THE GRANITIC ROCKS OF THE SIERRA NEVADA I 59 



The chemical analysis given below shows more titanium 

 oxide than is required for the biotite. Inasmuch as all the 

 iron oxide is magnetic and therefore probably magnetite, it is 

 likely that there is no ilmenite present. The remaining titanium 

 oxide is therefore supposed to be present in titanite, which is 

 the most common titanium mineral in the Sierra Nevada 

 granites. This mineral was not, however, found in the thin 

 sections. The relative proportions of these different minerals 

 are taken from the calculation, as given below. 



It is well known that as a general rule, the less siliceous ele- 

 ments crystallize out first and the more siliceous last in rock 

 magmas. In most quartz-diorite and granitic magmas the alkali- 

 feldspar and quartz are usually the last elements to crystallize, 

 and they are, also, the most acid of the components of the rock. 

 A possible explanation of the occurrence of aplite dikes in quartz- 

 diorite and granitic magmas would appear to result from this law 

 of crystallization. We have but to suppose that after the crys- 

 tallization of the less siliceous constituents there is a residual 

 mass of orthoclase and quartz in solution which is afterwards 

 forced into fractures which form in the already consolidated 

 granite, perhaps as the result of cooling. The laws of thermo- 

 chemistry would appear to be applicable to such a scheme. Heat 

 would be generated by the crystallization of the minerals of the 

 granite and this heat would perhaps aid in establishing convec- 

 tion currents to transport the residual, more siliceous, constituents 

 away from the already consolidated material. Moreover, as 

 suggested by Dr. Hillebrand, the more siliceous material would 

 be crowded away by the minerals which crystallize first, in the 

 same way as the salt of sea water is crowded out by the crys- 

 tallization of the water, so that the residual sea water, after a 

 portion has crystallized or frozen, contains more salt, propor- 

 tionately, than the sea water before crystallization began. 



The following calculation of the relative molecular propor- 

 tions of the various minerals found in the granodiorite-aplites 

 is based on the average of two complete chemical analyses by 

 Dr. Hillebrand, given in the table below. The calculation is 



