276 



Prof. J. A. Ewing and Mr. W. Low on the 



that each cutting caused a marked loss of permeability. This 

 will also be apparent from the following table, which gives a 

 series of values (taken from the curves) of the magnetic 

 induction before and after cutting, for corresponding values 

 of the magnetizing force : — 



Table I. 



— Effect of Successive Cuttings. 











Thickness 



of equiva- 



Magnetizing 



Induction, SQ (C.G.S. units). 



lent air-space, in 

 millimetres. 



force, £> 

 (C.G.S.units). 











Solid 



Bar cut 



Bar cut 



Bar cut 



For the 



Mean for 





bar. 



in two. 



in four. 



in eight. 



first cut. 



seven cuts. 



■ 7-5 



8500 



6900 



4800 



2600 



0027 



0036 



10 



11000 



9000 



6400 



3770 



0-026 



0032 



15 



13400 



11550 



8900 



5550 



0023 



0-030 



20 



14400 



13000 



10750 



7150 



0019 



0026 



30 



15350 



14550 



12940 



9800 



0-014 



0020 



m 



16400 



15950 



15000 



13300 



0011 



0013 



70 



17100 



16840 



16120 



15200 



0-008 



0-009 



The last two columns of the table have been calculated on 

 the supposition that the effect of each cut is equivalent to the 

 introduction of a film of air, or rather of space the permeability 

 of which is equal to unity, between the cut faces, with no 

 alteration in the permeability of the metal itself. They show 

 the thickness in millimetres which this equivalent air-space 

 would need to have to explain the observed loss of permeability 

 on the part of the bar. They are calculated by a simple 

 application of the method introduced by Hopkinson in pre- 

 determining the magnetic field in dynamo machines*. Calling 

 33 the induction before cutting and 33' the induction for the 

 same value of «£) after cutting, /n the permeability of the 

 uncut metal, I the effective length of the bar, and x the 

 thickness of the air-space equivalent in " resistance " to the 

 cut, the line-integral of the magnetizing force is : — 



33Z 



wi 



before cutting the bar, and 



from which 



\- %> r x after cutting the bar ; 



~/A 23' ) 



The last column but one in the table gives values of this 

 * J. and E. Hopkinson, Phil. Trans. 1886, Part I. 



