50G 



PROFESSOR KNOTT ON SOME RELATIONS BETWEEN 



A comparison of these numbers with the numbers given in Table II. above will show 

 that the twists in the thinnest strip, though smaller than these in the wire, are of the 

 same order of quantity. The strip, in fact, is quite comparable to the wire as regards 

 sensitiveness to the twisting strains of superposed magnetising forces. I am not aware 

 that the distribution of magnetic force on the surface of a strip of rectangular section, 

 when a current is flowing along the strip, has been even attempted.* But from our 

 present point of view it is easy to see in a general way that the amount of twist will 

 depend in great measure upon the value of the magnetic force along the medial line of 

 the strip. Consider a small square central surface element, with its sides parallel and 

 perpendicular to the edges of the strip. Such an element will tend to be distorted into 

 a rhombus form with its longer diagonal inclined at 45° to the medial line. The longer 

 axes of the two corresponding elements on the opposite sides of the strip will be 

 perpendicular to each other. Hence the originally rectangular parallelopiped formed by 

 the opposing elements, and the cross planes joining their edges each to each, will be 

 twisted into a warped rhomboidal figure with anticlastic surfaces for its sides. So far as 

 the direct strain effects of the magnetising forces are concerned, there will be distinct 

 advantage in the circular section over the rectangular section ; but this will be partly 

 balanced by the greater ease with which the strip yields to twisting. 



The same considerations would lead us to expect the twisting effect in different strips 

 to be a simple function of the current density, so long as the resulting magnetic force 

 remains small. Since in the present case the strips have all the same thickness, the 

 current densities will be proportional to the quotients of the currents by the breadths. 

 On forming these quotients, and arranging them in order of magnitude with their 

 corresponding twists, we shall find that they fall naturally into five groups. Taking the 

 mean of each group, we get the following table of relations between current densities and 

 twists : — 



No. of points 



Current Density 



Field Reversal 



Current Reversal 



in each Group. 



proportional to 



Twist. 



Twist. 



1 



3-09 



19-5 



8-3 



3 



1-96 



13 



4-3 



4 



1-23 



10-2 



2-7 



4 



•84 



7'8 





(3) 



•77 





1-6 



3 



•49 



5-7 



•9 



Plotting the twists in terms of the current densities we obtain nearly straight lines 

 if we neglect the first group of highest value ; and slightly curved lines if we take this 

 first single point into account. The result sufficiently well bears out the statement that 

 the Wiedemann effect in strips of different breadth, other things being the same, is 



* For the circular magnetisation in a cylinder of elliptic section, see a paper by M. Janet in the Journal de 

 Physique, t. ix., 1890. 



