IGNEOUS ROCK-SERIES AND MIXED ROCKS 39 1 



example, to obtain by interpolation the chemical composition 

 of a member of the series intermediate between two known 

 members. To predict by extrapolation the composition of a 

 hypothetical member beyond the limits covered by actual repre- 

 sentatives is, of course, a more speculative matter, since we have 

 no precise data for prolonging the empirical curves. There are, 

 however, some obvious considerations. The sum of all the 

 ordinates MP, MQ, etc., for a given rock must be equal to MK, 

 K being the point in which the vertical through M meets the 

 straight line YX. Hence all the curves must be contained within 

 the triangle VOX : prolonged to the right, they must all meet 

 at the point X, corresponding with a hypothetical rock with 100 

 per cent, of silica : prolonged to the left, they must meet the 

 line OY in points such that the sum of all the ordinates is equal 

 to OY, corresponding with a hypothetical rock devoid of silica. 



The simplest kind of variation conceivable is found when, 

 with increasing silica-percentage, the percentage of each base 

 changes at a constant rate (different for each). In other words, 

 the percentage of each base is then a linear function of the 

 silica-percentage. Such a series may be termed a linear series, 

 and its geometrical characteristic is that all the curves in the 

 diagram become straight lines. In the wholly ideal case of a 

 linear series extending to the ends of the scale, all these straight 

 lines would decline towards the right and meet at the point X. 

 It is safe to say that no such series exists in nature, nor has any 

 natural series been described corresponding with a portion of 

 such a diagram. It may, however be inquired whether, or to 

 what extent, natural rock-series fulfill the condition of linearity 

 within the limits of the actual representatives of the series. 

 Professor Brogger, in his memoir on the grorudite-tinguaite- 

 series. 1 makes approximate linearity a characteristic /property of 

 a Gesteinsserie : this is implied in his dictum "every mean of a 

 number of members of the series corresponds approximately 

 with a possible member of the series." But it is easy to show 

 by plotting graphically the analyses which he gives that this 



1 Eruptivgesteine des Kristianiagebietes (1894), Part I, p. 175. 



