132 Dr. Hugh Warth — Igneous Books Classified 



The total mean deviation is 26*2. In the above average we 

 omitted -5 per cent. TiO.,, -2 per cent. P3O5, 1-9 per cent. H., 0, 

 because these substances are exchided from the partition scheme. 



The next step that may now be taken is as follows : — Divide the 

 500 rocks into two kinds, those which have less than the average 

 of 57*0 per cent, silica and those which have more. I find that 

 265 rocks belong to the former with an average of 48"3 per cent, 

 silica, and 235 rocks to the latter class with an average of 

 66 '9 per cent, silica. The mean total deviation within these two 

 groups has now been reduced from 26-2 to 17-1. Dividing these two 

 groups once more according to their silica percentage, one obtains four 

 groups with respectively 43*4, 52-5, 61*0, and 72-7 per cent, silica. 

 The average deviation is now 13-2, or about one-half of the original. 

 It happens that these four groups nearly coincide with the old- 

 established division of rocks into acid, intermediate, basic, and 

 nltra-basic rocks, and it is noteworthy that this very simple 

 classification reduces the deviation already to one-half of its original 

 amount. 



As will be seen later on, it needs four times as many groups to 

 reduce the mean total deviation to approximately one-third of the 

 original deviation, and H. S. Washington's elaborate system reduces 

 it at the most to one-fourth. 



If the above-mentioned fourfold grouping of the 500 rocks be 

 continued by now partitioning according to the percentage of 

 alumina, eight groups are obtained with a deviation of 10*9. 



Further partition into IG groups yielded different results according 

 to the choice and order of substances. The following deviations are 

 obtained : — 



Okder of Substances. Total Deviatiox. 



Feo O3 + Fe 0, Mg + Ca 0, Al, Oj, Nas + Kj ... 10-5 



Fe2 03 + FeO, ALO3, MgO + CaO, NaoO + K2O ... 10-4 



Si 0.,, Fe., O3 + Fe 0, Mo:^0 + Ca 0, Na, + K^ ... 10-2 



SiOo, AI2O3, MgO + CaO, Na-O + K.TO 9-7 



Four bases, three last bases, two last bases, Na^ + K2 ... 9*5 



All four sets of bases, omitting successively the following : 



AI2O3, FeoOs-h FeO, MgO + CaO, NaoO + KoO ... 9-0 



This last method of grouping, which gave the best result, is 

 herewith adopted for use. 



Further partition into 32 groups reduced the total deviation as 

 follows : — 



Order of Substances. Total Deviation. 



Fe2 O3 + Fe 0, AI2 O3, Mg + Ca 0, Na, + K, 0, aU bases 7-7 



All bases, successively minus the following: 



AI2 O3. Fej 03 + FeO, Mg + CaO, NaoO + KoO, and 



finally all bases (^vith a few modifications) " 7'4 



The same principle might be applied for the purpose of still 

 further subdivision. With 128 groups it would be possible to treat 

 all the seven bases separately. It would, however, be necessary to 

 employ a larger number of analyses to secure accuracy. 



