Prof. H. Hennessy on Ronayne's Cubes. 185 



the penetration of the second cube through the brass which 

 forms the frame of the first. 



The prisms must be connected at top and bottom by two 

 similar and equal flanges, the edges of which must lie between 

 the diagonal of the cube and the extreme corner of the flange. 

 If too far from the diagonal, connexion with the prisms would 

 cease ; if too close to the diagonal, the second cube could not 

 pass between the flanges. 



The geometrical conception of a cube and the material 

 solid representing such a conception to the sight and touch 

 are different things. It is easy to conceive how one geome- 

 trical cube can pass through another of equal dimension by a 

 square opening whose diagonals are perpendicular to the 

 sides of the first cube. The triangular prisms left by this 

 opening would be equal; but they would touch by mere 

 lines, and could not be represented by a continuous solid 

 material substance. They would necessarily be distinct and 

 separate. 



If the second cube were passed through the first parallel to 

 the diagonal of the square on one of its faces, two triangular 

 prisms would be cut off each distant from the other by the 

 side of the cube. The sides of the base of each prism p would 



be manifestly p = a yl— —^) and the long sides a(S~2 — 1). 



But these prisms would again be unconnected. They could 

 be connected by triangular flanges having knife-edges, and, 



