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



I was led by this passage in Smith's ' History ' to more 

 closely examine the cubes, together with the box in which 

 they are contained. The box is mahogany, and it is fastened 

 by hasps of an old-fashioned pattern ; it is itself manifestly 

 in an old style of work. One of the cubes is made of hard 

 wood, the other consists of a brass shell or frame, in which 

 two pieces of hard wood fill up the vacant space so as to con- 

 stitute a complete cube. The brass work was not a casting, 

 but the result of combining pieces of hammered or sheet-brass 

 suitably cut out which were welded or soldered together, and 

 the whole was manifestly finished by the use of file and 

 hammer. The only mark on the brass is the number 1, 

 placed on a part of the shell as a guide for inserting one of 

 the supplementary wooden pieces. This figure is undoubtedly 

 in the old style, and Mr. Yeates is distinctly of opinion, that 

 the brass work is old-fashioned, as he satisfied himself, by 

 comparing it with old brass instruments, that it could be very 

 well assigned a date in the early part of the eighteenth 

 century. It was most probably the work of an amateur, or 

 done under the direction of a mathematician for a special 

 object ; for if it had been made by an instrument-maker for 

 the purpose of sale a number of similar brass cubical shells 

 could more easily have been made by casting. 



I have never seen any demonstration of the structure of the 

 cubical shell, but it soon appeared manifest that it is based on 

 the properties of a square. Lay off on the diagonal of one of the 

 faces of the cube from its middle point two parts, each equal 

 to half the side of the cube. Draw lines at the extremities of 

 these perpendicular to the diagonal, and two isosceles right- 

 angled triangles will be formed which constitute the bases of 

 two equal triangular prisms, between which a cube equal to 

 that from which the prisms were cut can slide. If the cube 

 slides parallel to the faces of the original cube the prisms 

 will be totally unconnected, and the whole problem turns 

 upon their material connexion while allowing the sliding cube 

 to pass between them. 



The annexed figures show the cubes separately, and also 



that a second cube of the same dimensions may be passed through the 

 same, the possibility of which he has demonstrated, both geometrically 

 and algebraically, and which has been actually put in practice by the 

 ingenious Mr. Daniel Voster of Cork, with whom I saw two such cubes." 

 (Smith's ' History of Cork,' 1st edition, 1750, vol. i. p. 172.) This passage 

 is quoted by Gibson, who says that Daniel Voster was probably father 

 to Elias, the author of the Arithmetic. But this is not correct — Daniel 

 was the son of Elias, as I find from the eighth edition published in 1766 

 that Daniel was editor of the book to which the name of Elias is prefixed 

 as the author, 



