MY CLASS IN GEOMETRY 



45 



of a cube having a base five inches square, and a wedge and pyra- 

 mid of similar base and height. The second series comprised a cyl- 

 inder, sphere, and cone, each five inches broad and high. Taking 

 the first series, a moment's comparison of the sides of wedge and 

 cube told that one contained half as much wood as the other ; but 

 that the pyramid contained a third as much as the cube was not 

 evident. Weighing the pyramid and cube brought out their re- 

 lation, but a more satisfactory demonstration was desirable, fdr 

 what was to assure us that the two solids were of the same specific 



Fig. 1. 



Fig. 2. 



gravity ? Taking a clear glass jar of an accurately cylindrical 

 interior, measuring seven and a half inches in width by ten in 

 height, it was half filled with water, and a foot-rule was vertically 

 attached to its side. The models, which were neatly varnished, 

 and therefore impervious to water, were then successively im- 

 mersed and their displacement of the water noted. This proved 

 that the pyramid had a third the contents of the cube, that the 

 same proportion subsisted between the cone and cylinder, and 

 that the sphere had twice the contents of the cone. Dividing the 

 wedge by ten parallel lines an equal distance apart, I asked how 

 the area of the smallest triangle so laid off, and that of the next 

 smallest, compared with the area of the large triangle formed by 

 the whole side of the wedge. " As the square of their sides/' was 

 the answer. Dipping the wedge below the surface of the water 

 in the jar, edge downward, it was observed to displace water as 

 the square of its depth of immersion. Reversing the process, the 

 wedge became a simple means of extracting the square root. 

 Dividing the vertical play of its displacement into sixteen parts 

 drawn along the jar's side, we divided the wedge into four parts 

 by equidistant parallel lines. Then, for example, if we sought the 



