XXXVl PROCEEDINGS OF THE GEOLOGICAL SOCIETY. 



tion of this theory, to keep these two classes of cases carefully 

 distinct. The former alone can furnish the e^ddence on which the 

 theory must rest. 



Again, in estimating the force of the induction from these esta- 

 blished cases, we must recollect that there are systems of lines of 

 elevation characterized by directions differing widely from each 

 other, but which would appear, at first view at least, to be referable 

 to the same geological period. Such cases will necessarily demand 

 a scrutinizing examination of the evidence on which the assertion of 

 the independence of such systems of lines of elevation is made to 

 rest ; for if no geological evidence, independent of the theory itself, 

 can be found for assigning distinct epochs to sets of lines character- 

 ized by different directions, the force of induction from those cases 

 where independent evidence does exist of a relation between epoch 

 and direction, vdll be diminished in a degree proportional to the 

 ratio which the number of exceptional bears to that of the established 

 cases. This, in fact, is the veiy point on which our acceptance of 

 this part of our author's theory must depend. 



I have already remarked that the theory of M. de Beaumont, as 

 now laid before us, consists of two parts : — first, that which asserts 

 the contemporaneity of origin of those lines of elevation which have 

 the same characteristic direction (with the exception of those cases 

 which present recurrences of the same direction) ; and secondly, that 

 part which asserts certain relations of symmetry between the great 

 circles of reference which respectively define those characteristic 

 directions. The first part would not require any very accurate 

 estimate of the limits of error in the determination of the positions 

 of these great circles, but such an estimate is so important in the 

 discussion of the second part of this theory, that I must here again 

 direct your attention to this point with more especial reference to 

 the European systems described by M. de Beaumont. 



Let us then suppose that we have a number of lines which belong 

 accurately to one parallel system. If through any two of these 

 lines we draw two great circles accurately perpendicular to them 

 (and which, for the greater distinctness, we may suppose to pass 

 through the middle points of the lines), these great circles will 

 intersect in the pole of the system to which the lines belong. 

 Suppose the position of one of these two lines to be accurately 

 given, but the other to be determined with a small error, as to its 

 direction. The direction of the great circle perpendicular to it will 

 be affected with an equal error. Now if the angle between the two 

 great circles be large, the coi\sequent error in the position of the 

 point of their intersection will be only small ; but if the angle 

 between these two great circles be small, the consequent error in 

 their point of intersection will be comparatively large. The case 

 is exactly analogous to that of two straight lines intersecting each 

 other at a small angle and passing through two fixed points ; a 

 small change in the angular position of either line will make a com- 

 paratively large change in the position of the point of intersection. 

 Thus, suppose one system of lines to be a real system situated in 



