100 ON THE TABLES OF MODIFICATIONS. 



supposed to take place. The angle at which the two 

 planes d, resting on P', meet, may be supposed to 

 increase until those planes would nearly approach to 

 one plane, corresponding with class b or the angle 

 at which the two planes d, which meet at the edge of 

 the cube, incline to each other, may approach nearly 

 to 180, when those two planes would nearly become 

 one analogous to class c. Or if the two planes d, 

 which meet at the edge of the cube, be conceived to 

 incline more and more on that edge, they will at 

 length approach nearly to the position of the planes 

 of class f y but they can never coincide with those 

 planes. 



These remarks on the nature of the differences 

 which may be conceived to exist among the individual 

 modifications belonging to some of the classes con- 

 tained in the following tables, might be easily ex- 

 tended to all. But it will not be difficult for the 

 reader to apply them himself to all the other variable 

 classes contained in the tables. The nature of the 

 variation, however, in many of the classes, will be 

 pointed out in the tables. 



When the sets of new planes, resulting from the 

 individual modifications belonging to any one of the 

 classes, are so much extended as entirely to efface 

 the primary planes, a series of entirely new solids 

 will result. The planes of these new solids will 

 generally possess one common character throughout 

 the series ; that is, their planes will generally be all 

 triangular, or all quadrilateral, or all pentagonal, or 

 be of some other polygonal form ; but the planes be^ 

 longing to each individual of the series, will differ 

 from those belonging to every other individual, in 

 their angles, or the relative lengths of some of their 

 edges. 



But although it is general/^/ true that the planes of 



