406 P)'of. T. G. Bonney — Eemarhs on Serpentine. 



be proved by the properties of conjugate diameters that the ratios 

 of the axes of the ellipsoid of distortion will be, 



J=| (V l+m= cosec^ a-f 2m + Vl+m^ cosec' a— 2m ) 



. \^'^^ 



1=^\ (v 1+m^ cosec^ a+2m — V 1+m^ cosec^ a— 2m. ) 



b 



And by means of the equation to the ellipse, taking for the 

 co-ordinates b cos and b sin 0, 



o , 1 , 1 + m^ coseo^ a — 2m^ 



cos- = 1+ -^ ---^ (2) 



2 (Vl+m^ cosec^ aY—Am'' 



Since m cannot be greater than unity, nor cosec a less than unity, 

 the second term is always positive. Hence, cos^ is always greater 

 than -J, and less than 45°. The inclination of the cleavage to the 

 shear will commence at this angle, and diminish continually as the 

 shear increases. 



To express the alteration in the dip of the bedding, or of any 

 other plane, caused by the shear, supposing its inclination to the 

 direction of the shear to have been ^ and to become yjr, it can be 

 proved that, 



cot Y^ = cot ^ + cot a. 



It must be remembered that a is not independent of m. But 

 practically m might be taken as unity, and then, if by means of the 

 observed distortion of an object, we could find either of the ratios of 

 the axes of distortion, we could find a the angle of shear, from the 

 corresponding equation of (1) ; and the inclination of the plane of 

 cleavage to it from (2); and, the dip of the cleavage — being 

 known from observation, we should then know 6, the dip of the 

 shear ; or the direction in which the movement took place : ignoring 

 subsequent disturbances. 



IV. — Remarks on Serpentine. 

 By Prof. T. G. Bonney, D.Sc, F.E.S., Pres. G.S. 



rj^HE very full and able review of Dr. Sterry Hunt's paper on 

 X " The Geological History of Serpentine," ^ gives me an 

 opportunity, of which I have been for some time desirous, of com- 

 menting on certain parts of it relating to my investigations of the 

 t^'pical rock which bears that name. In commenting adversely 

 upon these, I must not be supposed to express a difference of 

 opinion in regard to every part of the paper, because thei'e are many 

 relating to the Archgean schists with which I am in general agree- 

 ment. 



In a matter of this kind, where so much depends on the meaning 



of a word, it is necessary to be clear and precise in our definition. 



No term has been more vaguely used than ' serpentine.' In the 



first place, it is applied both to a mineral and a rock. Again, in the 



1 See page 276 of the present volume. 



