. 119. OF THE CONNEXION OF FORMS. 125 



position from the other regular six-sided prism, which li- 

 mits the series of rhombohedrons. The faces of the two 

 prisms differ in their situation for 30 and 150 : and the 

 prisms therefore themselves are two different well defined 

 forms, which must not be confounded with each other. 



If, in the algebraic expressions in . 54., m is made = |, 

 and 2 2n . a 2 is substituted for a 2 ; the expressions produced 

 refer to the cosines of the edges for P + n. They are : 



cos.x = _(?l!^L7\ ; 

 V4.2 2 .a 2 + 27' 



cos.z = _(ll?^ZL?7Y 

 V4.2 2 .a 2 + 27' 



The series of isosceles six-sided pyramids between its 

 limits, receives the following designation : 

 R_ co ... P + n ... P+ co. 



Several members of this series, together with its limits, 

 occur in rhombohedral Fluor-haloide, rhombohedral Quartz, 

 rhombohedral Corundum, &c. There exist also series 

 appertaining to rhombohedrons of certain subordinate se- 

 ries, and which, on that account, receive a co-efficient in 

 their representative sign, like the rhombohedrons from 

 which they are derived. Examples of the series | P + n, 

 3 P + n, and P + n, have been found in rhombohedral 

 Corundum ; of the two first also in rhombohedral Quartz, 

 of the first in rhombohedral Iron-ore, &c. 



4. DERIVATIONS FROM THE HEXAHEDRON. 



. 119. DIFFERENT POSITIONS OF A MOVE ABLE 

 PLANE. 



A plane, moveable round the terminal point of 

 a rhombohedral axis of the hexahedron, is liable 

 to assume four different classes of positions. One 

 of these is exactly determined, and admits of only 



