12 



PROFESSOR CARGILL G. KNOTT ON 



It will be noticed that the means are not simple arithmetical means. They are 

 obtained by weighting the individual values in accordance with the accuracy of the 

 experiments on which these values depend. 



Finally, we may calculate the ratio bjB for each current thus : — 



B 



b a 



a ' A 



A_ 

 ~B 



Collecting, then, all the results that are of importance, we obtain Table II., showing the 

 ratios between the sectional and axial inductions in each tube, and also the ratios between 

 the axial inductions in the thin-walled and thick-walled tubes. 



Table II. 



Current = 



•49 



1-05 



2-09 



A'/A 



•3007 



•2739 



•2604 



B'/B 



•3087 



•2802 



•2799 



a'/a 



•427 



•4056 



•392 



b'/b 



•424 



•4058 



•3999 



a/A 



•2738 



•2536 



•2488 



b/B 



•3367 



•3220 



•3208 



For a tube of radii a and ft (a>/3) the sectional current i produces (in accordance 

 with the usual theory) at any point r a field 



a 2 - ft 2 r • 



If I is the length of the tube, the total sectional induction across a radial section is 



f&'=/lfjL'hdr 



(8 



= ^'( 1_ i ATi lo S-? j2 ) 



where, for simplicity, we assume // to be constant over the section, and where p = a/j3. 

 With the same assumption, we find for the total axial induction the expression 



33 = l/ni log p 2 . 



It is advisable to distinguish /a from yJ, since clearly the average magnetic force due 

 to a given axial current is greater than the average magnetic force due to a sectional 

 current of the same value ; and we have seen above how much the permeability varies 

 with the force. 



