j44 Mr Haldinger cm the Series of Crystallisation of Apatite. 
and if the more obtuse rhombohedron is so much diminished in 
size, till the horizontal projections of the two forms are equal, 
the axis of the latter will be one-half of the axes of the former. 
The same process of laying tangent planes into the terminal 
edges, applied to the more obtuse rhombohedron of the two, 
produces another still more obtuse ; this rhombohedron a fourth, 
and so on. If the axis of the fundamental rhombohedron is a^ 
that of the first derived will be J a, of the second J a ; J a, 
I a, being three members of a series, which continued on both 
sides, can be represented thus : 
f.n, J.a, \.a, 4.a, S.a 
The ratio of the axis in this series, therefore, is that of 
0^1 QO Ql 02 03 
^ ^ ^ j ^ ^ ^ 
that is to say, the series proceeds according to the powers of the 
number 2. 
In the method of crystallographic designation of M. Mohs, 
the letter R is used for denoting the fundamental rhombohe- 
dron, whose axis is = a. Every derived rhombohedron of the 
series is expressed by the same letter, to which is added that 
exponent of the power of 2, which indicates the place of the 
member in the series, so that the fragment of the series given 
above, will be represented by the following succession of crys- 
tallographic signs : 
R— 3, R— 2, R— 1, R, R-f-1, R+2, R-fS, 
The very idea of a series leads to the inquiry about what will 
be its limits. In the series of rhombohedrons it is evident that 
the limits cannot be attained, till the axis of one of its members 
becomes = 0, or — oo ; for every finite quantity, whether great 
or small, can be multiplied or divided by 2 ; but it is impossible 
to go beyond the values of 0 or oo. In order to obtain 0 for 
the value of the axis in a member of the series of rhombohedrons, 
the axis of R, must be multiplied with 2~'* ; and in order to 
obtain co, the same a must be multiplied by 2^ . The respec- 
tive signs of the two limits will therefore be R — x , and R-f x , 
and those of the series of rhombohedrons between its limits : 
R — X - - - R — 2, R — 1, R, R-j-l, R-p2, R-j-x. 
The horizontal projection of all the members of the series is one 
and the same regular hexagon ; so is also the section perpendi- 
cular to their axes. R — x having the same figure, but an in- 
