PROJECTION IN TWO DIMENSIONS. 13 



X and each other at the point x=^a, y = o, one being 

 situate above the axis and the other below. 



Locus of the Extremities of the Major and Minor Axis. — 

 Both the magnitude of the major axis of the projectrix 

 and its inclination to the axis of x are functions of m. If 

 r be the length of the major axis^ from equation (8) we 

 have 



r= 



-s/i+m*— 'v/(i + 3m*)(i— m*) 



eliminating m between this equation and (7)^ we obtain 

 for the polar equation to the curve traced out by the 

 extremities of the major axis 



""^ V|+(sec^6'-|-)^ ^^^ 



From the form of the equation it is evident that the 

 major axis will hi 

 be the case when 



2c 



major axis will have a maximum value -y-, and this will 



cos 6= v^l-. 

 The form of the curve is shown in the annexed figure, 



E ;■ \ 



Fig 3 



/ '. c 





X^^bJ 



where the dotted curve represents a circle of the dimen- 

 sions of the primitive circle. The curve cuts the axis of 



