232 



PRACTICAL MATHEMATICS 



Also 



p = A = 0-6928 



and 



q = = 1-732 



These are the semi-minor and semi-major axes of the momental 

 ellipse. 



yi 



(1) r 30 * = 0-78 I 30 o = -__ = 16-44 



(2) r 45 o = 0-91 I 45 ,=-J1_ = 12-08 



(3) y- M4 V -_-= 7-69 



These results may be verified by calculation for 

 I a = P cos 2 a + Q sin 2 a 



I 30 - 20-83 cos 2 30 + 3-333 sin 2 30 

 = 16-45 



I 45 o = 20-83 cos 2 45 + 3-333 sin 2 45 

 = 12-09 



I 60 o = 20-83 cos 2 60 + 3-333 sin 2 60 

 = 7-718 



