TUANSACTIONS OF THE SECTIONS. 79 



suits, that its cohesive power should vary according to any continuous 

 law in passing in any direction from one point of the mass to another, 

 or according to any discontinuous law in passing along a vertical line, 

 so that a difference of constitution in the successive horizontal strata of 

 a stratified mass is of no importance. The effects of planes of less re- 

 sistance existing iiTegularly in the mass are also taken into account. 



Taking a mass thus constituted, Mr. Hopkins investigates mathema- 

 tically the manner in which fissures will be formed in it when subjected 

 to tensions in assigned directions impressed on it by extraneous forces, 

 and sufficient to overcome its cohesive power. After thus establishing 

 various propositions, he proceeds to apply them to the dislocation of 

 the crust of the earth, the tensions to which the mass is, in this case, 

 subjected being produced by its elevation and consequent extension. 



One of the first inferences from this theory is that the directions of 

 dislocation must in general bear definite relations to what may be termed 

 the actual geological conformation of the disturbed district, i. e., to that 

 external form which would be presented to us if any one originally un- 

 broken horizontal stratum extending throughout the whole mass were 

 at present to form its surface. In many cases it is easy to determine 

 these relations ; in others it is more difficult to do so, particularly in 

 those in which the disturbed district is of limited extent, and irregular 

 form and boundary. If there be a distinct axis of elevation, our system 

 of fissures (always supposing them referrible to the cause here supposed) 

 will be parallel to it, whether curvilinear or rectilinear ; and if another 

 system exist, the fissures composing it must meet those of the former 

 system approximately at right angles. If there be a distinct centre of 

 elevation our systems will diverge from it, and another system may 

 exist concentric about it. The latter kind of elevation will in general 

 be on a much more limited scale than the former, and may be frequently 

 superimposed upon it ; and if this kind of double elevation take place at 

 once, a corresponding modification will result from it in the directions 

 of the fissures. Two or three striking examples of this kind were se- 

 lected by Mr. Hopkins from the mining district of Derbyshire and the 

 adjoining coal district of Nottinghamshire, which, while they appeared 

 to offer obvious exceptions to the law of parallelism as usually inter- 

 preted, are strictly in accordance with his theory. 



Another important inference from this theory is that of the simulta- 

 neous formation of any system of fissures such as above mentioned, as 

 far at least as regards the decided commencement of their formation. If 

 there be two systems, they may either have been formed at the same or 

 at different epochs. 



These fissures must be regarded as the -primary phenomena of this 

 branch of the science. The secondary ones of faults, mineral veins, 

 anticlinal lines, &c. &c. are easily deducible from them. It is im- 

 possible, however, in a limited abstract to enter into the particulars of 

 this part of the subject, which may be found in considerable detail in 

 the author's original memoir, in the Transactions of the Cambridge Phi- 

 losophical Society, vol. vi. part 1 . 



Another view of the phcenomena of elevation consists in regarding 



