determine
these, one of the series must be chosen as the fundamental form, and
for this purpose a tetragonal pyramid of the first variety, designated
by Ρ as its sign, is selected. The angle of one of its edges,
especially the middle edge, found by measurement, determines its
angular dimensions ; while the proportion of the principal axis (a) to
the lateral axes supposed equal to 1, gives its linear dimensions. The
parameters, therefore, of each face of the fundamental form are 1 : 1 :
a.
Now if m be any (rational) number, either less or greater than 1, and if from any distance ma in
the principal axis planes be drawn to the middle edge of P, then new
tetragonal pyramids of the first kind, but more or less acute or
obtuse than P, are formed. The general sign of these pyramids is mP,
and the most common varieties 1/2P, 2P, 3P ; with the chief axis equal
to 1/2, twice or thrice that of P. If m becomes infinite, or =: oo, then the pyramid passes into a prism, indefinitely extended along the principal axis,
