164 THE ROYAL SOCIETY OF CANADA 



metal bar, but on an entirely separate support, a glass tube, of 1.4 

 cms. intern'al diameter, was fixed in such a position that the longitu- 

 dinal axes of the bar and the tube were approximately coincident, 

 but the end of the tube was separated by a few millimetres from the 

 end of the bar. The end of the glass tube remote from the bar was 

 closed by an adjustable plug of metal, and a little lycopodium powder 

 was scattered throughout the length of the tube. On striking the 

 end of the metal bar farthest from the tube a smart blow with a 

 hammer it was found that dust figures were very easily produced 

 in the tube. 



It may be well to point out here what are the advantages in 

 this modification over the method previously indicated. In the 

 first place the apparatus is a little simpler, involving as it does merely 

 a short length of a round bar of the metal with a shallow groove at 

 the central point. Lengths have been used as short as two inches. 

 But a more important advantage is the fact that it is much easier 

 to obtain the dust figures with this apparatus. One blow of the 

 hammer is usually sufficient to produce a train of the figures a metre 

 or more long. Furthermore, the method is admirably adapted to 

 high frequency vibrations, a frequency as high as 50,000 per second 

 having been attained. Such use cannot, of course, be made of Kundt's 

 apparatus. Finally the latter method has one marked defect. One 

 is never sure of the exact temperature of the metal rod at the time 

 when the dust figures are formed because the stroking with the 

 chamois, even though but a few strokes are necessary, quickly 

 raises the temperature of the rod to some unknown value. 



The theory of the free long|itudinal vibrations of a bar, where 

 the damping can be neglected or, as in the present case, the damping 

 is not sufificiently great to have an appreciable influence on the period, 

 leads to the equation of motion 



^ = C^Î^,whereC=A' 

 df dx^ P 



Here y represents the displacement at the time / of a plane perpen- 

 dicular to the axis of the bar whose undisturbed position is at a 

 distance x from the origin; E is Young's modulus for the material 

 of the bar, and p is its density. 



To find the normal modes of vibration it is usual to assume 

 that y varies as cos {nt-\-e) so that the equation becomes 



^ + !!:3,=o 



dx" Û 



iRaleigh, "Theory of Sound," Vol. 1, page 245. 



