228 

 Since 



PRACTICAL MATHEMATICS 



A 



sn 



Then 



_ cos 2 6 sin 2 6 



P z f 



r 2 cos 2 6 r 2 sin 2 6 _ 



FIG. 59- 



Let the co-ordinates of the point R, with reference to the axes 

 OX and OY, be x and y. 



Then r cos = x and r sin = y 



Therefore ~ + ^ = 1 - 



This is the equation to an ellipse whose semi-axes are p and q, 

 and the point R must lie on this ellipse. It follows, therefore, 

 that if P and Q, the principal moments of inertia, are known, 





VA" 

 ^ 



and q = ^ TZ, the semi-axes of the momenta! ellipse 



can be calculated. This ellipse can then be drawn, and if any 

 radius be drawn and its length measured to the same scale as 



^ 

 p and q, the moment of inertia about that radius = -^. 



