Magneto-optic Properties of Crystals, 25 



pendicular to the fibre; in this case two opposing arrange- 

 ments are present, and it is difficult to pronounce beforehand 

 which would predominate*. 



The same difficulty extends to crystals possessing several 

 planes of cleavage, oblique to each other, and having no com- 

 mon direction. In many cases, however, the principle may 

 be successfully applied. We shall content ourself in making 

 use of it to explain the deportment of that class of crystals, of 

 which, as to form, Iceland spar is the type. 



For the sake of simplicity, we will commence our demon- 

 stration with an exceedingly thin rhombus cloven from this 

 crystal. Looking down upon the flat surface of such a rhom- 

 bus, what have we before us ? It is cleavable parallel to the 

 four sides. Hence our answer must be, " an indefinite num- 

 ber of smaller rhombuses held symmetrically together by the 

 force of cohesion." Let us confine our attention, for a mo- 

 ment, to two rows of these rhombuses; the one ranged along 

 the greater diagonal, the other along the less. A moment's 

 consideration will suffice to show, that whatever be the num- 

 ber of small rhombuses supposed to stand upon the long 

 diagonal, precisely the same number must fit along the short 

 one ; but in the latter case they are closer together. The matter 

 may be rendered very plain by drawing a lozenge on paper, 

 with opposite acute angles of 77°, being those of Iceland spar. 

 Draw two lines, a little apart, parallel to two opposite sides of 

 the lozenge, and nearly through its centre ; and two others, 

 the same distance apart, parallel to the other two sides of the 

 figure. The original rhombus is thus divided into four smaller 

 ones ; two of which stand upon the long diagonal, and two 

 upon the short one, each of the four being separated from 

 its neighbour by an interval which may be considered to re- 

 present the interval of cleavage in the crystal. The two which 

 stand upon the long diagonal, L, have their acute angles op- 

 posite; the two which stand upon the short diagonal, S, have 

 their obtuse angles opposite. The distance between the two 

 former, across the interval of cleavage, is to the distance be- 

 tween the two latter, as L is to S, or as the cosine of 38° 30' 

 to its sine, or as 4 : 3. We may conceive the size of these 

 rhombuses to decrease till they become molecular ; the above 

 ratio will then appear in the form of a differential quotient, 

 but its value will be unaltered. Here, then, we have along 

 the greater diagonal a row of magnetic or diamagnetic mole- 

 cules, or * centres of force,' to use a term of Mr. Faraday's, 

 the distance between each two being represented by the figure 



* It is probable that the primitive plates themselves have different ar- 

 rangements of the molecules along and across them. 



