The correlation between the size and the An composition of plagioclase can be represented as to be linear by equations of the forms, Y = aX + b or log Y = aX + b, where Y is the size and X is An %. In most cases, a>0, which are called the positive correlation. Of two positive correlation types, the curvilinear one, of which regression is figured between log Y and X, is the most essential case in any rock series. The factor responsible for resulting to the latter case is considered as fractional crystallization under the condition of steady freezing rate in light of Shimazu's physical consideration (1959) on magmatic differentiation. Another factor is also fractional crystallization with increasing rate of freezing, which might have brought a correlation in the form of the linear regression of Y to X. It is noted that the linear regression type is mostly found among the phenocrysts in calc-alkali rocks, and even in tholeiitic or alkali rocks, it is restrictively seen in groundmass minerals and microphenocrysts being smaller size than 0.3mm in length. Some other factors are accounted for such more complicated correlation types besides the positive one as the negative correlation, or the independent, between X and Y, as shown in volcanic rocks of calc-alkali series.
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