412 The Rev. S. Haughton on Slaty Cleavage, 



the planes of cleavage ; from this fact we may infer that a line 

 perpendicular to the plane of cleavage is also an axis of the ellip- 

 soid, and that the third axis will lie in the dip of the cleavage 

 plane and perpendicular to the other two axes. 



If we assume the axes of the ellipsoid to be a, b, c, the axis of 

 a being the intersection of cleavage and bedding, the axis of z 

 perpendicular to the cleavage plane, and the axis of y in the dip 

 of the cleavage plane ; if </>, </>' denote the angles made with the 

 plane of cleavage by two planes of bedding, both passing through 



the axis of x ; and if -, -7 be the distortions in these planes esti- 

 p p' 



mated parallel to the intersection of cleavage and bedding, then 



it is easy to see that we have the following equations from the 



nature of an ellipsoid : — 



sin^ <f) cos* <l> 1 ^ 



^ b^ ~~ p^ 



sin*<^' cos*<^' 1 



11 ' .' 



Solving these equations for -r and -, we find — 'srf ^o 81 



o c 



(3) 



(sin (f> sin </>' \ /sin <^ sin <^'\ 

 * 1/ sin (</) + </)') sin (<^ - ^0 





(cos^' cos<^\ /cos</)' C0S</)\ 



sin (<^ + </>') sin (</) — ^') 



. (5) 



From equations (4) and (5) we can calculate -r and — , which 



are the distortions in the dip of cleavage and perpendicular to 

 cleavage, referred to the distortion in the intersection of cleavage 

 and bedding as unity. All that is requisite, in order to know 

 the complete form of our ellipsoid of distortion, is to ascertain 

 the distortion of fossils in two planes making difi*erent angles 

 with the plane of cleavage. This I have succeeded in doing in 

 a few instances, which no doubt could easily be multiphed if the 

 attention of observers were directed to the subject. I shall now 

 mention a few of the instances in order. 



Example 1. — Carboniferous Slate of Ardoginna near Ardmore, 

 Co. Water ford. 

 The fossils made use of to determine the distortion in these 

 slates were Orthis crenistria, Athyris concentrica, and Spirifer 



