BioLoGy AND MATHEMATICS 245. 
Knows neither weal nor woe, knows 
Neither praise nor blaming. 
To unknown lands I stride in war, in whirlwind. 
I know no aim, no end and no beginning. 
I beget and I destroy, not prating, never angry, 
The elephant and the worm, the 
Wise man and the foolish. 
So live as all live. Float out on the 
Flood eternal 
One instant brief, and vanish then forever. 
Presume not stupid-bold with me to wage a contest, 
With me eternal mother of all living and all dead.”’ 
So thunders Nature with a million voices 
In hail, in surge, in storm-wind and the lightning. 
So much for the continuity world-scheme in biology. 
But the latest advances in mathematics have rendered 
unnecessary for biology the wearing of this mis-fit garment. 
The new mathematics gives now a standpoint for the expla- 
nation and treatment of natural phenomena from which the 
individuality of the biologic elements need not be suppressed. 
It has triumphed for its own domain in cases where the con- 
tinuity methods were wholly inapplicable, where arithmology, 
discrete mathematics was called-for and victorious. 
Such are the problems which relate to the properties of 
whole numbers, solved so brilliantly in number-theory. 
Such again are the questions relating to the enumeration of 
the geometric forms within parameters which satisfy given 
conditions. These even in the simplest cases showed themselves 
insoluble until finally between 1860 and ’70 the French math- 
ematicians created special discrete methods. Thence sprang a 
wholly new branch of mathematics, Enumerative Geometry. 
A third, an epoch-making universe of discrete mathematics 
is the wonderful Invariant Theory of the great Sylvester and his 
brother-in-arms Cayley, two men whose loss left the English- 
speaking world without a single mathematician of first rank, of 
the rank of Hilbert and Poincaré. 
In chemistry this discrete mathematics has shown itself of 
such use and power that we may assuredly say chemistry owes 
its present stand-point almost wholly to two lines of advance 
both discrete, the atomic structure theory of Kekule, and 
Mendelieev’s periodic system of the chemical elements. 
The brilliant and rapid advances in chemistry have come 
not from suppressing but from stressing the individuality of the 
elements. Its mathematics has been essentially discrete. 
- The arithmologic scheme of chemical research, the atomic 
structure theory of Kekule, coincides completely with the scheme- 
of the symbolic invariant theory, though both were worked out. 
independently. 
