"(0-e+) 
d Lie... wile a 
rata) Wes) 
elastic curve H = f (x) becomes 
QS. 8 fi 2ex8 
but C=0 
Pie ec). wills 
By she a eS $s 
y (5 ~) Al 8 7) +B 
but B=0 
Mees Z 
limits «=0, t= 
r : 1 
Es=ppa(P+3W) since I=5,0¢ 
and W=wi. 
s = the deflection at the centre if the weight was there. 
l 
— a 
limitsa—— #—~— 
g 2 
ag Ai a’ w a 2 ) 
a ——— ae — os —— Pan 
aga re) ial 3 (3! a) nl sO 
s’ = the deflection at aim when the weight is at the center. 
The weight of the beam was acting all the time so that we 
only measured the deflection due to the weight P. Therefore 
the part containing W in the preceding formula will disappest: 
By the principle of reciprocal relations a wel ht 4 
distance from the centre we will produce the same deflec- 
tion at the centre as the same weight placed at the center would 
produce at wm, If the weight had been at the centre we 
should have 
te i 
Eas 
but we have seen that 
