Alumina with Silica, Lime and Magnesia. 327 



optically positive uniaxial 3Ca0.5Al 2 3 compound appears 

 noticeably biaxial in certain sections, and this may have been 

 due to solid solution, but if so the extent of solid solution is 

 not great. The unstable 5Ca0.3Al 2 3 compound and also the 

 CaO.Al 2 3 compound showed slight variations in the optic 

 axial angle which might be ascribed to the effects of solid solu- 

 tion, but in such instances the quality of the material was not 

 favorable for decisive optical tests. Evidence of slight solid 

 solution of MgO and also A1 2 3 in spinel was indicated by 

 refractive index determinations on preparations adjacent to 

 spinel in composition. — CaO may also take up small amounts 

 of MgO in solid solution, so far as could be ascertained by the 

 microscopic examination. 



The geologic significance of these binary series. — In the 

 preceding pages the optic properties of the several different 

 compounds of the different series have been cited in detail and 

 this evidence, in turn, has been used in general presentation of 

 this problem in the first part of this paper. The bearing of such 

 data, however, on geologic work has not been mentioned, and 

 it may be of interest to outline in a few paragraphs the partic- 

 ular kinds and scope of evidence which the different methods, 

 chemical, physical and optical, furnish in a problem like the 

 present one, which in turn is only a detail of still larger prob- 

 lems whose ultimate solution will be of fundamental importance 

 in the consideration of questions of rock and ore genesis and 

 allied phases of geologic inquiry. 



In the general attack upon complex problems of this nature, 

 experience has shown that exact and definite data along three 

 distinct lines of evidence, chemical, thermal, and optical, are 

 necessary and usually adequate for their satisfactory solution. 

 No one of these three lines is of itself sufficient for the 

 complete solution of the problem, nor yet are they entirely 

 independent of each other. Although supplementary to a 

 certain extent, they overlap in their spheres of application, so 

 that the results obtained by one method can be and usually are 

 confirmed by those of a second, thus strengthening the foun- 

 dation of fact on which subsequent reasoning is based. — By 

 careful chemical work the purity of the preparations is insured ; 

 by thermal measurements the relative energy content of the 

 different preparations at different temperatures is investigated ; 

 while by optical methods the number of compounds in a given 

 preparation is determined (mineral composition), their optical 

 constants ascertained and their special relation to each other 

 recognized (texture). — To present more clearly the scope of 

 these three fundamental lines of evidence which are essential 

 for the solution of problems of this type, it will be well to 



