156 TERMINOLOGY. . 143. 



longing to the combined forms. If A, or A', or both at the 

 same time change their places, G', G', &c. necessarily must 

 change theirs likewise. 



The straight line GG', joining the points G' and G, is 

 the intersection of the faces of the two forms, and repre- 

 sents, therefore, their edge of combination (. 142.) ; it lies, 

 on that account, both in the plane ABGG', or in the face 

 ABC of the one, and in the plane A'B'GG', or in the face 

 A'B'C' of the other pyramid. Hence it appears that the 

 situation of the line GG' depends upon the relations of the 

 bases, or of the horizontal projections, and upon those of the 

 axes ; or in gen'eral, upon the dimensions of the combined 

 forms themselves. 



If we now produce the obtuse terminal edges AB and 

 A'B' of the combined pyramids, till they intersect each 

 other in F ; F will again be a point common to both the 

 forms. Hence it follows, that F, G and G' must be situ- 

 ated in one straight line ; and that if the one of the va- 

 riable points F and G' moves, the other likewise must be 

 affected by this alteration. This demonstrates the imme- 

 diate dependence of the situation of F upon the dimensions 

 of the combined forms. 



The horizontal plane HZ intersects the obtuse terminal 

 edges of the pyramids in E and E'. The situation of these 

 points, or their distance from the centre M, is likewise va- 

 riable ; but it depends upon the dimensions of the combined 

 forms, exactly as the rest of the variable points, and be- 

 comes determined for determined forms. 



Thus the length of the lines EF or E'F will be perfectly 

 determined, being a function of the above-mentioned re- 

 lations. 



The line EF or EF' is termed the Line of Combination. 

 Its length can be measured by comparing it with the ter- 

 minal edge, or with the diagonal, of which it is a part, or 

 in which it lies, if produced to a sufficient length. A single 

 equation is sufficient for expressing this line in the rhom- 

 bohedral system. Two expressions are required in the 

 pyramidal system, on account of the differences arising 



