ANNIVERSARY ADDRESS OF THE PRESIDENT. XXXIU 



directed. Our object is to ascertain whether these Hues can be 

 grouped into parallel systems, and if so, to determine the great circle 

 of reference of each system. If we wish to construct these great 

 circles by the graphical method, we must proceed as already 

 indicated. We must mark these lines with great care on a terrestrial 

 globe, and then through their middle points draw great circles 

 respectively perpendicular to them. Supposing this operation to be 

 performed with perfect accuracy, and the given lines to belong to a 

 certain number of parallel systems, that fact would appear by the 

 accurate convergence of the great circles perpendicular to the 

 respective lines all converging to a certain number of points, each of 

 which would be the pole of the corresponding system of lines. 

 These poles being thus determined, the corresponding great circles 

 of reference are immediately known. 



In actual practice it would be impossible to perform this operation 

 with absolute accuracy, and the consequence would be that the great 

 circles which ought to converge exactly to the respective poles of the 

 different systems would only pass near to them, and thus by their 

 mutual intersections would indicate approximately the positions of 

 the poles, instead of determining them with perfect precision. 



Instead of adopting this graphical method, we might proceed by 

 actual calculation from the data above stated ; and in doing this, we 

 might either adopt methods which would give us results of mathe- 

 matical accuracy, or those which give only approximate results, but 

 still of sufficient accuracy for all the purposes we have in view. 

 These latter methods, being in general infinitely more simple than 

 the exact methods, are those usually adopted in all complicated 

 geometrical and physical researches, and have been generally followed 

 by the author of the investigations before us. 



I have here supposed the given lines of elevation to be capable of 

 being accurately grouped into distinct systems. It is not, however, 

 to be expected that the entire number of such lines, as they exist in 

 nature, should admit of being so grouped into a comparatively small 

 number of accurately parallel systems. Whatever, therefore, might 

 be the precision with which our graphical process should be per- 

 formed, we might still expect that the great circles perpendicular to 

 the given lines of elevation, instead of passing exactly through a 

 certain number of poles, would only pass near to them, in the same 

 manner as above described under the supposition of the graphical 

 process being hiaccurately performed. In such case each system of 

 lines would have no exact pole, and no exact great circle of reference. 



Another source of indeterminateness in the positions of these cir- 

 cles must necessarily exist in the imperfect determination by obser- 

 vation of the directions of the lines of elevation. The possible 

 errors from this cause must probably ever remain considerable, on 

 account of the want of more definite character in many of the phse- 

 nomena to be observed. 



I have hitherto spoken of a grouping of our lines of elevation into 

 separate systems, depending only on the directions of those lines. 

 There is also another obvious principle on which we may group 



VOL. IX. c 



