TRANSCENDENTAL SPACE. 
CHARLES H. CHANDLER, 
Professor of Mathematics, Ripon College. 
In this paper the term “ transcendental ” has not the same 
signification as when it is applied to quantities incapable of 
representation by a finite algebraic expression, but it is used to 
denote that which is beyond the limits of experience; and the 
question is presented whether certain space under consideration 
is not more than transcendental as distinguished from that 
which is empirical, or, according to Kantian terminology, is 
“ transcendent. ” 
However cordial the welcome constantly offered by the present 
age to new and broader forms of truth, it is probable that there 
is no field of investigation in which radically new positions are 
less generally expected than in mathematics. The fact that 
there is still in very general use, as a text-book, a mathematical 
treatise which has brought down through more than twenty 
centuries the name of its author, even though the Euclid of to¬ 
day is very different from the original work, still has seemed to 
furnish an ever ready proof that, whatever else might change, 
mathematical principles remain the same “ yesterday, to-day, 
and forever. ” 
That biological or electrical science should manifest more or 
less of the traits characteristic of youthful immaturity, that in 
those realms of thought views formerly maintained should be 
repudiated, and opposing theories vigorously asserted, might 
reasonably be expected. Somewhat maturer sciences might per¬ 
haps so add to their stores of truth as greatly to modify their 
general aspect. But to many it has seemed evident that, 
while the changes in a system of thought and research 
of the venerable character of mathematics may, perhaps, 
