39 2 ALFRED HARKER 



must not be understood in too literal a sense. Indeed, Brogger 

 himself abandons the principle ; for, in calculating by extrapola- 

 tion the composition of a hypothetical end-member of the series, 

 he supposes that, while some of the bases vary in arithmetical, 

 others vary in geometrical proportion : a supposition inconsistent 

 with linearity. 1 If a few rock-series be actually plotted in dia- 

 grams, it soon becomes apparent that, while some of the bases 

 often give sensibly straight lines within the limits of the actual 

 rocks, others give lines very decidedly curved. We may note 

 in passing that some kinds of variation in igneous rock-masses 

 connected with differentiation in situ involve much more con- 

 siderable departures from the linear type. Such, for instance, is 

 the "concentration" of the more basic constituents in certain 

 parts of a rock-body, as investigated by Vogt and others. 



It appears then that in general the diagram of a rock-series 

 will consist of curved lines to indicate the variations in percent- 

 age amount of the several bases. Of these curves we may dis- 

 distinguish two kinds : [a] When the constituent in question 

 first increases to a maximum and then decreases, or increases 

 first more rapidly and then less rapidly, or decreases first less 

 rapidly and then more rapidly, the curve will be convex upward ; 

 (a) When it decreases to a minimum and then increases, or 

 decreases first more rapidly and then less rapidly, or increases 

 first less rapidly and then more rapidly, the curve will be concave 

 upward. This classification is not an exhaustive one, for there 

 may be curves which are inflected, being convex in one part and 

 concave in another, but it will be sufficient to consider the 

 simpler cases. Since the sum of the ordinates for all the bases 

 falls off steadily in linear fashion, its curve of variation being 

 the straight line YX, it follows that in any series, other than an 

 ideal linear one, some of the bases must give convex and others 

 concave curves. 



II. MIXED IGNEOUS ROCKS 



Considerable differences in composition may exist among 

 members of the same rock-series, and still greater differences are 

 x Ibid., p. 172. 



