arid Mmeralogy, 157 
nearer the axis or middle point ? those sections will truncate 
the edges of the original rhomboid : from which will arise the 
form of a combination of two rhomboids^ having the edges of com- 
bination parallel^ and consequently exhibiting the same relation 
in their dimensions as those two preceding rhomboids (1), accord- 
ing to the order in which they were named, as Fig. 4. PI. VIII, 
15. Eapressim of the propoidion between the two rhomboids ^ 
by means of their axes. — To give the foregoing proportions a 
more convenient expression, suppose the horizontal projections 
of the rhomboids, or the sides of those projections, to be equal, 
the axis of the new rhomboid (12) will then become equal to 
hay' the axis of the original rhomboid. It follows, that, if two 
rhomboids produce parallel edges (f combination with each other^ 
the axis of the one must be half that of the other ^ the horizontal 
projections being equal. This is merely the proportion between 
the two rhomboids, expressed by their axes, on the supposition 
of equal horizontal projections. The absolute dimensions of the 
rhomboids must be such, that both together may be capable 
of contributing to bound the solid. 
16. That proportion universal. — On each of the rhom^ 
bolds formed by the foregoing process (12), the same process 
may again be repeated. A new rhomboid in its turn will result, 
whose axis, if the horizontal projections are equal, being half 
the axis of the rhomboid immediately preceding, will conse- 
quently be fitted to produce parallel edges of combination with it. 
Yl ., Inversion of the process. — The process (12.) may be in- 
verted. Draw the diagonals : through every two oblique and 
one horizontal diagonal, extend cutting planes, and deduct the 
portions which lie without them. The remainder, the part in- 
closed within the cutting planes, will likewise be a rhomboid. 
18. Proportions of the new rhomboid. — The axes of both 
these rhomboids are equal. The horizontal projection of the 
new rhomboid is the fourth part of the horizontal projectiou be- 
longing to the original rhomboid ; the sides of the former are 
equal to half those of the latter : and consequently, when the 
horizontal projections are considered equal, the axis of the se- 
condary will be double that of the original rhomboid. 
19. This proportion is likewise universal.-^Thh process 
may be continued indefinitely (16); and of all the rhomboids 
