the Temperature Coefficient of a Magnet. 45 1 



III. On the Determination of the Temperature Coefficient 

 of a Magnet. 



The following general and sensitive method may be added 

 to the known methods of W. Weber and Lamont. The bar 

 to be examined is brought near to a reflecting magnetic needle 

 in the horizontal plane of the needle so that its centre point 

 lies in the meridian of the needle, and so that it, acting together 

 with the earth's magnetism, brings the needle into an east-and- 

 west position. Let the bar in this position make an angle <p 

 with the meridian. If now the magnetism M of the bar 

 change by an amount AM, the needle will alter its position 

 by the small angle Ae. Then, apart from corrections (com- 

 pare below), it is easily seen that we have 



-jj- =|tan 9 . Ae. 



We observe that this method may be made very sensitive by 

 choosing the distance of the magnet from the needle so that 

 the angle (j> shall be small. 



For the practical employment of this method it is very con- 

 venient to have the magnetic bar on the rotating arm of a 

 graduated circle. As a magnetic needle I have employed a 

 steel disk with reflecting surfaces. The method of procedure 

 is then as follows: — 



In order to measure the angle (/>, the magnetic bar is rotated 

 from its original position until the image of the scale is seen 

 in the second reflecting surface. This rotation amounts then 

 to 2(f). The rotating arm in the two positions differing by 2^>, 

 is struck, and the magnet rotated in each observation between 

 the strokes, i. e. when cold and when hot. The influence 

 of small unintentional rotations of the magnetic axis of the 

 bar, such as might be produced by the heating itself, is thus 

 avoided. 



Let A be the distance of the scale from the mirror at the 

 one temperature t. Let the positions e x and e 2 of the needle 

 be observed upon rotation of the bar through the angle 2cf>, 

 and at the other temperature t' the positions e\ and e' 2 - If 

 we denote e 1 — e 2 by n and e\ — e f 2 by n' ', then the relative 

 loss of magnetism, 



AM tan 6. 



and the temperature-coefhcient therefore, 



in (f> ( n — n 

 8A(t — f) 



~_ tan cf> (n — nf) 



