826 REPORT—1885. 
lying in the plane of bedding, since its form expresses completely the 
distortion of such objects. If the radius of the original sphere before 
distortion be /, the dimensions of any fossil lying in the bedding-plane 
ee have been altered in the ratio p : k along the dip, 
and in the ratio b: k along the strike. If there 
be no alteration along the direction of the strike, 
b=k; but without making this assumption, we 
may say, in Professor Haughton’s terminology,' 
that the distortion along the dip is ? or the dis- 
tortion along the strike - 
It is of importance to notice that although the 
rock is supposed to undergo an expansion along 
the cleavage-dip, the distortion along the dip of 
the bedding may be either an expansion or a com- 
pression, according as the angle between the bed- 
ding and the cleavage is small or great; for it is 
easy to see from equation (i.) that p may be either 
greater or less than b. If the bedding-plane happen 
to make such an angle with the cleavage that p=b, its strain ellipse is 
a circle, and the fossils suffer no deformation in the bedding-plane. It 
follows from equation (i.) that in this case 
bed 
b? a? 
a ° 
ts a Saami 
a7P 
for smaller values of ¢, p is greater than b, and the distortion of the 
fossils is a relative expansion along the dip of the bed ; for greater values 
of , p is less than b, and the distortion is a compression along the dip. 
If, as Professor Haughton maintains, in the rocks examined by him, the 
strain ellipsoid be one of revolution, having a=b, the circular sections 
must be parallel to the cleavage. In this case there will be no deforma- 
tion of fossils when the bedding and cleavage coincide, but in every other 
position of the bedding relatively to the cleavage there will be a com- 
pression of the fossils in the direction of the dip. These conditions do 
not appear to be always verified even in the localities studied by Professor 
Haughton.” Reverting, then, to the general case, it is manifest that the 
distortion along the dip is an expansion = when the bedding and cleavage 
coincide, and a compression ; when they are at right angles. For any 
other position the distortion 2 may be determined from the equation 
(5) = (2) cost + (2) sary 7 ee a 
* Loe. cit. p. 410. There seems to be some obscurity here. The only two lines. 
which are at right angles to one another, both before and after distortion, are those 
parallel to the dip and strike respectively. 
* Bg.,in the Portmadoce district, both in the Lingula Flags of Borth and the: 
Tremadoc beds of Garth Hill. 
a 
