36 W. E. Ford — Chemical, Optical and other Physical 



These analyses were subjected to the following calculations : 

 The molecular ratios were obtained from each analysis ; the 

 discrepancies between these numbers and theory were averaged 

 and from these new values the analyses were recalculated and 

 then reduced to a 100 per cent summation. This was done in 

 order that the unavoidable errors of analysis should be equally 

 distributed over the various garnet molecules present and not 

 concentrated in the subsequent calculations upon a single 

 molecule, as would otherwise have been the case. From the 

 analyses modified in this way the percentages of the mole- 

 cules corresponding to the different garnets present were 

 derived. Then these results were tabulated according to 

 increasing indices of refraction and a careful study made of 

 them in order to discover the part each garnet molecule 

 played in determining the index of refraction of each com- 

 bination. The assumption was made that it would be found in 

 this series, as has been proved in a number of other cases, that 

 the index of refraction of each specimen would have a direct rela- 

 tionship to the indices of refractions of the component garnet 

 molecules and to the percentage of each in the whole. None 

 of the analyses gave the theoretical composition of any one of 

 the different members of the garnet group, but in a few cases, 

 namely analyses 1, 4, 11, 12, 22 and 23, they approached 

 closely to theory. In no case, therefore, would the index of 

 refraction be exactly equal to that of a single garnet but would 

 always be derived from the influence of the presence of at 

 least two different garnet molecules. But by a study of this 

 table tentative values were assigned to the indices of refrac- 

 tion of the individual garnets and then from these assumptions 

 theoretical values for the indices of refraction were calculated 

 for each analysis. From the results obtained it was possible 

 to discover in what regard the original assumptions were in 

 error and how to modify them in order to bring the measured 

 and calculated values into closer accord. After several 

 attempts of this kind assumptions were made which gave in 

 the large majority of cases a very close agreement between the 

 measured and calculated values. These results are given in 

 the table on page 37. As under the ordinary conditions a 

 determination of the refractive index of a mineral can hardly 

 be considered accurate beyond the third place of decimals, the 

 measured and calculated values of the indices are not given 

 beyond this point. In fact the chances are, that in the major- 

 ity of these determinations, the measured values are accurate 

 only to ± - 002. The discrepancy in each case between the 

 measured and calculated values is given in the last column 

 under the heading error. It will be noted that this discrep- 

 ancy is, in about half of the cases, within the probable limit 

 of error in the observations, and that it does not materially 



