88 
Proceedings of the Royal Society of Edinburgh. [Sess. 
As regards the actual composition of individual rocks, an examination 
of the list will show that the rocks are brought together sufficiently close 
for all possible requirements. The chief divergence happens to occur in 
the silica. It amounts repeatedly to 10 per cent., but is to a very large 
extent compensated for by an increase in the percentage of Ti0 2 and T 2 0 5 
and also H 2 0. The latter is no doubt in a large measure replacing silica 
as a solvent. It will be noticed that within the limit of each group the 
rocks have been arranged in descending order of their Silica percentage. 
This arrangement brings similar rocks still closer together, and the actually 
neighbouring rocks are so near in composition that in a great many cases 
they are practically identical, although from widely distant localities and 
differently named. 
There is also a theoretical test for the proximity of rocks in their 
groups, as has already been shown in my previous paper. The mean 
deviation of rocks from a given average may be calculated as follows : — 
We take, for instance, 500 rocks and write down for each rock how much 
its silica percentage differs from the average silica whether positive or 
negative. If we then add up the 500 figures which represent these 
differences we have only to divide the sum by 500 in order to find the 
mean deviation of the silica in all the rocks. We do the same for the 
alumina and afterwards for all the remaining oxides, certain of them being 
in the present example taken together in pairs Fe 2 0 3 + Fe0, MgO + CaO, 
Na 2 0 + K 2 0. Adding up the deviations of all the constituents, we obtain 
the total equal to 26*2. After dividing the rocks into 16 groups, I obtained 
such approximation that the total deviation within the groups amounted 
to an average of 9'0. Doing the same in our present classification, we find 
the total deviation within the 64 groups reduced to 7 3. This is a far 
greater advance than it might at first sight appear to be. In the case of a 
single item of composition the deviation would diminish in direct proportion 
to the number of groups, whilst with many items considered together the 
deviation changes only in proportion to the square root if not the cube root 
of the number of groups. It was found in a former case possible to reduce 
the total deviation to about half by means of only 4 groups. In the 
case of 16 groups the classification was not extended to the individual bases 
MgO, CaO, Na 2 0, and K 2 0, but to the sums MgO + CaO and Na 2 0 + K 2 0. 
In the case of 64 groups these bases were individually treated, as an 
examination of the rock list will show. 
As far as possible the specific gravities of the rocks have also been 
added and means were calculated. In doing so all the vitreous or partly 
vitreous rocks were, however, treated separately, the figures for the latter 
