DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 187 



perpendicular to the plane of the inductor. The current as measured 

 by the galvanometer in the first case will be C sin \ S (1 -j- /) and in 

 the second C sin D (1 + /), where C is the constant of the galvano- 

 meter and ^ is the logarithmic decrement. 

 Hence 



T[f' _ Tif" 



* 



sm 



In this way we can obtain a series of equations containing A t , A llt , 

 etc., and can thus find these by elimination. 



This completes the exploration, and we have as a result a formula 

 giving the magnetic potential of the field in absolute measure through- 

 out a certain small region in which we can experiment. 



The next process is to consider the action of this field upon any body 

 which we may hang in it. 



CRYSTALLINE BODY IN MAGNETIC FIELD 



Let the body have such feeble magnetic action that the magnetic 

 field is not very much influenced by its presence. In all crystalline 

 substances we know there exist in general three axes at right angles 

 to each other, along which the magnetic induction is in the direction of 

 the magnetic force. Let k 1} Jc 2 and k a be the coefficients of magnetiza- 

 tion in the directions of these axes and let a set of coordinate axes be 

 drawn parallel to these crystalline axes, the coordinates referred to 

 which are designated by x', y' and z', and the magnetic components of 

 the force parallel to which are X', Y' and Z'. 



The energy of the crystalline body will then be 



E = - \fff (k,Z' 2 + Jc, Y n + fc s Z") dx'dy'dz' 



In most cases it is more convenient to refer the equation to axes in 

 some other direction through the crystal. Let these axes be X, Y, Z. 

 Then 



Y , dV dV dV dV 

 X =d^ = ^ a + ^ a + dz a 

 Y' = etc. 



