198 



PROFESSOR C. G. KNOTT ON THE 



true according to Joule's researches. Then the amount of twist per unit 

 length of the wire will be 



T = ^(a a + j8>/j8 = /*(a 8 /j3 + aj8) . 



If a is constant, t has a maximum value when 



If jB is constant, there is no such maximum value of r. A comparison of curves 

 A and B (Plate XXIX.) bear this out fully. 



Hence, in the case of constant circular magnetisation and varying longi- 

 tudinal magnetisation, the twist will first increase and then diminish as the 

 latter is increased to its saturation point. For a stronger circular magnetisa- 

 tion the maximum point is pushed further on, until, when the circular 

 magnetisation has reached the saturation point, there will be no subsequent 

 fall off in the twist, i.e., no true maximum point. These remarks apply strictly 

 to a thin iron cylinder. In the case of a wire the effects are complicated. 

 Still the curves on Plate I. bear out in a remarkable way these conclusions. 

 Thus in fig. A the maximum point obviously occurs further to the right in the 

 higher curve. In the following table a direct comparison between the linear 

 current strength and the helical current strength, which corresponds to the 

 maximum twist, is established : — 



Linear Current, ..... 

 Helical Current for Maximum Twist, 



0-575 

 2 



0723 



2-2 



1-891 

 2-4 



3157 

 3-1 



4-068 

 3-5 + 



The highest curve has no distinctly marked maximum, a result in close agree- 

 ment with the foregoing deductions. The other series of curves bear out the 

 same conclusion. 



Joule also found that the extension for a given magnetisation was smaller 

 when the wire was subjected to a greater tension. Hence, in general, we 

 should expect the twist in a wire due to superposed circular and longitudinal 

 magnetisations to be less for the greater tension, since the longitudinal exten- 

 sion will be diminished. This conclusion is quite borne out by curves C and 

 D. .With only one exception (namely, C III.) an increase in tension is 

 accompanied by a decrease in twist. This result is not in accordance with 

 Wiedemann's, who found the twist to be nearly independent of the tension. 

 Possibly, however, he worked with a thickness of wire which for the special 

 combination of current strengths and tensions was not sufficiently sensitive to 

 the change of tension. A glance at the curves C and D shows how much 

 greater is the sensitiveness to tension change for certain combinations than for 

 others. 



