ANNIVERSARY ADDRESS OP THE PRESIDENT. xlix 



number of tliem intersected each other withm a space of compara- 

 tively small extent in central Europe, and he appears to have been 

 struck virith this fact. It was, however, only the consequence of the 

 assumption he had expressly or tacitly made in determining the 

 positions of his circles of reference ; for he assumes the lines of 

 elevation of each system to be comprised in a zone which will com- 

 monly be bisected by the great circle of the system, and, since all 

 the lines of his different European systems lie nearly in the same 

 region, many of the corresponding great circles of reference must 

 necessarily meet in the central part of that region. The proximity 

 of these points of intersection to each other seems, however, to have 

 suggested some point near to them for one of the pentagonal centres. 

 It was finally chosen in lat. 50° 46' N. and long. 8° 55' E. of Paris, 

 near to Remda, in Saxony. The second condition was, that the great 

 circle DH of the reseau should coincide vidth the great circle of 

 reference of the system of Tenara. It makes an angle of 13° 9' 41" 

 with the meridian at the point D. It also passes through Etna. 

 The position of the reseau is completely fixed by these assumed con- 

 ditions, but since it may require correction when our data shall be 

 more complete, M. de Beaumont considers the present determi- 

 nation as only 2)rovisional, though, probably, not erroneous in any 

 material degree. He has given, in his work (PI. v.), the pentagon 

 which has its centre near Remda, delineated on a map of the region 

 included in it. It comprises the whole of Europe, a small part of 

 Asia, and a large extent of Northern Africa. The great circles of 

 refe?'ence of all the European systems are also delineated on the same 

 carefully executed map. The pentagon and map are drawn accord- 

 ing to the gnomonic projection on the tangent plane to the earth's 

 surface at the point with which D coincides. 



"We must now proceed to compare the positions of these great 

 circles of reference with the circles of the pentagonal reseau in the 

 determinate position assigned to it. And here I may remark, that if 

 it were the question, whether the coincidence between these two 

 groups of circles were exact or not, it wovild be easy to decide it. 

 The difficulty arises from the fact of the coincidence sought being 

 only approximate, for this involves the further question — is the coin- 

 cidence sufficiently near to justify the conclusion that the general 

 phsenomena of elevation are not only due to a physical cause per- 

 fectly general as regards the whole of the earth's surface, but also 

 such that the pentagonal reseau shall be the accurate geometrical 

 type of the resulting phsenomena ? 



In the first place, we find the great circles of reference for the 

 following ten systems represented on the map as passing through the 

 pentagonal centre D : — 



System of Tenara. 



System of Thilringerwald. 



System of the Rhine. 



System of the Ballon s. 



System of Finisterre. 



System of the Netherlands. 



VOL. IX. d 



