240 REPORT—1857. 
would deflect without the chain, which being obtained and reduced in the 
ratio of the girder attached to the girder detached, gave the true deflection. 
My first intention was to make the experiments with a girder which was a 
correct model of the actual bridge, which would have-indicated =4,rd of the 
actual deflection, but I found the deflection of the wave to be so small that 
it was difficult to measure it-with sufficient accuracy, and I therefore had a 
wooden box made of the correct depth, with the sides as thin as it would stand, 
viz. 1 deal plank, in order to obtain greater deflection of the wave, with the 
correct depth of the girder, and with the chain attached to it as in the pro- 
posed bridge. 
I could no longer obtain the actual deflection of the Londonderry Bridge 
by multiplying the experimental deflections by 33, but knowing that the de- 
flection of a model on the correct scale would be =4,rd of the Londenderry 
girder, and knowing by experiment how much the model was deflected when 
unattached, the actual deflection of the Londonderry girder is obtained by 
reducing the observed experimental deflection in the ratio of the rigidity of 
the actual model to a true model, and then multiplying by 33. 
The deflections of this girder, taken without the chains attached, with a 
weight of 168 Ibs. on the centre, was °75 of an inch; with the chain attached, 
and with the weight placed + from the high tower, it was as follows :— 
lbs. 3 from High Tower. Centre. + from Low Tower. 
in. in. in. 
56 "030 ‘010 010 
112 "060 040 ‘010 
168 075 040 010 
Experiment 2. 
56 “030 020 “000 
112 050 040 “005 
168 075 “050 “005 
The ratio of the deflection of the wave at ith the distance, where the 
greatest amount arises when the chain is attached, to that in the middle 
when not attached, is as 1 to 10 only; but it was evident from the large 
deflection at the centre and from no rise occurring at the opposite end, that 
the girder was too rigid to indicate the wave, and that the deflection observed 
was greatly due to the chain not coming to its bearing. 
I therefore decided, in order to magnify the wave and make its amount 
more distinct, to have a girder made of angle-iron + inch thick and a quarter 
the depth of the former girder, but simply suspended from and not attached 
to the chain. 
The deflection of this girder without the chains, with a load of 42 lbs. 
placed on the centre, was 1°2 inch. 
The deflections of the wave with the chain attached, and 297 lbs. distributed 
over the girder when the weights were placed at + from the high tower, 
were with— 
lbs. 3 from High Tower. Centre. + from Low Tower. 
in. in. in. 
56 — 10 —0l +°05 
112 —20 —'04 +:12 
168 — 28 —-06 +'16 
Experiment 2.—In this case the weights were placed } from the low tower. 
56 +06 —01 —12 
112 +:15 —'05 —'25 
168 +°18 —'07 —  —36 
The deflections here averaged *32 inch with 168 Ibs., equal to ‘08 inch with 4 
42 \bs., or 7th the deflection of the girder without the chain. j 
