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Shaft moving with Uniform Speed along its Axis. 751 



The statement just made does not seem to apply to the 

 problem treated in this paper. For the contraction due to 

 the helical motion of the shaft is given in terms of the 

 resultant velocity by the usual formula ; and according to 

 deduction (I.) in §4 the state of strain in the periphery of a 

 solid shaft is in no way different from that of a thin tube of 

 the same external radius and in the same state of motion. 

 In the limiting case no distinction can, therefore, be drawn 

 between the strain in the rim of a rotating disk and a 

 rotating ring. The radius of each must contract in the same 

 ratio as the circumference, viz. in the ratio 1 to s/ \ — n 2 /c 2 . 



We have then ?* w = r \/ 1 — co 2 rJ/c 2 , where r a = radius 

 when the angular velocity is co ; this gives 



dr=drj(l-a> 2 rjfc 2 y /2 - 



Summarizing these results, we have then : — 

 The radius and the circumference of a solid disk rotating 

 with constant speed about an axis at right angles to its plane 



contract in the ratio of 1 to \/l — u 2 /c 2 , where u is the 

 velocity at the rim. 



A measuring rod laid along the radius contracts in the 

 ratio of 1 to [1 - i(i 2 /c 2 ) 3/2 , where iii is the velocity at that 

 position in the disk. 



The simplicity of the assumptions made and the analysis 

 given in this paper give support to the view that the above 

 conclusion is correct, within the limitations of the Euclidean 

 outlook adopted. It takes a middle course between the 

 results stated by Einstein and Jeans and the solution given 

 by Lorentz. It is conceivable that a solution may, however, 

 be found beyond the limits of Euclidean geometry which may 

 include all points of view. 



§ 6. Note on the Wiedemann Effect. 



A vertical iron wire carrying a current twists in a vertical 

 magnetic field. This is recognized as an effect of magneto- 

 striction due to the resultant magnetic field in the wire. 

 The effect is simplified if a steel tube is used in which a 

 spiral, or more accurately a helical, magnetic field acts whose 

 axis coincides with the axis of the tube. This is produced 

 by combining a longitudinal field with a circular field due 

 to a current flowing in a wire passing along the axis of the 

 tube. 



