Geometric Properties of the Magnetic Curve. 315 



Fig. 4, 



is perpendicular to the axis N a?', N S is the constant differ- 

 ence between the cosines of the polar angles c' N x and c S x. 

 When C S X is an obtuse angle, as in Fig. 5, the cosine of its 



Fig. 5. 



supplement C S N (or SX) added to that of C N S (or N X), 

 will, in like manner, be found to give the constant sum N S, 

 provided the other extremities, n and s, of the revolving radii 

 continue to be in a line perpendicular to the axis ; as will 

 readily appear by inspecting the figure. 



On this principle I have contrived the following instrument 

 for describing mechanically the magnetic curve. 



The ruler N n, Fig. 6. is furnished with a sliding collar, 

 which, by means of a screw, may be fixed at any point in its 

 length. The collar has a hole at the edge of the ruler, for the 

 passage of a pin, which fixes it to a board (previously covered 

 with a sheet of paper), at the point intended as the pole N ; 

 so that the ruler may turn round this point as a centre. 



