1299 
a change of phase of (hat wave and it is easy to see that it cor- 
responds with the change which one would deduce from the changed 
velocity of propagation between 0 and /. For our purpose only 
the “dispersed” wave (5) is of importance, so (5) is the only a 
persed wave which is left. It will disappear if 9,2, + He, = 
Now we must imagine the deviations in part ‘0 to l as a: 
by elastic deformation of the bar which is homogeneous in the con- 
dition of rest. One can imagine that for this purpose constant forces 
are used. Afterwards we will come back to the question whether 
the action of the accidental deviations of density can be described 
correctly in this way. In any case the problem is now sharply 
determined. It quite corresponds with the analogous treatment of 
Desir. 
Let a piece of the length of /, be stretched to /. The tension 
required therefore we will represent by the formula 
LS a =l1.\2.. 
S—E 5 Ee 5 = . ° a e ° 7 
tae (sz) ke 
in which again « denotes the deviation from Hooke’s law. In the 
new condition a small increase of length will bring about a change 
of tension, which can be cee from a modulus #, if we take 
dS l ae je 
Ezi =Er E, = 
dl sce oa Fi 
For the change /, of the eth on the small portion between 
O and / we find approximately 
En 
EEn 
as the density o changes inversely proportional to 7. From this 
result follows that really the wave (5) disappears if the law of 
Hooke is fulfilled. For the fraction in (5) one finds: 
EEL + a) 
Qo 
pe I TONER a Oy (8) 
La gears” EA aR i Sasa TS 
We shall oppose to the given treatment the more direct method 
because it proves that the advantage of neglecting the terms with 
a in the equation of motion (4) is but apparent. 
For the originally homogeneous bar the equation of motion, taking 
into account (7) and the applied-forces P is: 
+ a 5 35 c 2 
eee ee EE er (9) 
There we split the deviation § into three parts § —§, + &, + 8, 
where <, is the statical deviation in consequence of the forces 
83 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
