XXXU PROCEEDINGS OF THE GEOLOGICAL SOCIETY. 



sentiug the ecliptic coincides with the small circle representing either 

 of the tropics, for a very small space on either side of the point of 

 contact. The line of elevation may therefore be considered as he- 

 longing to the same system of small circles, as that small circle with 

 which it coincides. Any other lines of elevation belonging in like 

 sense to the same system of small circles as the first-mentioned line, 

 are said to be 'pavaUel to it. All these lines will be parallel to the 

 same great circle — that of the system of small circles to Avhich they 

 all belong, and are said to constitute ?i parallel system of snch lines. 

 This great circle is of the first importance in our author's theory. 

 He has called it le grand cercle de comparaison. I shall term it the 

 great circle of reference. It defines the characteristic direction of 

 each system of mountain chains or other lines of elevation. 



I have already said that each line of elevation is considered 

 strictly as a portion of a great circle, and only approximately as a 

 portion of a small circle, and that too when the line itself is suffi- 

 ciently short. Were we at liberty to speak of them as really portions 

 of small circles, we might more simply define a parallel system as 

 consisting of lines every one of which w^as parallel to one and the 

 same great circle, in the same sense as that in which a small circle is 

 said to be parallel to the great circle of its system. This definition, 

 though only approximate, does really convey the essential notion of 

 a parallel system of lines of elevation, so far as it forms the basis of 

 the actual investigations of M. E. de Beaumont, the greater part of 

 which lead to results which, though having all the accuracy which 

 the nature of the subject can possibly require, are still, strictly 

 speaking, only approximate*. 



We are now prepared to enunciate the two general prd]iositions of 

 M. E. de Beaumont's theory. The first asserts generally the 

 parallelism of lines of elevation of contemporaneous origin ; and the 

 second asserts the existence of certain symmetrical relations between 

 the great circles of reference of those different parallel systems. 

 The term contemporaneous is interpreted, I believe, by our author 

 in its strict and literal sense, as indicating one great eifort of the 

 elevating forces, and not a succession of minor efforts during a de- 

 tenninate and comparatively short geological period. The nature of 

 the symmetrical relations above spoken of will be explained when I 

 come to the explanation of the second part of this theory. 



Let us now proceed to the application of the preceding consider- 

 ations. Suppose we have any number of lines of elevation, such as 

 mountain chains, anticlinal and synclinal ridges and valleys, faults, 

 &c., the position of each line being known by the latitude and longi- 

 tude of its middle point, and the angle which it makes with the 

 meridian at that point, i. e. the point of the compass to which it is 



* If through the middle pomts of any number of lines of elevation, we draw 

 great circles perpendicular to those lines respectively, and these perpendiculars 

 all meet one and the same great circle at right angles, then will the lines of 

 elevation be parallel to each other. This is the way in which our author de- 

 fines a system oi parallel lines. It is manifestly equivalent to that given in the 

 text. The one great circle to which all the others are perpendicular is the great 

 circle of reference of the system. 



