G. F Becker — Finite Elastic Stress-Strain Function. 337 



tion of tbe section. Catskill is simply epochal but " Chemung" 

 carries with it the conception of those physical and biological 

 characteristics which mark the great closing period of the 

 Devonian. 



Chemung, therefore, and not Catskill is the epoch whose 

 name should be applied to designate the whole group, while 

 Catskill must be retained in its original signification only. 



University of the City of New York. 



Art. XLYIIT. — The Finite Elastic Stress-Strain Function / 

 by Geo. F. Becker. 



Hookas Law. — The law proposed by Hooke to account for 

 the results of experiments on elastic bodies is equivalent to : — 

 Strain is proportionate to the load, or the stress initially applied 

 to an unstrained mass. The law which passes under Hooke's 

 name is equivalent to : — Strain is proportional to the final stress 

 required to hold a strained mass in equilibrium.* It is now 

 universally acknowledged that either law is applicable only to 

 strains so small that their squares are negligible. There are 

 excellent reasons for this limitation. Each law implies that 

 finite external forces may bring about infinite densities or 

 infinite distortions, while all known facts point to the conclu- 

 sion that infinite strains result only from the action of infinite 

 forces. When the scope of the law is confined to minute 

 strains, Hooke's own law and that known as his are easily 

 shown to lead to identical results ; and the meaning is then 

 simply that the stress-strain curve is a continuous one cutting 

 the axes of no stress and of no strain at an angle whose tangent 

 is finite. Hooke's law in my opinion rests entirely upon ex- 

 periment, nor does it seem to me conceivable that any process 

 of pure reason " should reveal the character of the dependence 

 of the geometrical changes produced in a body on the forces 

 acting upon its elements."f 



Purpose of this paper. — So far as I know no attempt has 

 been made since the middle of the last century to determine 

 the character of the stress-strain curve for the case of finite 

 stress. £ I have been unable to find even an analysis of a 

 simple finite traction and it seems that the subject has fallen 

 into neglect, for this analysis is not so devoid of interest as to 

 be deliberately ignored, simple though it is. 



* Compare Bull. Geol. Soc. Araer.. vol. iv, 1893, p. 38. 

 f -Saint- Venant in his editiou of Clebsch. p. 30. 



\ J. Riccati. in 1 747. a brief account of whose speculation is given in Todhunter's 

 history of elasticity, proposed a substitute for Flooke's law. 



