43 
fi(at—x) 
but then reflexion occurs, and we have 
_ [i(at - x) _ fx (at— 21 + x) 
It is to be observed that for any point x equation (3) 
• cc • 2/ — 
applies from £=-^tilH= — — , whilst (4) applies from t= 
2^ — x , , 2Z 4~ x 
to t = 
a ci 
I will not go into the question of the reflection at the 
mass M, but notice that Avhen the wave is reflected at the 
fixed point 
- 2— 
dx a 
Therefore tension=2V jEjj. or double our previous result. 
We infer then, that half the velocity of impact needed to 
break the wire near the mass is sufficient to break it at the 
fixed point, but that in both cases the breaking does not 
depend on the mass. 
These results were submitted to a rough experiment. An 
iron wire, No. 13 gauge, about 27 feet long, and capable 
of carrying 3-|cwt. dead weight, was seized in a clamp at 
top and bottom, the top clamp rested on beams on an upper 
floor, whilst the lower served to receive the impact of a 
falling mass. The wire was kept tort by a 561b. weight 
hung below the lower clamp. The falling weight was 
a ball having a hole drilled in it sliding on the wire. It is 
clear that, although the clamp held without slipping, the 
blow must pass through it, and will be deadened thereby, 
so giving an advantage to the heavy weight. If the wire 
breaks some way up the wire, or at the upper clamp, it may 
be considered that the wire near the lower clamp stood the 
first pnset of the blow, and hence that if the wire had been 
long enough it would have stood altogether. 
