TERMINOLOGY. . 111. 



ries. Let ACXB be the principal section of R. Produce 

 the axis AX, and from the points B and C draw lines paral- 

 lel to it ; every line drawn perpendicularly from these upon 

 the axis, will be equal to the side of the horizontal projec- 

 tion of R. 



The inclined diagonal of II becomes the terminal edge 

 of R + 1. The inclined diagonal of R + 1 passes through 

 the point S, the centre of the inclined diagonal XC of R. 

 Hence draw the line AB' through S, and produce this line 

 till it arrives at the parallel from C ; AB' will represent 

 the inclined diagonal, BAB'X' the principal section, and 

 AX' = 2. AX consequently the axis of R + 1. 



The inclined diagonal of R + 1 becomes the terminal 

 edge of R 4- 2. The inclined diagonal of R + 2 passes 

 through S', &c. Draw the line AB" till it arrives at the 

 parallel from B ; AB" will be the inclined diagonal of 

 R + 2, AB'X"B" its principal section, and AX" = 2. AX' 

 == 4. AX its axis. 



Thus, considering AB" as the terminal edge of R + 3, it 

 will be found, that AB'" is its inclined diagonal, AB"X'"B"' 

 the principal section, and AX"' = 2. AX" = 4. AX' = 

 8. AX the axis of R + 3 ; and in this manner we may con- 

 tinue the series, as long as we please. 



The axis of R being = a, that of R + 3 is = 2 3 .a, that 

 of R + n = 2 n . a, that of R + n + 1 == 2" + . a. These 

 values substituted in the expressions . 50., give the cosines 

 of the terminal edges for any required member of the series 

 of rhombohedrons. 



.111. LIMITS OF THE SERIES OF RHOMBOHEDRONS. 



The limits of the series . 110. are, on one side 

 a plane perpendicular to the axis, on the other a 

 regular six-sided prism of an infinite axis. The 

 transverse section of that prism is equal and paral- 

 lel to the transverse section of the fundamental 

 form ; the figure of the plane perpendicular to the 



