O DR. J. BOTTOMLEY ON COMPOUND 



Sa denoting the area of the primitive figure, which we 

 may also write A, and X«x denoting the area of some 

 geometrical figure built up by piling one on another the 

 successive projected rectangles. This area we may also 

 denote by A^;. In a similar manner we may pile one on 

 another the projections on lines parallel to the axis of y, 

 and if A^ denote the area of the figure so generated, being 

 the limit of 2c^, we shall have on addition 



A,. + Ay = A/" + Am" = A. 



Of the two axes rigidly connected with the movable area, 

 one may be termed the primitive axis, and the other the 

 complementary axis. If L be the greatest dimension of 

 the curve parallel to the primitive axis, and if we draw 

 parallel to the axis of .r two straight lines distant from 

 each other mL • then, in building up the a?-projection, we 

 have some choice in the manner of doing so, provided 

 that none of the curve so generated lie outside the above- 

 bounding lines. In what follows I have proceeded accord- 

 ing to the method adopted in projecting a solid, given in 

 a previous paper. 



Let the primitive axis AB and complementary axis ED 



