THP] SCIENTIST. 
It is reason alone that enables us 
to appreciate duly the eloquence of 
a Lacordaire, the deep })bilosopby of 
a Lamarck or tbe tangled subtleties 
of a Stuart Mill. 
Reason is tbe ever l)urni ng lamp 
witbin tbat guides us tbrougb tbe 
mazes of convicting tbeory; it is tbe 
toucbstone of all knowledge ; tbe 
sole and final arbiter between trutb 
and error. Reason is tbe compass 
by wbicb tbe mental bark of eacb 
must be steered, if it would escape 
being buffetted belplessly tbis way 
and tbat way by tbe waves of con- 
troversy and opposite opinion, to be 
finally sbattered on tbe breakers of 
despairing doubt, and would reacb 
tbe peaceful b arbor of certainty and 
knowledge. 
Depreciate pure science as you 
may, it is impossible to deny tbe 
power of geometry to educate tbe 
reason. Here we can leap to no false 
conclusions, but must proceed step 
by step in tbe patb of our argument, 
a fiaw in wbicb at once becomes pat- 
ent and binders our arrival at an 
absurd conclusion. Jt is as true of 
geometry as of every otber brancb 
of science, tbat tbcre is no royal road 
to learning, but bowever for a wbile 
obscure may be our progress, tbere 
are no will-o'tbe-wisps in tbe sbape 
of false tbeories to lead us into 
swamps of eri-or from Avbicb tbcre 
can be no escape. 
Where, indee'd, can we find a 
sounder cbaj)tcr of logic tban in a 
proposition of Euclid of logic lead- 
ing from tbe simplest of axioms by 
a series of beautiful syntbetic i>ro- 
cesses to tbe soundest of practical 
conclusions. Tbe cbain of reason 
bas to be carefully unfolded link l)y 
link. Xotbing can be omitted, notb- 
ing may be skipped over. Omit one 
of tbe preceding propositions and 
tbe Pons aKuiorum becomes impos- 
sible. 
Tbere is notbing in tbe evolution 
of knowledge tbat can in any wise 
compare witb tbe development of 
tbe matbematics from tbe times of 
Descartes to tbe present, and tbe end 
is not yet. AVlien tbe minds of 
Leibniz and Newton almost simul- 
taneously brougbt fortb tbe cal- 
culus tbat bas w^'ougbt sucb wonders 
in tbe analytics of matbematics, 
even tbeir great geniuses could 
never bave foreseen tbe more mag- 
nificent and later conceptions of 
Hamilton and Grassman, tbe appli- 
cations of wbicb in our own day bid 
fair to revolutionize tbe workings of 
our science wbile leaving its princi- 
ples intact. Tbe more rigorous our 
reasoning the more subtle tbe 
methods of our analysis, tbe more 
simple and therefore tbe more in- 
trinsically beautiful our conclusions. 
Tbe singularly elegant Infinitesimal 
Calculus bids fair to be entirely sup- 
planted, except as a matter of his- 
torical mathematical development, 
by the even more singularl)^ elegant 
Calculus of Quaternions, which offers 
us a more powerful weapon of rea- 
soning, of equal accuracy and more 
general conclusiveness. The memory 
is no lono-er taxed with formula' — 
