﻿236 Dr. J. Morrow on the Lateral Vibration of Bars 



obtained directly from the general differential equation, and 

 the last is the result of eliminating A and B from any two of 

 equations (3). ■• 



An approximate determination of — from equations similar 



to (5) has been made by Bonkin and by Seebeck for very 

 long and fine wires on the assumption that the vibration is 

 but slightly affected by the existence of rigidity, namely 



as a closer approximation Seebeck found 



y x _ iW P / 4 /El , 12 + i»w* EI\ 



"^-^M ^7 + ~~F~~ P/ 



from which to estimate the period of the i th tone. 



An approximation of a very different character is given 

 in the next paragraph. 



§6. Writing ^ =w ff = m (g) 



we have in the case of no tension and dealing with the 

 fundamental only ^ = ^ = 2 . 365) 



and, since for such values tanh <fi varies very slowly with <£, 



Tl 2 

 when ~ymj is small we may put 



tanh ^= 1-0178. 



The third of equations (5) becomes 



Under these circumstances ^ does not vary rapidly with#. 



civ 



Hence, when the effect of P is small, 



Determining the constant K by <p = = 2'365 and using (6) 



wefind ^ = 21-806-3-61^ (7) 



Combining this with equations (5) 



^ = 46-08 + I ^ I -23-7(l + -02536g) i , 



and expanding by the Binomial as far as the second term, 



/W=22'38 -'218^ ; 



