EECEEATIVE SCIENCE. 



273 



that there will be three of them ; that they 

 will be of equal length ; and that each one 

 will be at right angles to the other two. To 

 render all this perfectly evident, let a cube of 

 soap or turnip be taken, the diagonals drawn 

 on its faces, and the wires inserted through 

 it to show the position of these internal lines, 

 or axes, as they are usually termed. 



Suppose the query to be asked, What is the 

 longest line that can be placed within a cube ? 

 Take the hollow envelope, and opening one 

 face as a sort of lid, make the experiment with 

 a wire ; it will be found that the longest line 

 which can be placed within a cube, is that pass- 

 ing from one solid angle to the 'opposite solid 

 angle. Furthermore, that there are .four such 

 longest lines, and that they cross or intersect 

 each other at the centre (see Fig. 6) ; hence 

 c B 



Fig. 0. 



they also constitute a second series of axes. 

 And lastly, a third series of axes may exist, 

 passing from the centre of edge to the centre 

 of opposite edge, as shown in Fig. 7. Of 



Fig. 7. 



these there are necessarily six, being half the 

 number of edges. 



Before going any further with the study 

 of this solid, it will be desirable that the 

 student should possess the power of deline- 

 ating it with its axes, and sections, and 

 also the other solids which may be contained 

 within it, as shown in Fig. 8. For this pur- 



Fig. 8. 



pose draw a square of the size required 

 (Fig. 1, D, A, E, h) ; from d draw the line to 

 c, at an angle of thirty degrees with the line 

 D, A ; then from the angles a, b, and H, draw 

 other lines perfectly parallel to d, c. Make 

 each of them half the length of the sides 

 of the square, and then join c and B, 

 B and F, F and g, g and c, and the figure is 

 completed. To draw the three regular axes, 

 the diagonals of the faces should be drawn 

 and the axes made to connect their inter- 

 sections (see Fig. 5). It is highly desirable 

 that these isometrical drawings of the cube 

 be made ; they tend greatly to render the 

 forms familiar to the student, and if the axes 

 and lines of construction are put in in dif- 

 ferent colours from those which represent the 

 edges of the solid, the figures become more 

 distinct, and may be made to form very 

 pleasing, because symmetrical, drawings. 



Suppose a cubical block of stone be given 

 to a workman, out of which he is desired 

 to cut the largest slab that he possibly can. 

 It is obvious that he must cut it diagonally 

 across two faces, and through two edges ; as, 

 for example, through the lines d b, b f, r h, 

 and H D (Fig. 5). In this way he would get 

 a plane section, the form of which would be 



IS 



