Prof. Tyndall on the Vibrations of Strings. 71 



18. The motion of the end of the string in contact with the fork 

 is hardly sensible ; and still through this apparently motionless part 

 of the string the whole of its motion is transmitted. 



19. I relax the string by turning the peg, and now it suddenly 

 divides itself into two ventral segments, separated from each other 

 by a node. When the synchronism between the fork and string is 

 perfect, the vibrations of the string are steady and long continued ; 

 but a slight departure from synchronism introduces unsteadiness, and 

 the vibrations, though they may show themselves for a time, quickly 

 disappear. 



20. I relax the string still further ; it now divides itself into three 

 vibrating parts ; relaxing still further, it divides into four vibrating 

 parts ; and thus I might continue to subdivide the string into ten or 

 even twenty equal parts, separated from each other by a number of 

 nodes one less than the number of ventral segments. 



21. In the arrangement now before you, the fork vibrates in the 

 direction of the length of the string ; its tendency, therefore, is to 

 throw the string into longitudinal vibration. But, in fact, every 

 forward stroke of the fork raises a protuberance upon the string, 

 which runs to its fixed end and is there reflected, so that when the 

 longitudinal impulses are properly timed, they produce a transverse 

 vibration. I take a heavy string in my hand, stretch it, and move 

 my hand to and fro in the direction of the string. It vibrates as a 

 whole, and I notice that it is always when the string is at the two 

 limits of its excursion that my hand moves forward. Jf the string 

 vibrate in a vertical plane, my hand, in order to time the impulses 

 properly, must move forward at the moment the string reaches the 

 upper and also at the moment it reaches the lower limit of its excur- 

 sion. A little reflection will make it plain that, in order to accom- 

 plish this, my hand must execute a complete vibration while the 

 string executes a semi- vibration * ; in other words, the vibrations of 

 my hand must be exactly twice as rapid as those of the string. 



22. Precisely the same must be true of a tuning-fork to which a 

 proper string is attached. When the fork vibrates in the direction 

 of the string, the number of complete vibrations which it executes 

 in a certain time will be twice the number executed by the string. 



23. If in this case the fork and string vibrate with sufficient rapi- 

 dity to produce musical notes, the note of the fork will be an octave 

 above that of the string. That it is so, has been proved by M. Melde's 

 direct observations. 



24. Taking hold of the end of this heavy string, I cause my hand 

 to move to and fro, not in the direction of the string, but at right 

 angles to that direction. The string now swings as a whole in a 

 vertical plane. Here every upward movement of my hand coincides 

 with an upward movement of the string, every downward movement 

 of my hand with a downward movement of the string. In fact 

 the vibrations of hand and string in this case synchronize perfectly ; 

 and if the hand could emit a musical note, the string would emit a 



* A complete vibration, it will be borne in mind, consists of one com- 

 plete excursion to and fro. A semi- vibration, on the contrary, consists of 

 an excursion from one limit of the vibration to the other. 



