PERTHITIC FELDSPARS. 135 



The magnifications used were naturally varied according to the width 

 of the particular lamellae in the section under measurement, \\itli 

 the basal sections particularly, it was foimd convenient to diminish 

 the intensity of the illumination by lowering the condensing system 

 and slightly raising the objective so as to bring out the contrast be- 

 tween the refractions of the two kinds of feldspar, thus clearly marking 

 their respecti\'e boundaries. Crossing of the nicols was, however, 

 constantly resorted to to make sure of the correct position of the 

 boundaries. In the case of the brachypinacoidal sections it was in 

 general found more convenient and quicker to measure with crossed 

 nicols. Sometimes both the width of the microcline and al!)ite bands 

 were measured, but in general only the albite was measured, the micro- 

 cline being determined by difference. 



In order to obtain a true estimate of the accuracy of these measure- 

 ments, the deviations of the individual measurements from the mean 

 should have been found and the precision measure computed by the 

 usual methods. Such a procedure involves a great expenditure of 

 labor and is, in the present case, unwarranted because, however pre- 

 cise the results may be, there would still remain the rather consider- 

 able error (estimated to be probably ± 1 per cent) which arises from 

 the fact that there are included within the microcline member many 

 minute lamellae or stringers of albite impossible to measure exactly. 

 There is also the impossibility, as will be pointed out later, of getting 

 at the exact composition of the albite phase itself. It seemed, there- 

 fore, sufficient to choose as units, in judging the precision of the 

 results of the micrometric measurements, the separate lines of measure- 

 ment. Accordingly, in Table No. I are given for inspection, the total 

 length measured for each section, the numl)er of lines, their average 

 length, and the average deviation from the mean of the volume per- 

 centages obtained from each line. The deviation of the mean itself 

 from the true value is V/i times as probable as any single observation, 

 n being the number of separate observations (here the numljer of 

 separate lines of measurement). In the column headed A.D. are given 



the products -p^ for each feldspar measured. This indicates that, 



so far as errors of observation are concerned, the means are probably 

 within one per cent of the true ^'alue. An estimate of the probable 

 error (P. P].) by the usual formula, using the single lines of measure- 

 ment as the units of observation, would have given slightly smaller 

 values than those given under A.D., but the computation is hardly 

 worth while in this instance. Inasmuch as the average width of a 



