t may be performing
their functions with an accuracy almost instinctive. Nay more: an
exceedingly complicated diagram which has grown up gradually as the result
of investigations successively {437} made, may be carried in the memory and
become the subject of successful peripatetic contemplation. On this point a
decided _experimental_ opinion is here expressed: but were further
instances asked for, they may be found in Stewart, Monge, and Chasles, all
of whom possessed this power in an eminent degree. Indeed, without it, all
attempts to study the geometry of space (even the very elements of
descriptive geometry, to say nothing of the more recondite investigations
of the science) would be entirely unproductive. It is, moreover, a power
capable of being acquired by men of average intellect without extreme
difficulty; and that even to the extent of "mentally seeing" the
constituent parts of figures which have never been exhibited to the eye
either by drawings or models.

That such men, if once imbued with a love for geometry, and having once got
over the drudgery of elementary acquisition, should be favourably situated
for its cultivation, follows as a matter of course. The great difficulty
lay in finding sufficient stimulus for their ambition, good models for
their imitation, and adequate facilities for publishing the results at
which they had arrived. The admirable history of the contents of their
scanty libraries, given by MR. WILKINSON, leaves nothing more to be said on
that head; except, perhaps, that he attributes rather more to the
_influences_ of Emerson's writings than I am able to do.[2] As regards
their facilities for publication, these were few, the periods of
publication being rarely shorter than annual; and amongst so many
competitors, the space which could be allotted to each (even to "the best
men") was extremely limited. Yet, contracted as the means of publication
were, the spirit of emulation did something; from the belief that
_insertion was an admitted test of superiority_, it was as much an object
of ambition amongst these men to solve the "prize question" as it was by
philosophers of higher social standing to gain the "prize" conferred by the
_Academie des Sciences_, or any other continental society under the wing of
Royalty, at the same period. The prize (half a dozen or a dozen copies of
the work itself) was not less an object of triumph, than a Copley or a
Royal medal is in our own time amongst the p