HARDWICKE'S SCIENCE-GOSSIP. 



latter are more irregular even than in I and 2 

 (see fig. 31), an evidence of still greater hardness, due 

 probably to an increased percentage of silica. In the 

 very quartzose beds of this district — the rocks as seen 

 through a lens being largely composed of grains of 

 quartz — the cleavage is still apparent, although very 

 irregular, and passing through the beds perpen- 

 dicularly, or at very high angles. 



Among other beds in this district, formed of much 

 the same material as those described, but differently 

 aggregated, we may particularise three : — 



(a.) Dark and very hard beds, exceedingly fine- 

 grained ; the cleavage-planes are wider apart than in 

 1 and 2, one inch often intervening between two 

 planes. S. G. 2'659. 



(b.) Hard beds the same as a, but coarse in texture. 

 Brown patches numerous, and plainly visible to the 

 naked eye. S.G. 2 - 688. 



(c.) Still coarser beds of a brownish- white tint. The 

 grains of quartz are distinctly seen without a lens, 

 and are opaque white, and non-crystallised. This 

 rock is in reality a gritstone. The term "sand- 

 stone" is not applicable to any beds described in this 

 paper. Clay-slates gradually appear to merge into 

 gritstones. A chemical and microscopic examination 

 would no doubt reveal other interesting differences and 

 peculiarities in the rocks of this district, but enough 

 evidence has been adduced to prove that they have 

 been metamorphosed, and in different degrees. The 

 cleavage has clearly been formed after the metamor- 

 phic action. S. G. 2"6c;5. 



The refraction of the cleavage-planes propagated 

 through these beds appears to have depended, as 

 has already been pointed out, not on the density of 

 these rocks, but on their relative hardness. No 

 doubt the hard and soft beds differ chemically as 

 well as physically from each other ; the latter are less 

 metamorphosed, and are therefore more argillaceous, 

 or, in other words, less silicious than the harder 

 beds. But the state of aggregation of the particles 

 seems to have had less effect on the cleavage than 

 one might have supposed ; e.g., the beds o and a are 

 both very fine-grained and dark, but the cleavage- 

 planes in the former are very oblique and packed 

 exceedingly close together, whereas in the latter they 

 form large angles with the beds, and are wide apart. 

 As a matter of fact the beds a are much the harder, 

 and are no doubt the more silicious of the two. 



I conceive it to be possible to calculate the relative 

 hardness of two beds from the refraction of the 

 cleavage-planes alone, but extended observations 

 would be necessary in order to obtain a correct 

 formula for the purpose. 



Further north, and quite outside the yellow dots 

 marked on the one-inch map, or in the Bala (?) rocks, 

 beds of very hard clay -slate often show no cleavage 

 at all, while the soft beds exhibit it well. Fig. 32 

 is a typical instance. Indistinct lines of lamination 

 are traceable in (/and e, whereas in/ these lines are 



entirely obliterated by the oblique cleavage-planes. 

 But often, especially when the beds crop out, and 

 have therefore been exposed to weathering action, 

 the hard beds are broken up by almost vertical joints 

 (fig. 33), which doubtless mark the direction of the 

 cleavage-planes in these beds. It would be an 

 interesting experiment to submit alternate layers of 

 some hard and soft substance to great and mechanical 

 pressure, not only to prove the refraction of the 

 cleavage-planes, but also to show their regularity and 

 distinctness in the soft layers, their many infections, 

 and their vagueness in the hard ones. 



Professor Smith referred, some years ago, to the 

 persistency of the westerly dip of the cleavage in 

 Cardiganshire,* but we have seen that, in one portion 

 of the district at least, this is true only with regard to 

 the hard beds ; in the soft beds the cleavage dips E. 

 at a higher angle than the beds. 



E. Halse, A.R.S.M. 



Since writing the above, I have ascertained the 

 density and hardness of the beds a, and b, c, J, &c. 

 (Science-Gossip, Nov. 1881, fig. 144), the result of 

 which proves conclusively to my mind that the 

 refraction of cleavage-planes is due not to the relative 

 density, but to the relative hardness of rocks. The 

 S.G. of a = 2*734, of b &c. = 2782, difference = 

 0*048, or exactly the same as the difference between 

 the densities of the beds 1 and a. But the refraction 

 in the former case is only 23 , while in the latter it is 

 as much as 31 . Now the beds b, c, d, &c, are harder 

 than the beds a, $ ; in the former H = 3, in the 

 latter H = 2'5, while the hardness of the beds 1 and 

 u are about the same. It would appear from these 

 figures that the refraction is directly proportional 

 to the difference between the hardness of the beds, Gi- 

 ft ** , r ■ 



-o~=-T7-> where R = amount of refraction of one 



set of beds, and r of another set, and H the differ- 

 ence in the hardness of one set, and h' of the other set. 

 Substituting x for h\ we obtain the formula 



r' X H 



x — — — — , which, after ascertaining H and R in one 



set of beds, will enable us to obtain the difference in 

 the hardness of any set of beds exhibiting refraction 

 by merely measuring the amount of that refraction* 

 But this law must not be considered as established 

 until repeated observations in different districts have 

 amply verified it. 



Since I last visited the slate-quarry a fresh section 

 has been displayed ; a clinometer now showed the 

 planes a dipping about 8o°, and the beds /', c, &c, 

 about 55 , which gives a refraction of 25 . This 

 shows that the beds vary in relative and absolute 

 hardness at different points ; the irregular lines of the 

 beds a and it are also evidences of variation in hard- 

 ness. To ascertain then the mean refraction of the 



* '■ Memoirs of the Geological Survey," Vol. II., 1848. 



