ISO 
THE SCIENTIST. 
pure reason is all we need. And 
who can say what may be the out- 
growth of a closer application of the 
methods of the Ausdemu} gslehre or 
Extensirm-Calculus of Grassman ? 
The discovery of Sylvester's The- 
orem inckidiDg the particular case 
of Newton's rule, and of Fourier's 
Theorem, including that of Descartes' 
I'ule, both of the utmost importance 
in the Theory of Equations, are 
additional examples of the acquisi- 
tions to the realm of science made 
in modern times b}" the labors of 
mathematicians. 
The influence of mathematical 
methods on the laws of thought 
themselves is, too, overwhelming. 
It is only because of their strict con- 
formity with the processes of mathe- 
matical reasoning that the laws 
enunciated by the theory of evolu- 
tion have met with such general ac- 
ceptance. The studies of that emin- 
ent Irisli mathematician, the late 
Doctor Boole, in logic, the science 
of thought itself, resulting in the 
application of strictly mathematical 
rules to the statement of the abstract 
truths of that science, founded upon 
what is known as the qualincation 
of the predicate, may ultimately 
Avork a change in the very forms of 
exact thinking. 
No less than reason, do the math- 
ematics cultivate the imagination. 
It has been said with truth that he 
who, of all antiquity, deserves to be 
ranked next to Homer for strength 
of imagination, is Archimedes, the 
mathematician of Syracuse. And 
who that has ever read a section of 
the Principia or studied a chapter 
in astronomy, will deny that New- 
ton, that giant intellect of modern 
times, was a man of the most pow^- 
erful imagination ? The works of 
Argand, Servois, Francais, Ger- 
gonne and other mathematicians too 
numerous to mention, teem with evi- 
dences of the imaginative powers of 
the geniuses whose labors they rep- 
resent. The discovery of the law 
of gravitation by Newton, the inspi- 
ration of Hamilton that gave us the 
system of quaternions, the founding 
of the modern geometry by the im- 
mortal Foncelet, show more evidence 
of brilliant imagination than do any 
poems, with scarcely an exception, 
that have been in recent times pro- 
duced. 
In the department of ti'anscenden- 
tal geometry and the domain of 
dimensional space, there are great 
opportunities for the imaginations 
of future thinkers. The number of 
geometrical prime-forms is only lim- 
ited, maybe, by the horizon of our 
intellectual vision. The processes 
which enable us to apply accurate 
reasoning concerning the workings 
of forces at infinite distances to pro- 
duce finite effects are still in the 
embryonic stage of development, 
and the vei'y nature of the most 
mysterious and subtle of Nature's 
agencies — electricity — will, if ever 
discovered, be probably disclosed to 
us by the imaginative thought of some 
one or other eminent mathematician. 
The existence of the luminiferous. 
