408 Mr. H. Tomlinson on the Increase in Resistance 



Values of — -r — • 

 s e 



Steel. 



(2) 3-619] 



(3) 3-602 I Mean 3-525 



(5) 3-355 J 



Iron. 



(1) 4-289 ] 



(2) 3-699 L Mean 3-951 



(3) 3-864 J 



Brass. 



(1) 2-203 



It would seem that the increase per cent, of resistance for a given 

 lengthening of a wire is greater in iron than in steel, and much greater 

 in both iron and steel than in brass, but that the increase per cent, of 

 resistance per unit of stretching-force employed is greater in brass than 

 in iron, and greater in iron than in steel. 



The torsional rigidity of the wires was then ascertained, the vibrators 

 used being similar to those used by Sir William Thomson in his experi- 

 ments on the rigidity and viscosity of metals (Proc. of Ifcoy. Soc, May 

 1865), namely, thin cylinders of sheet brass, turned true outside and 

 inside, supported by a thin, flat, rectangular bar. The wire to be tested 

 passed perpendicularly through a hole in the middle of the bar, and was 

 there firmly soldered. The cylinder was tied to the horizontal bar by 

 light threads, so as to hang with its axis vertical ; the other end of the 

 wire was securely soldered into a stout iron bar, firmly held in a vice 

 attached to a rigid support, Two experiments with different lengths of 

 wire were made with each wire, the result of each of the two experi- 

 ments agreeing very closely, as, for instance, we may take as an average 

 example Steel No. 3, in which the torsional rigidities in grammes per 

 square centimetre in the two trials were 783'5 x 10 6 and 782*2 x 10 6 . 



If we assume the wires to be isotropic, we can, from the values of e 

 and the rigidity, which latter value will be denoted by r, obtain the ratio 

 of lateral lineal contraction to longitudinal dilatation ; denoting this ratio 



by a, we shall obtain (Thomson and Tait's Nat. Phil. p. 521) a = ^ — 1, and 



therefore easily deduce the increase of resistance that would follow in 

 the case of each wire from mere increase of length and diminution of 

 section, without considering any other alteration of resistance that 

 would result from stretching. Calling els the increase of resistance that 

 would result from mere increase of length and diminution of section, 

 we can prove that 



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