O •%*- 



JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. VII AUGUST 19, 1917 No. 14 



PHYSICS. — Note on the vibration frequencies of elastic systems. 

 M. D. Heksey, Bureau of Standards. (Communicated by 

 Louis A. Fischer.) 



Introduction. This paper deals with the free vibrations of 

 perfectly elastic bodies. Damping and forced vibrations are 

 excluded from consideration. The purpose is to present the 

 most complete statement, regarding the vibration frequencies of 

 such bodies, that is possible in advance of any knowledge of the 

 geometrical shape of the bodies. 



The paper is referred to the attention particularly of persons 

 engaged in acoustics, or in the development of time-keeping 

 devices, or in problems of engineering construction where res- 

 onance has to be avoided. Still others, however, may find the 

 paper suggestive in showing what can be done by combining 

 dimensional reasoning with ordinary physical reasoning, in 

 cases where either one alone would be fruitless. 



The reasoning is analogous to that of a previous paper entitled 

 The Theory of the Stiffness of Elastic Systems, Ho which it may 

 be regarded as a sequel, and to which reference must be made 

 for the general conceptions and definitions involved. For con- 

 venience, however, the following statement of notation is given: 



6 = temperature 



1 dF 1 

 E = Young's modulus ; a = — —— 



E do 



1 Journ. Wash. Acad. Sci., 6: 569-575. 1916. 



437 



