6 



DR. J. BOTTOMLEY ON COMPOUND 



II. On the Composition of Projections in Geometry of Two 

 Dimensions. By James Bottomley_, B.A., D.Sc.^ 

 F.C.S. 



Read January 13th, 1885. 



In previous papers (Proceedings, vol. xxi. page i88 et seq. ; 

 Memoirs, vol. viii. 3rd series, page 218 et seq.) it has been 

 shown how, by the composition of two projections, namely, 

 of that of a line on a line, and of that of a plane on a 

 plane, we may derive from a solid another solid of which 

 the volume bears to the volume of the former the ratio w% 

 where n denotes the cosine of the angle between the primi- 

 tive axis and the fixed axis. The kind of projection there 

 contemplated has its analogue in geometry of two dimen- 

 sions. The projections to be compounded in this case are 

 those of two lines on two lines. As the simplest case, let 

 Oa^, Oy be two fixed rectangular axes, and ABC a rectangle 



in the plane of these axes ; let / and m be the cosines of 

 the angles made by AC with O.^" and Oy. Project AB on 

 O.^' ; then we shall have 



DE = mAB. (i) 



