Viscosity and Rigidity of Iron and of Steel. 183 



7, 8, 9, 10, 11, 12 from a second piece of wire, Nos. 15, 16, 17, 

 18 from a third piece of wire. Comparison of data is to be 

 made only for wires drawn to different diameters from the same 

 sample of iron.* All wires are annealed at red heat in air. 



To this may be added the following data for soft iron fila- 

 ments drawn from the same wire. co is the maximum. 



No. 



2p 



wxlO 3 



^xlO 6 



/^xlO 3 



5, 16 



0-032 



2-9 



212 



2-4 



1, 18 



0-025 



2-8 



241 



2-3 



It has been stated that the wires to which table 5 refers were 

 all soft. Their diameters vary over the very large interval 

 0-022 cm to 0-231 cm , and the rates of stored twist from 04° to 

 15°. Nevertheless the maximum obliquity, co, of the external 

 fiber is nearly the same for all the rods. In other words, the 

 limits of torsional resilience of soft iron are reached when the 

 obliquity of the external fiber exceeds 0'0032 radians, f After 

 this, iron yields to the torsional couple and the result is indefi- 

 nite permanent set. 



Inasmuch therefore as co is comprehended within about the 

 same interval (0 to O003) for all the wires irrespective of thick- 

 ness, it is expedient to discuss the variation of <p (p. 177) with 

 reference to co. Indeed the diagram of <p as a function of co 

 shows the characteristic family of curves with remarkable 

 terseness. <p increases with co at a rate which is greater in pro- 

 portion as the thickness of the wires, 2^0, diminishes, and 

 which decreases and finally approaches zero when co is a maxi- 

 mum. The detorsion due to magnetization ceases to increase 

 when the sections of the rod slide on each other. Indefinite 

 twisting beyond the elastic limits has no effect so long as the 

 wire is not appreciably hardened. But it is the dependence of 

 <p on p to which I desire principally to advert. The following 

 series of values obtain for w= 0-003. 



* Imperfections in the wire plate prevented me from drawing all the wires 

 from a single sample of iron. 



f The literature on torsional strains is so voluminous that I can scarcely sup- 

 pose similar simplifying observations have not been made. But I have found 

 none. Permanent and temporary torsions have been compared with regard to 

 their relations to stress, to the mechanical condition of the material carrying 

 stress, etc., by Wertheim (Comptes Rend., si, p. 411, 1855; Ann. de Ohim. (3), 

 1, p. 195, 1857); more elaborately even by Wiedemann (Wied. Ann. vi, P- 485, 

 1879; ibid, vii, p. 496, 1879; Phil. Mag. (5), is, pp. 1, 97, 1880), and by Perard, 

 (Revue univ. d. Mines, 1879). Reference is also to be made to Tresca (C. R., 

 lssiii, p. J 104, 1871), to De Saint-Venant. who has investigated the mechanics of 

 ductile substances, and to others. In Wiedemann's last research, correlated values 

 of temporary and permanent torsions are discussed both as they exist immediately 

 after imparting strain and as they esist "after an indefinite lapse of time. I have 

 no such comprehensive purpose in view ; nevertheless the great convenience of 

 the variable w is obvious from the way in which I am able to use it. 



