ED) Dr. A. Elsass on a new 
so much that the thread shows its second, third, or fourth mode 
of vibration ; and the period of excitation becomes equal to 
3T,, 4T,, 11, where T, denotes the period of the fundamental 
vibration of the thread. According to theory, a definite form 
of vibration of the thread must make its appearance when the 
time of rotation of the siren T=2T,,, 3T,, &e. ; so that, for 
example, if T=2?T,=37,, the thread vibrates in four half- 
waves, and for T=Z7,=2T; the thread shows its third form 
of vibration. The velocity of rotation of the siren can be 
maintained constant without trouble only when the period of 
excitation is equal to that of the vibration of the thread ; and 
if a vibration of the thread belonging to some other ratio of 
periods shows itself for a moment, it does not produce any 
perceptible disturbance. It is precisely this peculiarity—that 
the vibrations of the thread can be maintained without change 
only when the periods are equal—that renders this form of 
apparatus so suitable for the demonstration of the laws of the 
vibrations of threads. 
We may now give some examples of the use of the 
apparatus. 
In order to show that the numbers of vibrations of the over- 
tones of a thread are in the ratio of the natural numbers, it is 
only necessary to count the revolutions of the siren when it 
puts a thread ora thin metallic wire into vibration with 1, 2, 
3, &c. half-waves. In Table I. I have brought together four 
series of observations, made with four different threads each 
1 metre in length. JI. denotes a cotton thread with a tension 
of 50 gr.; Il. bookbinders’ thread with a tension of 50 gr. ; 
III. a thread of button-hole silk with a tension of 9 gr. ; and 
IV. a brass wire of about 0°15 millim. diameter and 200 gr. 
tension. The number denotes the order of the vibration 
and N the number of vibrations. 
TABLE I. 
n. Na 45 Nie Nui. Nv. 
sate ABB iy ese ts 16g 565 
oe S6B Mi o6T 1) 336 112°7 
Beck 1291 | 100-2 50'4 168-2 
A cna) \ meee eek Or dl” |) 60 neta 
The number of vibrations N was determined from three 
independent observations—by reading the dials of the siren 
every 2 minutes, adding together the numbers of revolutions, 
