130 CORRELATION OF GEOLOGICAL FAUNAS. [bull. 210. 
a brief lapse of geological time. This brief time, represented by the 
preservation of the bionic equilibrium of a faunule aggregate, is taken 
as the measure of the unit of geological time — the hemera. The visi- 
ble expression of the hemera is the temporary fa unule, the analysis 
of which into its constituent species constitutes the faunule list of a 
particular locality (geographically) and particular zone (stratigraph- 
ically ) . 
For the purpose of ascertaining the bionic value of fossils it is 
necessary to know the list of species occurring together in the same 
faunule, or temporary association of species, and the abundance or 
rarity of each in that combination; and second, it is necessary to 
obtain such faunules at frequent intervals separate from one another, 
in order to ascertain how constant is the appearance of the species in 
the general region over which the fauna is distributed. 
The bionic values ma}' be expressed mathematically by recording 
the number of times of appearance. These will then stand as nume- 
rators of fractions of which the denominator is the total number of 
faunules listed. 
When the faunules are from the same formation, but from sepa- 
rate stations, the statistics will show the frequenc} 7 of geographical 
distribution of the species. If the distribution is wide and general 
the numerator will be high, if the species is local in distribution the 
numerator will be low. The place of the species in the general fauna, 
based on such estimate of its bionic value, may be called its distribu- 
tion value, by which will be meanl the power of the species to spread 
itself geographically and to preserve its life under diverse conditions 
of environment. 
In like manner, the frequency of occurence of a species in different 
faunules found at successive horizons throughout the strata of a single 
section will express bionic value of a different kind, viz, the power of 
the species to reproduce itself and maintain its place in the midst of 
the competing species with Avhich it lives. This may be called its 
range value. It will be expressed by a high figure when the species 
appears at a large number of the horizons of the column examined, 
and when it is of rare occurrence in such faunules its numerator will 
be relatively small. 
The third kind of bionic value will be expressed by the abundance 
or rarity of individuals of the species in the particular fauna! combi- 
nation of each faunule. This may be spoken of as frequency value. 
To estimate the predominant characteristics of the fauna, then, 
three measures of bionic values for each species may be summed up, 
and the species whose bionic values of these three kinds (viz, distribu- 
tion, range, and frequency values) reach the highest total average will 
constitute the standard dominant list of species of the particular fauna. 
The application and illustration of these rules are given in the 
preceding pages of this bulletin. 
