First. 
Second. 
Notation. 
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392 Mr. WuHEWELL on the Classification 
By the law of right derivatives a form is deduced by retaining 
the base, and changing the axis in any ratio (p : 1). 
The number p is called the index of right derivation, or the 
first index. 
By the law of scalene derivatives a form is deduced as follows. 
A plane is made to pass through one angle of the base, parallel 
to the slant side passing through the next angle, and is determined 
by the manner in which it cuts the diagonal, or perpendicular 
drawn in the base, through the next angle. In the square and 
oblong-pyramidal systems the plane would intercept, in the 
diagonal produced, a line which is in a given ratio (m : 1) to 
the semi-diagonal. In the rhombohedral system it is in such 
a position, that it would intercept in the perpendicular produced 
a line which is in a given ratio (m : 1) to the perpendicular. 
Thus in the square and oblong-pyramidal system (Fig. 2.) let 
MC'=m . MC, and let C'V’ be parallel to CV. The figure bounded 
by all such planes as BC’V’ will be the one derived by the second 
law from BCI. 
In the rhombohedral system let CM be the perpendicular of 
the triangle (Fig. 1.). Let MC’=m.MC, and C'V’ parallel to CV. 
The figure bounded by all such planes as BC’V’’ is derived by the 
second law from BCY. 
In the octahedral system the process is the same as in the 
square pyramidal, with the understanding, that any one of the 
lines drawn from the center to the angles may be made the 
axis. 
In all these cases the number m is the index of scalene de-. 
rivation, and the form is said to be derived according to m. 
By means of these two laws of derivation may be obtaimed 
any form or face whatever, of which these respective systems are 
susceptible. 
Let O, P, Q, R represent the fundamental form in the octa- 
