10 Mn HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



cause is the true one. we must shew that, supposing all local and jjartial 

 causes with which we are acquainted to be removed, it would produce 

 effects strictly in harmony with those laws to wliich the actual pheno- 

 mena are observed to approximate. The most obvious cause of deviatit)n 

 in our phenomena from strict geometrical laws, is irregularity in the 

 intensity of the elevatory forces, and in the constitution of the masses 

 on which they are supposed to act. Abstracting these sources of micer- 

 tainty, we liave before us a definite problem, viz., to determine the nature 

 of the effects produced by a general elevatory force acting at any assigned 

 depth on extended ])ortions of the superficial crust of the earth, and witli 

 sufficient intensity to produce in it dislocations and sensible elevations. 

 To this simple and definite form the problem may Ik- reduced; and at 

 least a correctly approximate solution of it iimst necessarily be obtained 

 by some means or other, before wi- can pronoimce on the adei|uacy of 

 the assigned cause to jiroduce tlie observed effects. The complete solution 

 of the problem jiresents many difficulties, which, however, are avoided 

 by restricting ourselves to u first approxhiialion, which will amply suffice 

 for all practical aj)|)lications of our results. This approximate solution 

 is what 1 have now to ofl'er ; and I may b*- allowed to observe, that tliose 

 who may object to the mathematical resources of which I have availed 

 myself, are at least lM)mid to offer a solution eijually conclusive and 

 available by some method more adapted to the general reader. A slight 

 examination however of the problem will suffice to shew that it can 

 admit of no accurate solution indejiendently of reasoning too intricate t»i 

 he clearly eml)odie<l in any language but that of mathematiud analysis. 



The hypotheses from which I set out, with res])ect to the action 

 of tlie elevatory force, are, I conceive, as simple as the nature of the 

 subject can admit of. I assume this force to act under portions of 

 the earth's crust of considerable extent at any assignable depth, either 

 with imiform intensity at every point, <ir in some cases with a some- 

 what greater intensity at j)articular points; as for instance, at points 

 along the line of maxinunn elevation «)f an elevated range, or at other 

 |«)ints where the actual phenomena .seem to indicate a more than or- 

 dinary energy of this subterranean action. I su])po.se this elevatory force, 

 wliatevcr may Ik- it« origin, to act upon the lower surface of the uplifted 



