JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. VI OCTOBER 4, 1916 No. 16 



PHYSICS. — The theory of the stiffness of elastic systems. 1 By 

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

 Louis A. Fischer.) 



Introduction. The stiffness of a body, or of a system of 

 bodies, we define as the ratio of the force 2 applied to the deflec- 

 tion produced. It is. not, of course, an intrinsic property of the 

 body or system itself, but depends also on the manner of apply- 

 ing the force, and on the point whose displacement is to be ob- 

 served. The stiffness of a body under given conditions is, how- 

 ever, its most important elastic property. The conception is 

 useful in dealing with the vibrations of structures; the yielding 

 of the supports of instruments; the design of aneroid barometers, 

 pressure gages, torsion meters, 2 etc.; and with springs wherever 

 they occur. But the tendency in elasticity, as in other branches 

 of physics today, appears to be to desert the obvious and to 

 court the remote. Instead of treating stiffness directly, writers 

 on elasticity make a detour, first determining the strain distri- 

 bution throughout the interior of the body; a procedure which, 

 besides being laborious, limits the validity of the result to cer- 

 tain rather simple geometrical shapes. This detailed analysis is 

 indispensable for some purposes but not for all, as the theorems 

 presented in this paper will show. All of these theorems have 



1 This work was done at the Jefferson Physical Laboratory, Harvard Uni- 

 versity. It is expected that it will be published in more detail upon the com- 

 pletion of a series of experiments on the subject recently begun at the Bureau 

 of Standards. 



2 The reader interested in galvanometer suspensions or other torsion prob- 

 lems can readily modify the formulas of the present paper so as to make them 

 apply to couples instead of to translational forces. 



569 



