part 4] MICEOMETEIC STUDY OE THE ST. AUSTELL GEANITE. 551 



These curves bring out two points of general interest. Where 

 one slide only is available the standard deviation is naturally large, 

 but the curve falls so rapidly that, when three slides are taken, the 

 standard deviation is reduced by one half. Thereafter the curves 

 flatten, and for practical purposes the standard deviation becomes 

 sensibly constant. Again, it will be noticed that the standard 

 deviations of such constituents as orthoclase, present in large 

 crystals and irregularly distributed in the slides, are much greater 

 than those for plagioclase or mica present in smaller, more 

 uniformly distributed units. It follows that variations in the last- 

 named minerals are more significant than greater differences in the 

 first-named, especially when the number of slides is small ; and, 

 by consideration of the smaller units, an estimate may sometimes 

 be made of the value of a single slide, when nothing could be 

 inferred from the larger units. 



The usual convention (based on the consideration that the 

 chances are against the effect of sampling being greater than three 

 times the standard deviation) is to take all variations lying within 

 a range of three times the standard deviation as due to sampling, 

 while deviations beyond this range may be regarded as significant. 



Table III. — Volume Differences between Localities 48 a (Contact) and 

 48 (40 feet from Contact), Dyer's Quarry, Meledor. 



Mineral. Difference. Standard deviation X 3. 



Quartz +4'9 7"8 



Orthoclase -2"2 108 



Plagioclase — 2'1 4'5 



Coloured mica — 2'0 2"4 



Colourless mica +3'3 2 - 4 



Tourmaline — 0'3 1*8 



Topaz -2-2 1-2 



Fluorite +0-6 0-3 



For example, if there be a difference of 10 per cent, between 

 the amounts of quartz in two localities, and if the amounts rest 

 on three slides ; then, since 10 per cent, is greater than 3 x 2 - 6 

 (standard deviation for quartz in three slides), the difference may 

 be regarded as due to some other cause than sampling. 



A practical illustration of the application of this criterion will be 

 found in comparing the composition of the main rock at Dyer's 

 Quarry with that at the contact (Nos. 48 & 48«). Three slides 

 of the contact-rock Avere available, including one from the Geolo- 

 gical Survey. In Table III the differences between the percentages 

 for localities Nos. 48 and 48 a are set forth in the first column, and 

 the second contains the standard deviations (when three slides are 

 used) multiplied hj 3. Now, is there any significant quantitative 

 difference between the granite at the contact and that 40 feet 

 away ? The table at once shows that differences in the amounts 

 of quartz, orthoclase, plagioclase, and biotite lie well within the 

 limits of sampling. Muscovite, topaz, and fluorite, however, show 

 changes lying well be} r ond these limits, and may be considered as 

 significant. In approaching the contact at this point there has 

 been an increase in muscovite and fluorite, but a decrease in topaz. 



q. J. G.S. No, 31 G, 2p 



