570 Scientific Proceedings, Royal Dublin Society. 
shell composed of four layers will be slightly different. Where 
a limited number of similarly constituted shells are present in 
an assemblage of the nature indicated, there may be very little 
difference in the closeness of the packing of the different shells if 
the cncrements of the distances between similar ball centres found 
as we travel outwards from shell to shell, and caused by the 
increase of circumference, be compensated by an appropriate 
decrement in the radial distances and consequently in the thickness 
of succeeding shells; the solid contents of the spaces contained 
between the successive corresponding spherical surfaces being thus 
made equal. 
The other kind of wniform curvilinear distortion of a thin plate 
possible, viz. cylindrical curving is, it is evident, equally available 
with the spherical curving just referred to, when suitable homo- 
geneous assemblages are selected for modification.? . 
Besides these two kinds of distortion, Joca/ distortions piodicei 
local increase of closeness of packing are conceivable. The effect 
of these will naturally be the same as that of local shrinkages in 
thin solid bodies, and like these be productive of local torsional 
twists. 
Finally, a torsional twist, uniform along the length of a capil- 
lary assemblage of sufficient fineness, may increase closeness of 
packing in some cases. 
Assemblages consisting of large linked groups will especially 
lend themselves to the production of the modified homogeneity 
referred to. Thus wedge-shaped groups will be likely to pack 
closer when put together to form an arch if the assemblage is a 
thin one. 
A fundamental condition, in all cases, Siders is that the dis- 
tortion from the corresponding homogeneous arrangement shall 
not materially shorten or lengthen the distance separating two 
ball centres which touch one another. For, if it did, the centres 
could not continue to have approximately the same general 
arrangement throughout the assemblage. . 
Applying this condition, we see that if some of the lines which 
1 The axes of an assemblage may be inclined to the axis of the cylinder. If they 
are, their directions will, after distortion, become screw-spirals. 
