L 85 ] 

 XII. Intelligence and Miscellaneous Articles. 



ON THE DISTRIBUTION OF MAGNETISM IN CIRCULAR OR ELLIPTIC 



PLATES OF STEEL. BY E. DUTER. 

 HPHE object of the following experiments was to ascertain the in- 

 -*- fluence of the shape on the distribution of free magnetism in steel 

 magnets. My examinations were effected upon plates of a circular 

 or elliptic form, all cut out of the same steel and possessing the 

 same temper, their thickness being one millimetre. The longest 

 radii of the circles and longest axes of the ellipses are 15 centims. 

 Magnetization was obtained by means of a very flat induction-coil 

 formed by 400 metres of copper wire of 2 millims. diameter, 

 through which passes the current of ten good Buiisen elements. 



The method which I employed was that of M. Jamin ; it is the only 

 one which permits one to study any point one wishes of a magnet, by 

 measuring in each point the separating- force of a very small contact 

 of soft iron. To assure the complete success of the method in the 

 case under consideration, two precautions are indispensable : — 



In the first place, the magnet must have a perfectly polished 

 and clean surface ; the slightest trace of contamination tarnishing 

 the magnet affects in a most irregular fashion the force which 

 determines the separation. Further, every shock of the magnet 

 must be avoided, even that of the little pulling-stud, which, if it 

 falls suddenly on a point in the magnet, permanently alters the 

 tension existing in that point. 



The results I have obtained may be briefly stated thus : — 



1. The total quantities of free magnetism spread over circles or 

 ellipses are proportional to the surfaces. 



2. This magnetism may be regarded as distributed over threads 

 which affect the form of hyperbolas ; the non-transverse axes of 

 the hyperbolas are the axes of symmetry of the magnets, perpen- 

 dicular to the neutral line. The trans 7erse axes are directed along 

 the neutral line ; but their lengths vary from one thread to another. 



On each of these threads, the law of distribution of the free 

 magnetism is given by the formula 



I=A(a h — a- h ): 

 I is the magnetic tension at the points under consideration ; h is the 

 rectified length of the arc of an hyperbola defined as I have said 

 above, in which the point in question is situated ; this length is 

 reckoned from the middle zone. A and a vary from one thread 

 to another, according to the two following laws : — 



3. The tensions I x at the extremity of each hyperbolic thread are 

 given by the formula 



I, = g^-o arc tan jp or A ( ah ~ a ~ h ^ = goo arc tan \ : 



\ is the length of the hyperbola, reckoned from the middle zone 

 to its extremity ; L is the tension at the extremity of a thread of 

 infinite length ; Tc is another coefficient, which in the circles abso- 

 lutely depends only on the nature of the temper of the steel ; in the 

 ellipses also it remains a constant number, provided the transverse 



