43 



but then reflexion occurs, and wc have 



_ ij.(at - x) _ ijL(at— 21 + x) 

 (4) S=^^ I . " ^T"- _^ M— I 



It is to be observed that for any point x equation (3) 



X . 21 — X 

 applies from t=:- til] t=: % whilst (4) applies from t = 



21- X . . 21 + x 



to t= • 



a a 



I will not go into the question of the reflection at the 



mass M, but notice that when the wave is reflected at the 



fixed point 



^1 = 2^ 

 dx a 



Therefore tensions 2 V v/%i 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 

 ii'on wire, No. 13 gauge, about 27 feet long, and capable 

 of carrying 3 Jcwt. 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 onset of the blow, and hence that if the wire had been 

 long enough it would have stood altogether. 



