218 DR. J. BOTTOMLEY ON THE EQUATIONS AND ON 



XXII. On the Equations and on some Properties of 

 Projected Solids. By James Bottomley, B.A., D.Sc, 

 F.C.S. 



Read March i8tb, 1884. 



On a former occasion I brought before the Physical and 

 Mathematical Section of this Society a proposition in 

 projection, in which it was shown how, by the composition 

 of two projections, namely, of that of a line on a line, and 

 of that of a plane area on a plane area perpendicular to 

 the aforesaid line, we could derive from a solid three solids 

 with axes perpendicular to three planes at right angles 

 and of variable volume, the variation being subject to the 

 condition that the sum of the three volumes is constant 

 and equal to that of the primitive solid. 



I now propose to solve the following problem : Given the 

 equation to the primitive solid to deduce that of a derived 

 solid. 



Let the equation to the primitive solid referred to three 



rectangular axes be 



f{x, y, z)=o. 



