177 
the families to be represented in it should be somewhat comparable to reflec- 
tions on two mirrors showing images of objects lying between the mirrors 
placed at an acute angle, while the families in the present system are com- 
parable to images on two mirrors placed at an obtuse angle. Consequently, the 
ideal system showing all the relations of every two or every group of more than 
two of all the families, separately as well as jointly, successively as well as simul- 
taneously, is something like a net of infinite extent with innumerable millions of 
crystal beads, each on a mesh of a different colour, and each reflecting the 
images of other beads, according to the illustration used above. (ce. f. p. 104.) 
Now, I come to an explanation of the system in particular. As the 
dynamic relations of the series have been fully discussed under the review of 
ENGLER’s principles and his system in the foregoing pages, I shall here limit 
my explanation to the relations of the families. In so doing, however, in order 
to prevent needless repetition, the explanation of the relations of each two 
families or the literature bearing on the same subject is given in almost all 
cases only once, either under the heading of one of the latter two families, or 
under that of the series to which one of the latter two belongs. For example, 
the relation of families A—B, when it has been referred to or explained 
under family A, is omitted under family B. When the reader finds the latter 
is the case, as he is regarding family B in the explanation of the dynamic 
system, and desires to know the explanation.of the relation of the families 
A-B, he is requested to refer to the heading of family A, using the index 
given at the end of this paper, and examine the explanations under the latter 
family where he will find the information desired or reference to it. 
Subdivision ANGIOSPERMZE 
Class MonocoTYLEDONER 
Series I. Pandanales 
1 Typhacew”: These are related to the Sparganiacew in the axillary 
inflorescence and in the distichous leaves. At the same time, they show some 
resemblance to the Pandanacew in the structure of the male flowers. 
1) Images of an object on two mirrors placed at an obtuse angle are two, while those on two 
mirrors at an acute angle become four, five, six,...., as the angle diminishes. 
2) Nat. Pfl.-fam. II.—1, p. 185; Graven, P. —Typhacee, in das Pilanzenreich IV.—8, pp. 6-7. 
