Ivi PROCEEDINGS OF THE GEOLOGICAL SOCIETY. 



geometrical theory. I may not, perhaps, have accurately caught his 

 meaning, but it is e'sdclent that the distinction now pointed out 

 cannot be omitted in any definite theory on the subject. There is 

 only one limited position of a system in which the lines might be 

 equally regarded as belonging to a parallel of a -o?ie-system, or to 

 the divergent system of afuseaic. It is that which is distant by 90° 

 from each of the two diametrically opposite points in which the great 

 circles of the fiiseau meet ; for in that position small portions of the 

 diverging great circles of the fuseau will be parallel to each other, 

 according to M. Elie de Beaumont's definition of the term. This 

 remark applies, very approximately at least, to a limited system like 

 any one of our author's European systems, which may be considered 

 either as a part of a more extended parallel system comprised in a 

 zone between two small circles, and having its own great circle of 

 reference ; or as a part of the divergent system of ^l fuseau of which 

 the extreme points are distant 90° from the centre of Europe. On 

 approaching nearer to either of those points by extending any one of 

 these systems considerably beyond its European boundaries, the 

 hues of the fuseau would begin to have a sensible convergence 

 towards its exti-emity, and would no longer be even approximately 

 coincident with those of our author's parallel system, unless the 

 fuseau were much narrower than M. de Beaumont appears to con- 

 template. 



Setting out, then, vdth mechanical considerations, I should be 

 more ready to admit, as the general law of contemporaneous systems 

 of lines of elevation, the divergency of the fuseau than the parallel- 

 ism of the zone. I do not, however, insist upon the conclusiveness 

 of any mechanical reasoning in a case where the conditions of the 

 problem are so imperfectly known to us. M. de Beaumont's theory 

 of parallelism is a geometrical and not a mechanical theory, and 

 must be established or refuted by the observed geometrical cha- 

 racters of the phsenomena, and not by abstract mechanical reasoning. 

 At the same time, the geologist, whatever may be his faith in the law 

 of parallelism in the extended sense in which our author insists upon 

 it, will necessarily look for an explanation of its physical and me- 

 chanical significance. I confess that I am, myself, very imperfectly 

 satisfied with that which M. de Beaumont has given. 



After the formation of one system of lines of elevation, whether 

 parallel in a zone or divergent in a fuseau, a continued shrinking of 

 the internal nucleus would, according to this theory, gradually with- 

 draw its support from the internal surface of the solid shell, till it 

 should again suffer a sudden collapse, from which another system of 

 lines of elevation would result ; and in a similar manner we may con- 

 ceive the successive formations of any number of such systems. If 

 each system be regarded as a parallel system, its direction, as we 

 have seen, is represented by its great circle of reference, i.e. the 

 great circle parallel to the zone in which the system lies ; or if each 

 system be regarded as that of & fuseau, its direction might be repre- 

 sented by the great circle bisecting the fuseau. And here we may 

 naturally ask, whether we can derive from any mechanical view of the 



