228 Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 
accurately follow under the influence of the principal cause 
alone to which they are referrible. The coincidence between 
these perfectly definite laws and those deduced from our as- 
sumed general cause, independently of perturbing ones, must 
afford the strongest test of the truth of our assumption. The 
strength of the evidence thus derived, will of course depend 
in such cases upon the accuracy of the approximation to de- 
finite laws in the observed phazenomena ; but it is important to 
observe, that this first approximation must always be the most 
important one, and that it must be made the instant we begin 
to speculate on the causes of such phenomena as I have al- 
luded to, if the slightest value is to attach to our speculations; 
and also that accurate (or what is synonymous in all, or at 
least in all but the simplest cases,) mathematical methods of 
investigating the effects which would result from our assumed 
general cause, are just as necessary in the case we are sup- 
posing, as if the observed phenomena presented accurate co- 
incidences with the general laws to which they only approxi- 
mate. 
These remarks (sufficiently trite perhaps) are made with 
the view of meeting directly the vulgar objection of the use- 
lessness of applying mathematical investigations to geological 
problems. ‘To assert this is, in fact, equivalent to the asser- 
tion that that branch of the science with which we are imme- 
diately concerned presents no phzenomena characterized by 
general laws, or referrible to a definite and simple cause. 
Such however is not the case. The phenomena do distinctly 
approximate to obvious geometrical laws, and there is a sim- 
ple cause to which they may be referred, the effects of which 
it has been my object in the memoir in question to investigate 
on mechanical principles, in order that we may compare the 
laws obtained from these results with those to which the ob- 
served phenomena are found to approximate. 
The phenomena with which we are chiefly concerned in 
these investigations are those dislocations of the crust of the 
globe, which we recognise more particularly in faults and 
mineral veins, or rather in the narrow fissures in which what 
is properly termed the mineral vein is deposited. ‘The latter 
phenomena might, in fact, be almost entirely comprehended 
in the former, since it is found very generally, where mineral 
veins occur in stratified masses, that the strata are somewhat 
higher on one side of the vein than the other. In general 
this difference of level (not exceeding, perhaps, a few feet) is 
not sufficient to be designated as a fault, though it sometimes 
increases so much as to be considered such. In these cases 
it would appear absurd to suppose that the fissure of the 
