410 The Rev. S. Haughton on Slaty Cleavage, 



with many geologists I adopted Mr. Sharpe's views, and have 

 from time to time collected data for forming a more precise me- 

 chanical theory than that put forward in general terms by Mr. 

 Sharpe. I was, in short, convinced that if the theoiy were true, 

 it would bear accurate numerical investigation, and admit of 

 being stated with great precision. With a view to this numerical 

 testing of the theory, I have accumulated a great number of 

 observations and measurements of distorted fossils, which I think 

 are suflScient to enable me to state precisely the laws of slaty 

 cleavage and distortion of fossils. 



I shall now proceed to state the results I have arrived at, and 

 to illustrate them by detailed examples ; and I shall afterwards 

 point out the extent to which Mr. Sharpens results agree with 

 my own, and how far they anticipate them. 



The first fact observed by me was the following : — 



I. If the trace or intersection of the plane of cleavage and plane 

 of bedding be drawn, the greatest distortion or elongation of the 

 fossils lying in the plane of bedding is parallel to this intersection. 



In explanation of this law, it should be stated that each species 

 of fossil has a certain normal undistorted form which may be ascer- 

 tained, and that the measurements of the different parts bear, 

 within certain narrow limits, a constant ratio to each other; so that 

 when we examine a distorted fossil, we can calculate the amount 

 of relative extension or compression it has undergone in any 

 direction. Suppose, for example, that we draw any two lines at 

 right angles to each other, and that the ratio of M to N is the 

 ratio of the measurements of a known fossil shell taken parallel 

 to those two directions, and that the ratio of m to n is the ratio 

 of the measurements of the distorted fossil taken in the same 

 directions ; then, if we denote by p the distortion parallel to M, 

 we shall have 



m N ... 



P-n^'U W 



If the fossil had been originally of a circular shape, it would 

 become an ellipse by distortion, and p would be the ratio of two 

 rectangular diameters, which in one case become the axes of the 

 ellipse ; and it is plain, from the properties of an ellipse, that 

 the maximum value of the fraction denoted by p will correspond 

 with the axes of the ellipse. 



I have calculated the value of p repeatedly, from measure- 

 ments made on fossils from different districts of the south of 

 Ireland, North Wales, Cornwall, and Devonshire, and have always 

 found that the major axis of the ellipse of distortion is parallel 

 to the intersection of the planes of cleavage and bedding. Having 

 thus obtained a tangible starting-point for my theory, I began to 



