31 



Ordinary Meeting, January 13th, 1885. 



Professor W. C. Williamson, LL.D., F.E,.S., President, 

 in the Chair. 



"On the Composition of Projections in Geometry of Two 

 Dimensions," by James Bottomley, D.Sc, B.A., &c. 



(Abstract) 



In previous papers (Proceedings, Vol. XXI., p. 188, et seq. ; 

 Memoirs, Vol. VIII., third series, p. 218, et seq.), the author 

 considered the application of a new kind of projection to the 

 geometry of solids. The kind of projection there contem- 

 plated has its analogue in geometry of two dimensions. The 

 projections to be compounded in the first case are those of a 

 line on a line, and of a plane on a plane; in this case the 

 projections to be compounded are those of two lines on two 

 lines. As in three dimensions we ma.y derive from a solid 

 three solids of variable volume, but subject to the condition 

 that their sum is constant, so in two dimensions, from any 

 area bounded by straight or curved lines, may be derived 

 two areas such that their sum is constant, though each is a 

 variable magnitude, if we suppose the primitive area to re- 

 volve round any axis perpendicular to its plane. In the 

 present paper the author considers the question, given the 

 equation to the primitive curve, to find that of the projected 

 curve. If the primitive curve be a circle, the curve derived 

 from it will be an ellipse, the magnitude and inclination of 

 Peoceedings — Lit. & Phil. Soc. — Vol. XXIV.— No. 5. — Session 1884-5. 



