822 REPORT— 1885. 
perpendicular to the greatest compression, the angle 6’ which it makes 
after distortion will be given by the equation 
tan 6! = “tan 0; 
and if the number of such planes be indefinitely great, the closeness of 
their arrangement, after distortion, in the neighbourhood of the plane 
considered will be proportional to 
cos*8 a 
cos*0! 
This expression becomes ?}for 6’=0, and © for 6’/=90°; so the degree 
c a 
of closeness of the planes in the neighbourhood of the principal diametral 
plane of the strain ellipsoid is to that in the neighbourhood of the plane 
perpendicular to it in the ratio a? : c?, Now let all these planes represent 
Fie. 4. 
Before compression and elongation. After compression and elongation. 
flat fragments such as scales of mica originally arranged at random 
through the rock, and suppose the distortion such that a= 6c. Then 
after distortion the number of scales of mica making angles of less than 
1°, say, with the principal diametral plane will be about 36 times the 
number making angles of less than 1° with the plane perpendicular to it ; 
and it is easy to see that the rock must split with much greater readiness 
along the former plane than along the latter. The number 36, however, 
cannot be taken as giving any precise indication of the relative facilities 
of splitting in different directions, for, in the first place a slate-rock is not 
wholly made up of flat and linear particles, and secondly, the above 
mode of demonstration—that followed by Dr. Sorby and Professor Phillips. 
—takes account only of those flat particles whose planes have their 
strike perpendicular to the direction of compression, or of linear par- 
ticles whose long axes lie in vertical planes parallel to the direction of 
compression. A stricter investigation would be too tedious for insertion 
here. It is sufficient to notice that, according to the mechanical theory 
