2 ART. 6.- S. KUSAKABE : 



has from time to time been investigated by many scores of dis- 

 tinguished physicists and engineers. Indeed, the questions of 

 elasticity, having close relation, on one hand, to the strength of 

 materials, and, on the other to almost every branch of physics con- 

 stitute a problem whose solution has long been hoped for, but not yet 

 solved, either from its theoretical or its practical side. 



A law expressed by Hooke (1) with Latin terseness in the words 

 " Ut tensio, sic vis " is the foundation of the mathematical theory 

 of elasticity taken in the wide sense. The result of experimental 

 researches is that Hooke's law is nearly fulfilled, for all hard solids, 

 each through the whole range within its limits of elasticity. 



Coulomb first gave his theory of torsion for hairs and silk 

 threads (2) and then extended it to metal threads. (3) He brings out 

 clearly that the set-slide, — i.e. non-elastic permanent strain — produc- 

 ed by torsion is at first proportional to the total slide and then to the 

 elastic slide, and that the slide-modulus (réaction de torsion) remains 

 almost the same after any slide-set, that the elastic limit (at least in 

 the case of torsion) can be extended by giving the material a set. 

 Savart (4) endeavoured to extend experimentally the result which 

 Coulomb had obtained for the torsion of a wire, and concluded 

 thus : — " Quelque soit le contour de la section transversale der verges, 

 les arcs de torsion sont directement proportionnels au moment de la 

 force et à la longeur." 



The first formula for the torsion of square and rectangular 

 prisms, which was given by Eaton Hodgkinson, (5) has been proved to 



(1) Hooke. De potentiâ restitotiva ; London, 1678. 



(2) Coulomb. Mémoires des savants étrangers. Tom. IX. 1777. 



(3) Coulomb. Histoire de l'Académie des Sciences, année 1784. Paris, 1787. 

 M) Savart. Annales de chemie et de physique. Tom. 41, 1829. 



|5) E. Hodykinson. Experimental researches on the strength and other properties of cast 

 iron, 184G. 



