ee ee ee ee ee 
Bismuth and Cale-spar in Absolute Measure. 368 
The next process is to consider the action of this field upon 
any body which we may hang in i 
Crystalline Body in Magnetic Field. 
Let the body have such feeble magnetic action that the mag- 
netic 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,, k, 
and &, be the coefficients of magnetization in the directions of 
these axes-and let a set of codrdinate axes be drawn parallel to 
these crystalline axes, the codrdinates referred to which are 
designated by 2’, y’ and 2’, 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=—43f// (kX? +h, Y?+k,Z") de'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 
22a ’"B +2 
yaaa pg ey 
exava’t+y'p’+Zy" ‘ 
X= Xa4+ VYa'+ Za" 
Y’=X6+Vf'+ Zp’ 
Z’ =Xy+Yy’+Zy’ 
where a, 8, 7; a’ , 8, 7’; and @”, P”, 7” are the direction cosines 
of the new axes with reference to the old. 
We then find . 
BS -4 {Xk +h O+ky) $Y (ha? +h fo +k y") 
+2 (ka 4k, B+ ky”) + IXY (kaa +h Bp phyy)+2XZ 
Cyaal +h Bp" +kyy")+2VZ (ka a! hf phy y')\dedy de 
The most simple and in many respects the most interesting 
Cases are when the crystal has only one optic or magnetic axis. 
In this case k,= k,. : 
ce. * : 
E=-4/f {(X°4V?4Z)k,+ (Ka+ Ya! + Za’)'(k,—,)} de dy de 
Where a, a’ and @” are the direction cosines of the magnetic — 
axis with respect to the codrdinate axes. ; 
