﻿Yol. 64.] QUANTITATIVE METHODS TO THE STUDY OF EOCKS. 205 



the original constituent fragments and the interspaces. These are 

 then accurate^ cut out with scissors and their weight determined 

 separately, from which the percentage of the interspaces can be 

 at once calculated. The volume of the very minute interspaces 

 existing in the grains themselves cannot thus be determined, but 

 is not needed for the purpose in hand. The method which I have 

 adopted in determining the interspaces in the whole rock as it now 

 exists, is to boil thoroughly a portion in water in a flask, and tightly 

 cork it when full of hot steam, so that on cooling there is a partial 

 vacuum. After remaining for a lew days the fragment is taken 

 out, the loose water removed, and the weight of the fragment full 

 of water determined. If thought necessary, the process may be 

 repeated, so as to make sure that there is no increase in weight. 

 The fragment is then dried until its weight is constant. The specific 

 gravity of the rock being known, the volume of the open spaces 

 can then be easily calculated. Those completely closed may be 

 neglected for the purpose in hand, though in all cases they may 

 cause the determinations to be somewhat too small. There are 

 cases in which these two methods give nearly the same result, 

 but others in which they are absolutely different, •on account of 

 changes since deposition. 



In order to clear the way for subsequent descriptions, it may be 

 well to state a few general conclusions applicable to the case when 

 the grains may be treated as if they were spheres. Deposited 

 quickly and shaken very slightly, the interspaces may amount to 

 nearly half the volume, but the grains are theu in a state of 

 unstable equilibrium. On shaking, a sort of equilibrium is 

 established, when the tendency to settle into smaller volume aud 

 the resisting friction are nearly equal, in which case the interspaces 

 amount to about 40 per cent, of the volume. Another much more 

 stable equilibrium is when the grains, probably under greater 

 pressure, have arranged themselves so as to occupy the smallest 

 space without their shape being altered, namely, where the inter- 

 spaces amount to about 26 per cent. Another final condition occurs 

 rarely and partially in limestones that have been subjected to the 

 intense pressure which produced slaty cleavage, when the original 

 interspaces have been almost or entirely obliterated. It will thus 

 be seen that the detailed study of sandstones and some allied rocks 

 is a very special, wide, and complex subject, which is likely to lead 

 to a new class of results. 



Application to Particular Rocks. 



For some of the purposes of this paper limestones are by far the 

 most suitable. Thin sections of coarse-grained sandstones are 

 difficult to prepare, and teach so little that I have made very few. 

 Considering how many thin sections of limestone I have made, 

 very few are suitable for calculations, because the three axes of 

 the original fragments are not sufficiently equal to enable us to 

 treat them as spheres. In some cases, where the original deposit 



