CIRCULAR MAGNETISATIONS IN IRON TUBES. 



15 



for the a and b tubes ; but shall leave Tube B out of consideration, since Table I. applies 

 directly to Tube A. 



Calculating, then, the permeabilities for the fields due to the several currents, we find 

 as follows : — 





Permeabilities due to Current 



Tube. 











•49 



1-05 



2-09 



A 



376 



447 



533 



A' 



308 



350 



400 



ab 



352 



408 



507 



a'b' 



308 



348 



398 



From these we at once obtain the ratios (///ju) for the different currents and tubes. 

 These we shall call the calculated ratios ; while the ratios obtained from equations E by 

 use of the values of Table II., we shall call the observed ratios. It remains now to com- 

 pare these sets of ratios, as in Table III. 



Table III. 



Current 



Strengths in 



Amperes. 



Ratios of Permeabilities of Sectional and Axial Inductions. 



A'jA 



a'b' jab 



Obs. 



Calc. 



Obs. 



Calc. 



•49 

 1-05 

 2-09 



•902 

 •832 

 •781 



•819 

 •783 

 •750 



•978 

 •932 

 •910 



•874 

 •853 



•785 



It will be seen at once that a ready explanation is found for the diminution of the 

 ratio of the two inductions as the field is taken stronger. The numbers in the " calculated " 

 columns fall off according to much the same law as those in the " observed " columns. In 

 all cases, however, the calculated ratios are smaller than the corresponding observed 

 ratios. This may be explained in several ways, thus : either the average magnetic field 

 acting on the iron is over-estimated for the axial induction or under-estimated for the 

 sectional induction ; or the permeability is really greater under the influence of the 

 current passing through the iron than it is under the influence of an equal average mag- 

 netic field unaccompanied by such a sectional current. 



If the last be the true explanation, then a direct experiment should show an appreci- 

 able increase in the axial induction when a current is in addition sent along the iron 

 tube. Now, the effect of a sectional current sustained steadily while the axial is being 



VOL. XXXVII. PART I. (NO. 2). D 



