ANNIVERSARY ADDRESS OF THE PRESIDENT. XCVU 



at the commencement of his researches, and of which he availed him- 

 self in his lectures. He points to the advantages which the graphic 

 and trigonometrical methods each possess, observing that though the 

 former so well addresses itself to the eye, the latter more correctly 

 gives the mean of numerous observations. 



"The fundamental problem," observes M. Elie de Beaumont, after 

 alluding to the systems of small arcs of great circles, "presented by 

 a like system of small arcs observed on the surface of the globe, where 

 they are marked by the crests of mountains or by the outcrop of beds, 

 consists in determining the great circle of comparison, to one of the 

 elements of which each of the small arcs observed is parallel. 



" The small arcs determined by observation may be generally con- 

 sidered as being themselves infinitely small secants, or tangents to so 

 many small circles resulting from the intersection of the surface of 

 the sphere with planes parallel to the great circle of comparison, 

 forming the equator of the whole system. Each of these small circles 

 is a parallel with respect to the equator of the system ; it has the 

 same poles as it, and these poles are the two points where all the 

 great circles perpendicular to the small arcs, constituting the system 

 of parallel traces determined by observation, intersect. 



"The problem arising from such a system of parallel traces ob- 

 served on the surface of the globe consists in determining these two 

 poles, or, what amounts to the same thing, its equator ; i. e. the great 

 circle of comparison to which each of the small arcs observed may be 

 considered as parallel. This determination, M. Elie de Beaumont 

 observes, would be easy, and might be made after two, or at least a 

 few observations, if the condition of parallelism was rigorously satis- 

 fied : since, however, this in general is but approximatively accom- 

 plished, the determination of the great circle of comparison can only 

 follow from the means of numerous observations, well-combined with 

 each other ; and thus, while the observations are not very multiplied 

 or spread over a wide space, we can only advance towards this deter- 

 mination by successive approximations." 



M. Elie de Beaumont then points out the mode of arriving at the 

 results proposed, — one which requires to be studied in the memoir 

 itself, on account of the necessary formulae and tables. Employing 

 the method adopted, he enters into great detail respecting the evi- 

 dences of the systems treated of. 



With respect to the Westmoreland and Hundsriick system, one 

 referred to a geological date posterior to the Silurian rocks, including 

 the tilestone, but anterior to the old red sandstone or Devonian rocks, 

 M. Elie de Beaumont passes in review the different localities in 

 Europe which he includes in it, commencing in the north, and taking 

 a mean for the direction of the small arc of the great circle traversing 

 the centre of the locality. This gives for Lapland a direction of E. 

 22° 30' N. ; for Esthonia, E. 17° N. ; for Wisby, in the Isle of Goth- 

 land, E. 22° 30' N. ; for the Grampians, E. 38^ N. ; Keswick, West- 

 moreland, E. 37° 30' N. ; Church Stretton, Shropshire, E. 42° N. 

 Falmouth, Cornwall, E. 45° N. ; Freiberg, Erzgebirge, E. 27° 55' N. 

 Hof, Frankenwald, E. 28° N. ; Prague, Bohemia, E. 28° 40' N. 



VOL. V. — PART I. g 



