136 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



proaching it, according as the amplitude is increased or di- 

 minished. This displacement diminishes very rapidly for 

 each successive node that is displaced, from the first to the 

 last. Different threads having the same section have their 

 normal nodal distances, proportional to the fourth roots of 

 the quotients of the co-efficients of elasticity divided by den- 

 sity. If, now, a thread that is vibrating in its normal state 

 be shortened by a millimeter, for example, we observe the 

 following fact: First, the thread continues to vibrate regu- 

 larly, the amplitude of its free extremity varies, but that of 

 the diapason remains constant. Cutting off a certain other 

 portion, the rectilinear vibrations of the thread commence to 

 change, becoming curvilinear, their amplitude increases, and 

 that of the diapason begins to diminish. Continuing to 

 shorten the thread, the form of the vibrations of the thread 

 becomes still more pronounced. Finally, we arrive at such 

 a length that the amplitude of the diapason diminishes to 

 nothing. It is at this time impossible to make the diapason 

 vibrate. Continuing to shorten the thread, the same phe- 

 nomena are reproduced in an inverse order, the vibrations 

 of the thread become plane, and the amplitude of the diapa- 

 son returns to its normal value. These phenomena have been 

 observed by Mercadier on threads whose initial length Avas 

 fifty or sixty centimeters, and which have been shortened, 

 millimeter by millimeter, measuring each time the amplitude 

 of the extremity of the thread and that of the diapason ; and 

 he finds that the lengths of the threads for which the ampli- 

 tudes of the free end are a minimum and equal to that of the 

 diapason, are, beginning with the shortest, in an arithmetic 

 progression, of which the ratio is precisely the normal nodal 

 distances of the thread. And, again, the lengths of the 

 threads corresponding to the points of complete extinction of 

 the diapason are also, beginning with the shortest, in an 

 arithmetic progression, whose ratio is the normal nodal dis- 

 tance. And, again, each of the points corresponding to the 

 minimum amplitude of the thread is very nearly at an equal 

 distance from the two points of extinction of the diapason 

 between which it is comprised. The existence of these 

 points of extinction of the diapason constitutes a remarkable 

 fact. In generalizing from it, one is led to conclude that 

 any body, affected by a vibratory movement of a given pe- 



