158 Mohs’s System of Crystallograiiliy 
that result from it, any tw6 following in immediate succession 
will always exhibit such mutual proportions, as to produce pa- 
rallel edge^ of combination with each other. 
50. Series according to the powers f S.— All those rhom- 
boids which are produced by a given operation (that of IS, 17, 
or both,) are consequently subject to the general law, tJiat^ 
their horizontal projection being equals their axes must increase 
or diminish as the powers ftlie number S. These axes, there- 
fore, follow each other in a geometrical progression, and the 
rhomboids constitute a series, which may be developed out of 
any given member, and expanded indefinitely on both sides. 
51. Designation f the series. — Let the fundamental rhom- 
boid be designated by r ; the next more acute one, obtained 
from the second process (17), by r -b 1, so that this expression 
may point out the rhomboid’s place, or its distance from r; the 
next more obtuse one, obtained from the first process (IS), 
by r — 1, so that by this means the distance or the position, 
with regard to r, may in like manner be expressed ; and the rest 
in a similar mode ; then if the axis of r is put = 1, the first of 
the three following lines will represent the series of rhomboids, 
the second their axis, and the third those powers of S by which 
they are expressed. 
- - ~ r — S.r — S.r — l.r. r-f-l.r-fS.r-fS 
I , i . i . 1. S . 4. 8 . 
S-3. S-2. S-l. S-®. s^ . s^ . s^. 
SS. Limits. — These progressions may be prolonged oh both 
sides as far as we please (16. 19.) The horizontal projections 
being equal, the axes by this means perpetually augment on the 
one hand, and perpetually diminish on the other. If they be- 
come infinitely small, the rhomboids are converted into regular 
six-sided prisms^ the one of which has an axis infinitely great, 
the other an axis infinitely small. These prisms are named the 
limits to the series f rhomboids ; their designation is r + oo : 
and hence within its limits the series is 
r — 00 r — 1 . r. r -p 1 . . . . r - r -f oo 
Base of the regular Rhomboid Unlimited re- 
six-sided prism. whose axis gular six-sided 
— 1 . prism. 
