APRIL 12, 1901.] 
the work which should be done by the 
electrochemist in the laboratory, and finally 
decribes the training which the students in 
the Polytechnic Institute in Zurich receive. 
The point which is of chief interest here is 
that mathematics is required for every chemist, 
and physics is introduced in the broadest 
way into the course of every chemist. 
The scientific importance of this address 
is much greater than would be implied by 
its title. The question arises whether 
much that was said by Lorenz does not 
apply to other branches of science or, per- 
haps, to all, although it is true that some of 
the natural sciences, chiefly on account of 
the relative complexity of the phenomena 
dealt with, are not yet sufficiently advanced 
to enable the mathematical methods to be 
extensively applied to them, yet they are 
all rapidly approaching that stage which we 
may describe as the mathematical. 
Take as an example the science of chem- 
istry. Physics, the furthest developed of 
all the natural sciences, has long since be- 
come an exact or mathematical science. 
It has been only a short time since a stu- 
dent could get on fairly well in most 
branches of chemistry without any knowl- 
edge of the higher mathematics. But how 
different to-day? A chemist now who is 
not familiar with the calculus can have no 
adequate conception of the theoretical side 
of his science, as Van’t Hoff and others 
have repeatedly pointed out. In inorganic 
chemistry, at least in its latest develop- 
ments, the calculus is absolutely essential, 
since inorganic chemistry is touched at all 
points by physical chemistry, and who can 
know anything of physical chemistry with- 
out the calculus. Take on the other hand 
organic chemistry. There are certain very 
important phases of this subject into which 
the higher mathematics has not yet entered ; 
but in the study of the velocity of organic 
reactions, of the chemical dynamics and 
SCIENCE. 
571 
statics of such reactions, not only the cal- 
culus is required, but also a fair knowl- 
edge of thermodynamics. In physical chem- 
istry a knowledge of the higher mathematics 
and of physics is just as essential as a 
knowledge of chemistry itself, and thus it 
goes through the whole field of chemistry. 
A student who starts out to-day to be- 
come a chemist without a good knowledge 
of physics and mathematics is hopelessly 
handicapped at the outset, no matter to 
what division of chemistry he may turn his 
attention. 
In other branches of science we already 
see the dawn of the exact or mathematical 
period. ‘Take physiology, one of the most 
complex of the biological sciences. Certain 
phenomena of life have already lent them- 
selves to mathematical treatment, as is 
shown by the work of Loeb and others. 
The application of physical chemistry to 
physiology seems to mark the introduction 
of the mathematical method in dealing 
with the physics and chemistry of life. 
Take morphology—the work of Daven- 
port shows that even structure can be 
treated by the exact method, and makes it 
probable that the morphologist in the 
future will have to look to his higher 
mathematics. 
Other branches of science might be cited, 
but these suffice to show how rapidly the 
mathematical method is coming to be ap- 
plied to all scientific knowledge. Perhaps 
the most distinguishing feature of scientific study 
at the beginning of the twentieth century is the 
"introduction of the mathematical method into all 
those branches of knowledge which are suffi- 
ciently developed. 
One of the most important features, 
therefore, in scientific training to-day is a 
thorough course in the elements of the 
higher mathematics, and this should be 
followed in every case by an equally thor- 
ough course in physies. The student who 
is not thus equipped can never hope to pass 
