wherry: crystal form and optical properties 279 



the centers of gravity of the atoms in these layers, while in more 

 complex ones, the centers of gravity may be alternately slightly 

 to one side or the other of planes. ^ The spacings between the 

 planes prove to be more or less connected with the crystallo- 

 graphic axial ratios and other properties of the substances. The 

 less the spacing of the atomic planes in any direction in an aniso- 

 tropic substance, the greater should be the refraction in that 

 direction. In fact, if the layers in the different directions are all 

 close-packed, the difference in spacing may be the only cause of 

 anisotropism, and the factor p will then be inversely proportional 

 to the spacing d. It therefore appears probable that an exact 

 inverse relation may exist in some cases between the refraction 

 ratio and the crystallographic axial ratio of a substance. 



Crystallographic axial ratios (which will be referred to hereafter 

 simply as ''axial ratios") are usually stated to the fourth decimal 

 place. A variation of one minute in an angle, however, pro- 

 duces on the average a change of one unit in the third place, and 

 crystals are rarely perfect enough for measurements to agree 

 more closely than ±5'. The fourth decimal is therefore usually 

 entirely fictitious, and even the third often of doubtful signifi- 

 cance. Refractive indices also are often stated to the fourth 

 place, although the results of different observers usually differ 

 one or two units in the third place. The refraction ratios are, 

 accordingly, likewise obtainable with a certainty of but two or 

 three units in the third place. In general, therefore, inverse 

 agreement between the two ratios to one unit in the second place 

 may be regarded as complete. 



Furthermore it can not be assumed that the standard axial 

 ratio is a definite thing. Crystallographers are obliged in general 

 to choose one out of several possible forms as the unit, and to 

 take the axial ratio as inversely proportional to the intercepts 

 of that form on the axes. The criteria for selecting unit forms 

 are limited in number, comprising prominence, presence of 

 cleavage, and the yielding of simple symbols to the other forms 

 present by the derived ratio. The Fedorov rule, that substances 



'" The latter arrangement appears, for instance, in the Bragg diagram of cal- 

 cite (X-rays and Crystal Structure, p. 117). 



