1878-] 
The British Association . 
5ii 
ture ; but to her it is indifferent whether it be one or the 
other, and her conclusions are independent of either parti- 
cular hypothesis. Mathematics can tell us nothing of the 
origin of matter, of its creation or its annihilation ; she 
deals only with it in a state of existence ; but within that 
state its modes of existence may vary from our most ele- 
mentary conception to our most complex experience. 
Mathematics can tell us nothing beyond the problems which 
she specifically undertakes ; she will carry them to their 
limit, but there she stops, and upon the great region beyond 
she is imperturbably silent. 
Conterminous with space and coeval with time is the 
kingdom of mathematics ; within this range her dominion 
is supreme ; otherwise than according to her order nothing 
can exist ; in contradiction to her laws nothing takes place. 
On her mysterious scroll is to be found, written for those 
who can read it, that which has been, that which is, and 
that which is to come. Everything material which is the 
subject of knowledge has number, order, or position ; and 
these are her first outlines for a sketch of the Universe. 
If our more feeble hands cannot follow out the details, still 
her part has been drawn with an unerring pen, and her 
work cannot be gainsaid. So wide is the range of mathe- 
matical science, so indefinitely may it extend beyond our 
aCtual powers of manipulation, that at some moments we 
are inclined to fall down with even more than reverence 
before her majestic presence. But so strictly limited are 
her promises and powers, about so much that we might 
wish to know does she offer no information whatever, that 
at other moments we are fain to call her results but a vain 
thing, and to rejeCt them as a stone when we had asked for 
bread. If one aspeCt of the subject encourages our hopes, 
so does the other tend to chasten our desires ; and he is 
perhaps the wisest, and in the long run the happiest among 
his fellows, who has learnt not only this science, but also 
the larger lesson which it indirectly teaches — namely, to 
temper our aspirations to that which is possible, to mode- 
rate our desires to that which is attainable, to restrict; our 
hopes to that of which accomplishment, if not immediately 
practicable, is at least distinctly within the range of con- 
ception. That which is at present beyond our ken may, at 
some period and in some manner as yet unknown to us, fall 
within our grasp ; but our Science teaches us, while ever 
yearning with Goethe for “ Light, more light,” to concen- 
trate our attention upon that of which our powers are 
capable, and contentedly to leave for future experience the 
