On Double Refraction, 301 



When the three axes A, B, C are all equal, the three rectangular 

 compressions, produced by the aggregation of the molecules, will 

 destroy one another at every point of the molecule, and the body 

 which they compose will have no double refraction, and cleavages of 

 equal facility. Hence all crystals in which it is known by cleavage 

 that the particles cohere with equal force in three rectangular direc- 

 tions, have actually no double refraction. 



If the three attractive axes A, B, C are all unequal, the difference 

 of density which they produce in the molecules will be related to two 

 axes of double refraction, the strongest of which will be negative or 

 positive according as the compression along C is less or greater than 

 the dilatation produced along C by the united compressions of A and 

 B. Hence all crystals belonging to the prismatic system, in which 

 we are informed by cleavage that the particles cohere with unequal 

 forces in three directions, have invariably two, or, as we have already 

 explained, three unequal axes of double refraction, of which the 

 strongest is sometimes positive and sometimes negative. 



We have supposed the elementary molecules of bodies to be 

 spherical when existing singly, or beyond the sphere of their mutual 

 action ; but although their form must, in the case of doubly refract- 

 ing crystals, be changed into oblate, prolate or compound spheroids, 

 yet the deviation of these spheroids from the sphere may be so small, 

 that the forms of the bodies which they compose may be regarded 

 as arising from the union of spherical molecules. It is more proba- 

 ble, however, that the form of the molecules suffers a considerable 

 change, and we may consider that change as determining the exact 

 primitive form of the crystal and the inclination of its planes. 



The circumstance of almost all rhornbohedral crystals having neg- 

 ative double refraction, which can only be produced by axes of com- 

 pression in the equator of a prolate spheroid, excludes the supposi- 

 tion, that the ultimate molecules are sperical particles converted by 

 the forces which unite them into those oblate and prolate spheroids, 

 by means of which, according to the views of Huygens, all the va- 

 rieties of rhombohedrons may be formed ;* for if this were the case, 

 the obtuse rhombohedrons should possess one positive axis, and the 

 acute ones, one negative axis of double refraction. We are con- 

 strained therefore to suppose that in rhombohedral crystals the mole- 



* See HuYGENs's Traite de la Lumiere, chap. v. and the Edinburgh Journal of 

 Science, No. xviii, pp. .311, 314. 



