THE NORMATIVE AVERAGE DENSITY 383 



more abundant, and. therefore in general the less interesting, rocks. An- 

 other objection is that, in the case of many regions, the number of 

 analyses is too few to be really representative; while a third one is that 

 we can deal only with rocks near the surface and not with those at depths 

 which place them beyond our reach, except through crustal movements. 

 Each of these and other possible objections has some validity and is en- 

 titled to careful consideration, into which we can not enter here; they 

 will be discussed in the professional paper referred to above. It may be 

 said, however, in brief, that the force of these objections does not seem to 

 be as great as is supposed by some. In any case, data such as these are 

 the only ones available to us at present ; so that we should make the best 

 use of them which we can, without resorting to the very dubious pro- 

 cedure of applying so-called corrections, which are mostly based on per- 

 sonal opinions or estimates, and thus introduce quite uncertain subjective 

 elements and very possibly errors of unknown magnitude, as to either 

 extent or direction. The results presented here and in the future paper 

 are thus to be regarded as a first approximation to a solution of the prob- 

 lem, admittedly tentative, but sufficiently accurate to permit us to judge 

 of the direction and the order of magnitude of the differences. 



METHOD OF CALCULATION 



The average chemical composition of the area having been obtained 

 from the analyses, it is recalculated to 100 per cent. It is best to retain 

 the amounts of Ti0 2 , P 2 5 , and MnO, but the other minor constituents 

 may be disregarded. The percentage amount of Avater (H 2 0-(-) may be 

 retained, following the plan of Iddings; but I prefer to calculate the 

 densities on the basis of a water-free rock. My reasons for this, in brief, 

 are : although water is present in the rock magma or lava and also in the 

 original rock, yet the amount shown in the analysis can scarcely ever 

 represent this accurately; in many rock specimens much of the water is 

 present through alteration; lastly, but of great importance, much of the 

 water (H 2 0+) shown by the analysis does not exist as liquid water, but 

 as "combined water" or as hydroxyl, and we have no means of knowing 

 what density to assign to it. The density would certainly not be 1, almost 

 certainly more than 1, and the reciprocal of such a small value has a very 

 serious effect on the calculation of the density. I have, however, calcu- 

 lated all the densities on the two assumptions of a water-free rock (8 a ) 

 and one which contains the water shown in the chemical average (8 W ). 

 Both assumptions lead to the same results as regards the relation between 

 density and altitude, as we shall see. The calculated densities for water- 

 bearing rock are less than those for water-free rock; the loci and curves 



