462 A. A. JULIEN AMPHIBOLE SCHISTS OF MANHATTAN ISLAND 



considered, for each of which the factor a must be directly determined 

 by the photographic or by the drawing process. 



A. Schists of uniform texture, made up of elongated elements of the 

 predominant mineral, with equally thin intervening laminse of the other 

 minerals. Here it is only necessar}^, in an ordinary thin-section on the 

 schist plane, to estimate the ratio of the average area of the plates of the 

 predominant mineral, carefully measured on the schist plane, to their 

 area a' (=d'^), in approximately correct proportion for the volume of 

 that mineral in the rock, calculated from the theoretical cube of equiva- 

 lent volume. The average values of the three dimensions of the plates 

 of that mineral, length (/), breadth (6), and thickness (0, are ascer- 

 tained in the common thin-section through a large number of measure- 

 ments. Then, 



V ^ X 6 X ^ = d', 



that is, the cube root of the average volume of the plates is equal to the 

 length of side of cube of equivalent volume. Its square, c^'^ or face of 

 cube, is the average area required for plates of that mineral, as seen in 

 thin-section, in correct proportion to its real volume in the rock. The 

 proportion oil Y^ h : d!'^ \ -. a : a' yields the desired ratio of the areas of 

 faces of the actual and of the estimated plates. 



For measurement of the actual area the modification of the Delesse 

 process by Sollas* may be employed, namely, drawing outlines of min- 

 eral plates with help of camera lucida in not less than 24 fields of the 

 microscope, transferring to tinfoil, cutting out different parts, weighing 

 together those representing each mineral, and multiplying by respective 

 specific gravities ; or with greater accuracy and ease, in my opinion, 

 by directly dissecting the paper drawing itself, or still better by 

 the process explained in the example beyond, namely, making one or 

 more photomicrographs from parts of the thin-section, preparing, mark- 

 ing, and cutting out prints from the same. The average area of the 

 plates of the predominant mineral so obtained is then reduced by the 

 foregoing proportion to that of the true proportionate or estimated area, 

 and the entire mineral analysis corrected to corresi)ond. 



In two following cases an additional thin-section, in a plane inclined 

 at a definite angle to the schist plane, will become necessary to reduce 

 error derived from the lack of uniformity in texture of some schists, 

 likely to exceed any error produced by the practical difficalty in orien- 

 tation of the slicing plane required. We may have to deal with contin- 

 gencies modified by position of the blades, wliether with parallel or with 

 divergent axes, and whether with their planes in the schist plane or 

 irregularly disposed toward it. 



* Trans. Roy. Irish Acad., vol. xxix, pt. xiv, 1891, p. 427. 



