G. F. Becker — Finite Elastic Stress-Strain Function. 349 



Argument from finite vibrations. 



Sonorous vibrations finite. — In the foregoing pages the 

 attempt has been made to show, that a certain definition of an 

 isotropic solid in combination with purely kinematical proposi- 

 tions leads to a definite functional expression for the load- 

 strain curve. The definition of an isotropic solid is that usual 

 except among elasticians who adhere to the rariconstant hypo- 

 thesis, and it seems to be justified by experiments on extremely 

 small strains. But the adoption of this definition for bodies 

 under finite strain is, in a sense, exterpolation. It is therefore 

 very desirable to consider the phenomena of such strains as 

 cannot properly be considered infinitessimal. 



It is usual to treat the strains of tuning forks and other 

 sonorous bodies as so small that their squares may be neg- 

 lected, and the constancy of pitch of a tuning fork executing 

 vibrations of this amplitude has been employed by Sir George 

 Stokes to extend the scope of Hooke's law to moving systems. 

 It does not appear legitimate, however, to regard strongly 

 excited sonorous bodies as only infinitesimally strained. Tun- 

 ing forks sounding loud notes perform vibrations the ampli- 

 tudes of which are sensible fractions of their length. Now it 

 is certain that no elasticfan would undertake to give results for 

 the strength of a bridge similarly strained, or in other words 

 he would deny that such flexures were so small as to justify 

 neglect of their squares.* 



Sonorous vibrations isochronous. — The vibrations of sono- 

 rous bodies seem to be perfectly isochronous, irrespective of 

 the amplitude of vibration. Were this not the case, a tuning- 

 fork strongly excited would of course sound a different note 

 from that which it would give when feebly excited. Neither 



a =- 1 . l±MV , so that Mx)=Mx). 

 1 +fi(x) 



For pure elongation the lateral contraction is by definition zero, or c=0, and the 

 formula is 



a = fsW-fiW whence Mx)=Ux). 



2|1 +/*(*)] + 1 +/i(4)' JK) 



Hence all four functions of x are identical and a reduces to its well known con- 

 stant-form. — With a as a constant, equation (6) follows from the definition of o; 

 and substituting a 2 h — y/y and h/a—x/x o gives a 6ll =/i 9k . ]f W=6nlna one 

 may then write 



a= W/6n. h= W/9k. a , h=e W/M =l + w/M+ 



Here experiment shows that W may be regarded either as load or stress; and 

 reasoning indicates that it must be considered as load if M is determined for 

 vanishing strain 



* Ii is scarcely necessary to point out that many of the uses to which springs 

 are put, in watches for example, afford excellent evidence of the continuity of 

 the load-strain function for finite distortions. 



