532 Royal Irish Academy. 



the distance to be 23" (see Memoirs of the Royal Astronomical So- 

 ciety, vol. iii. p. 265), since which time it has been decreasing at the 

 rate of more than half a second per annum. The angle of position 

 scarcely appears to have changed since the time of La Caille ; whence 

 it may be inferred that the relative orbit is seen projected into a 

 straight line, or a very eccentric ellipse ; that an apparent maximum 

 of distance was attained in the end of the last or the beginning of 

 the present century ; and that, about twenty years hence, the stars 

 will probably be seen very near each other, or in apparent contact ; 

 but the data are at present insufficient to give even an approxima- 

 tion to the major axis of the orbit and time of revolution. 



VI. Observations of the beginning and end of the Solar Eclipse 

 of July 18, 1841. By Dr. Cruikshank. Communicated by G. 

 Innes, Esq. 



The eclipse was observed at Fyvie Castle, in latitude 57° 26' 40' /- 7 

 north, and longitude 9 m 32 s * 6 west, where there is a good clock by 

 Hardy and a fine transit instrument. The magnifying power of the 

 telescope used was about thirty. 



h m 8 s 



Time of the beginning of the eclipse. 2 15 4 ; uncertain to 10 

 Time of the end 2 57 30 2. 



ROYAL IRISH ACADEMY. 



[Continued from p. 397.] 



May 24, 1841 (Continued) .—The Rev. Charles Graves, F.T.C.D., 

 read a paper " On the Application of Analysis to spherical Geo- 

 metry." 



The object of this paper is to investigate and apply to the geo- 

 metry of the sphere, a method strictly analogous to that of rectilinear 

 coordinates employed in plane geometry. 



Through a point O on the surface of the sphere, which is called 

 the origin, let two fixed quadrantal arcs of great circles O X, O Y 

 be drawn ; then if arcs be drawn from Y and X through any point 

 P on the sphere, and respectively meeting O X and O Y in M and 

 N, the trigonometric tangents of the arcs O M, ON are to be con- 

 sidered as the coordinates of the point P, and denoted by x and y. 

 The fixed arcs may be called arcs of reference. An equation of the 

 first degree between x and y represents a great circle ; an equation 

 of the second degree, a spherical conic ; and, in general, an equation 

 of the nth degree, between the spherical coordinates x and y, repre- 

 sents a curve formed by the intersection of the sphere with a cone 

 of the rath degree, having its vertex at the centre of the sphere. 



Though it is not easy to establish the general formulae for the 

 transformation of spherical coordinates, they are found to be simple. 



Let x and y be the coordinates of a point referred to two given 



arcs, and let x', y' be the coordinates of the same point referred to 



two new arcs, whose equations as referred to the given arcs are 



y — y" = m(x — x"), 



y — y" = m' (x — x' 1 ), 



x", y" being the coordinates of the new origin ; then the values of 



