308 
most perfectly, not passing straight forwards, but turning 
about according to the manner in which the ultimate parti- 
cles lie in every part. It therefore appears that the fissile 
character of slate is due to a line of structural weakness, 
brought about by the manner of arrangement of the ulti- 
mate unequiaxed particles. The natural cleavage cracks, 
of course, bear the same relation to this arrangement as 
those so often seen in many crystalline bodies do to that of 
their ultimate atoms. They appear, in general, to have 
been mainly due to meteoric agencies ; their position having 
been determined by the structural weakness. In accounting, 
then, for so-called slaty cleavage, it is only requisite to shew 
how such particles could have had their position so changed 
that their arrangement should be altered from that found in 
rocks not having cleavage, to that in those having it ; which 
explanation must, of course, be such as would agree with 
every other fact connected with the subject. 
Now I trust I have already shewn that there is abundance 
of evidence to prove that rocks having slaty cleavage have 
been greatly compressed in a line perpendicular to cleavage, 
and elongated to a certain extent in the line of its dip. 
Taking for the amount of these changes those I have 
already mentioned for the slate of Penrhyn and Llanberis, 
it is easy to calculate mathematically what would be the 
arrangement of the unequiaxed particles in such a rock as 
Water-of-Ayr stone, if its dimensions were so changed. 
Supposing that A = the angle of inclination of the longer 
axis of any unequiaxed particle to the line along which the 
maximum elongation would occur, and that a — this angle 
after it had taken place, we should have, perpendicular to 
cleavage in the line of dip, tan a = ta iL^: ; in that of strike 
tan a = irV^r > anc ^> m tne P^ ane °f cleavage, tan a = ^L^"' 
0. 4 O '1.0 
From these relations it necessarily follows that the particles 
