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tinct from the feather, the eagle, ami others, with which they 

 have been hitherto confounded, and wliich he represents by 

 the Hebrew Aleph. 



The Rev. Charles Graves, F.T.C.D., read a paper " On 

 the Application of Analysis to spherical Geometry." 



The object of this paper is to investigate and apply to 

 the geometry of the sphere, a method strictly analogous to 

 that of rectihnear 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 

 ox, OY, be drawn ; then if arcs be drawn from Y and x 

 through any point p on the sphere, and respectively meeting 

 ox and ov in m and n, the trigonometric tangents of the arcs 

 OM, ON, are to be considered 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 ;/ represents a great circle ; an equation of the second 

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

 the «'* degree, between the spherical coordinates x and y, 

 represents a curve formed by the intersection of the sphere 

 with a cone of the «''' 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" = »« {« - «'0> 



y-y"= m' {x - x"), 

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

 values of a; and y to be used in the transformation of coordi- 

 nates would be 



