1030 Proceedings of Royal Society of Edinburgh. [sess. 
represents the component thus modified. “ These curves strongly 
resemble those of magnetite parallel to the face of the cube.” 
5. Wallerant’s Formula . — The next contribution to the in- 
vestigation was made by Wallerant ( Gomptes Rendus, Oct. 1901). 
His work is purely mathematical, and is not based upon any 
assumption as to the structure of the magnetic material. He 
remarks that the components, X, Y, Z, of induction along the 
quaternary axes are functions of the components of the field along 
these axes — i.e. of the direction cosines cos a, cos f3, cos y, of the 
Fi$- 8. Magneiite de Brozto. Premier disque parallels k la face du doditotalre 
Aimantatkm parallele et perpendicaialre an champ. Lea Hgftes pom till yes 
Indiqucnt 1*8 maxima et minima. 
field. He then develops these functions in increasing powers of 
the cosines, and, neglecting powers beyond the third while 
expressing the necessary conditions of symmetry, obtains the 
expressions 
X = E cos a(l + &cos 2a) , 
Y = E cos /?(! + h cos 2/3 ) , 
Z = Ecos y(l + A: cos 2y ) , 
where E is the induction along a binary axis, and h is a numerical 
coefficient whose value depends on the intensity of the field. 
To verify these expressions, he deduces the relation 3T + Q = 4E, 
where T and Q have the meanings given in connection with fig. 1, 
