SUMMARY OF CONCLUSIONS. 73 



ing that preparations which appeared completely crystalline in the 

 slides frequently proved not to have reached their maximum specific 

 gravity. It is very difficult to detect the last traces of glass with the 

 microscope. 



If our confidence in these determinations is justified, the form of 

 the specific-gravity curve is very significant. It was pointed out by 

 Retgers* that if the isomorphous mixture is merely a "mechanical 

 aggregate" the volume of which remains exactly equal to the sum of 

 the volumes of the components, then the specific-volume curve of the 

 mixtures for percentages by weight of the two components must be a 

 straight line. He also offers a number of isomorphous pairs for which 

 he finds the specific-volume curves to be straight lines, in support of 

 his hypothesis that this relation is general. Our values when plotted 

 in this way (fig. 24) also give a straight line with maximum varia- 

 tions amounting to 0.005, which is probably not greater than the 

 aggregate error in the syntheses and in the determinations of the 

 specific gravity. 



In spite of this apparent corroboration, it does not seem to us that 

 Retgers was quite justified in assuming that this relation is entirely 

 without limitation. The temperature at which the specific gravity 

 is determined is so far below the temperature of solidification (in our 

 case more than 1000 ) that the density at 25 will depend, to a con- 

 siderable degree, upon the coefficient of expansion of the material as 

 well as upon composition and molecular structure. The coefficient 

 of expansion will, in general, differ for different compositions, and is not, 

 in general, a linear function of the temperature. Considering Retgers's 

 generalization in the light of these facts, the relation of the specific 

 gravities at 25 would be necessarily continuous, but not necessarily 

 linear. 



The specific gravities of the glasses are also plotted (fig. 23) to show 

 the divergence from the line of the crystals toward the albite end of 

 the series, i. e., as the percentage of albite increases the density of 

 the glass is diminished more than that of the crystals. 



There is nothing new in the conception of isomorphism in the feld- 

 spars, but the positive character of our experimental results makes 

 them of more than ordinary interest by reason of the fact that so 

 good authority on the subject as Fouque and Levy has passed upon 

 it adversely on the basis of optical evidence derived from artificial 

 preparations. More recently Violaf has declared that the optical 

 evidence is insufficient to prove isomorphism in the natural feldspars 



* J. W. Retgers, Zeitschr. fiir. Phys. Chem., 3, p. 507, 1889. 

 \Loc.cit. 



