226 



If the two polar summits be entirely removed, there is laid bare 

 either a janal polyedron or a janal reticulation at either pole. The 

 two opposite reticulations have the same marginal signature, which 

 differs in nothing that needs here be noticed from that of a polar reti- 

 culation. This is reducible at either pole by the external primary 

 effaceables, or if it be a janal full reticulation, by its external second- 

 ary effaceables, either to a janal polyedron, or to a janal full reticula- 

 tion, or to & primitive, or to a fundamental janal reticulation] and 

 this reduction is possible in one way only. 



A. fundamental janal reticulation is made thus: Let a primary 

 polar plane reticulation, i. e. one which has no diagonals but the 

 bases of its marginal triangles, and no summits besides those of those 

 triangles, be laid on a mirror, with the triangles a little raised from 

 the mirror. The reticulation and its image form a fundamental janal 

 reticulation. 



If the primary be turned in any way about an axis perpendicular 

 to the mirror, while the image remains stationary, we have a primitive 

 janal reticulation. The edges in the mirror, common to both polar 

 faces, are the submargins of the polar faces, on which primitive sub- 

 margins rhombotomous tessaraces can be planted at pleasure in janal 

 coronation. 



The marginal triangles of the fundamental are all doubled, and the 

 bases of the pairs are zonal effaceables. Some only of the marginal 

 triangles of the primitive are doubled, and the bases of the pairs are 

 zonoid effaceables. 



There is only one way in which a given janal reticulation can be 

 constructed on a fundamental or on a primitive. The rules for con- 

 struction differ little from the rules for polar reticulations, and we 

 conceive that the marginal charges are imposed alike in the opposite 

 polar faces, thus preserving janal or contrajanal symmetry. Inspec- 

 tion of our signatures gives us the result in all cases. 



The janal reticulation is registered with its marginal signature, 

 which of course is the same at either pole, with its zonal signatures, 

 principal and secondary, and with its zonoid signature if it have second- 

 ary zoneless poles. 



An account is kept, in all constructions on a fundamental or primi- 

 tive, of primitive plane submargins, because it is on these only that 

 rhombotomous tessaraces can be deposited in janal coronation. These 



