2 Lord Rayleigh on Bells. 



nodal meridians, corresponding to 3, 4, 5 . . . cycles of 

 motion. A class of vibrations is also possible which are 

 symmetrical about the axis, the motion at any point being 

 either in or perpendicular to the meridional plane. But these 

 are of no acoustical importance. 



The meaning here attached to the word nodal must be 

 carefully observed. The meridians are not nodal in the sense 

 that there is no motion, but only that there is no motion 

 normal to the surface. This can be best illustrated by the 

 simplest case, that of an infinitely long thin circular cylinder 

 vibrating in two dimension!*. The graver vibrations are 

 here parely flexural, the circumference remaining everywhere 

 unstretched during the motion. If we fix our attention upon 

 one mode of vibration of n cycles, the motion at the surface 

 is usually both radial and tangential. There are, however, 2n 

 points distributed at equal intervals where the motion is 

 purely tangential, and other 2n points, bisecting the intervals 

 of the former, where the xnotion is purely radial. There are 

 thus no places of complete rest ; but the first set of points, or 

 the lines through them parallel to the axis, are -called nodal, 

 in the sense that there is at these places no normal motion. 



The two systems of points have important relations to the 

 place where the vibrations are excited. u When a bell- 

 shaped body is sounded by a blow, the point of application of 

 the blow is a place of maximum normal motion of the re- 

 sulting vibrations, and the same is true when the vibrations are 

 e: cited by a violin-bow, as generally in lecture-room experi- 

 ments. Bells of glass, such as finger-glasses, are, however, 

 more easily thrown into regular vibration by friction with 

 the wetted finger carried round the circumference. The pitch 

 of the resulting sound is the same as that elicited by a tap 

 with the soft part of the finger ; but inasmuch as the tan- 

 gential motion of a vibrating bell has been very generally 

 ignored, the production of sound in this manner has been 

 felt as a difficulty. It is now scarcely necessary to point out 

 that the effect of the friction is in the first instance to excite 

 tangential motion, and that the point of application of the 

 friction is the place where the tangential motion is greatest, 

 and therefore where the normal motion vanishes"!. 



When the symmetry is complete, the system of nodal 

 meridians has no fixed position, and may adapt itself so as to 

 suit the place at which a normal blow is delivered. If the 



* ' Theory of Sound/ § 232. 



t ' Theory of Sound/ § 284. That the rubbing finger and the violin- 

 bow must be applied at different points in order to obtain the same 

 vibration was known to Chladni. 



