Xlii PROCEEDINGS OF THE GEOLOGICAL SOCIETY. 



The centre of reduction of the great circle of reference for each 

 system, and its orientation, are investigated and determined, I shall 

 not here pursue this descriptive part of the subject, but shall recur to 

 it in the sequel. I proceed now to explain the second part of our 

 author's theory — that which assigns certain relations between these 

 great circles of reference. 



Theory of the Reseau Pentagonal. 



After having devoted so much attention to his theory of the paral- 

 lelism of mountain chains of contemporaneous elevation, and the 

 determination oi\h^ great circles of reference, it was natural to expect 

 that M. de Beaumont would be led to the examination of the rela- 

 tions which might exist between these great circles. He appears to 

 have long had the impression that these relations must be relations 

 of symmetry. I know not whence he derived these a-priori impres- 

 sions, but it would seem that they must have amounted almost to 

 conviction, to have induced him to undertake the laborious and 

 intricate calculations which have been necessary to enable him to 

 place his views in the form in which they are now brought before us. 

 And here. Gentlemen, whether we may agree with the views of this 

 distinguished geologist or not, let me claim the highest praise for the 

 candour with which he has developed them. Every step in the 

 process of his investigations has been explicitly stated, and all his 

 numerical calculations appear to have been elaborated M'ith the utmost 

 care ; and where their results are only approximate, no pains have 

 been spared to ascertain the probable errors to which they are liable. 

 In these respects he has left nothing in the mathematical part of his 

 investigations to be desired. 



After having established the positions of his great circles of refer- 

 ence, he was anxious to observe more especially the relations existing 

 between the directions of the great circles of his European systems. 

 For this purpose it was necessary to reduce them all to one centre. 

 This was done by drawing a great circle through the proposed centre 

 at right angles to any assigned great circle of reference, and then 

 drawing another great circle, also through the centre, perpendicular 

 to that previously drawn at right angles to the great circle of refer- 

 ence. The second circle thus drawn through the centre was parallel 

 to the great circle of reference, and therefore represented it in direc- 

 tion at the assumed centre. The circles of reference thus reduced to 

 one centre were represented by lines radiating from that centre, and 

 thus affording convenient means of comparing their respective di- 

 rections. 



Vannes, a town in the north-west of France, was first chosen as 

 the centre, and several great circles having been reduced to that 

 point, instances of approximate parallelism between some of these 

 circles, and of approximate perpendicularity between others, were re- 

 marked ; while some of the angles appeared to be bisected or trisected 

 by other lines, facts which seemed to indicate a certain degree of 

 symmetry. To examine these and similar facts the more carefully^ 

 our author finally chose three different centres — Milford Haven in 



