1 878.] 
The British Association. 
505 
of interpretation ; on the contrary, the difficulty at which 
we have arrived indicates that there must be some more 
comprehensive statement of the problem which will include 
cases impossible in the more limited, but possible in the 
wider, view of the subjedh. 
If, both in geometry and in algebra, we occasionally make 
use of points or of quantities which from our present out- 
look have no real existence, which can neither be delineated 
in space of which we have experience, nor measured by 
scale as we count measurement ; if these imaginaries, as 
they are termed, are called up by legitimate processes of our 
science ; if they serve the purpose not merely of suggesting 
ideas, but of adlually conducting us to practical conclu- 
sions ; if all this be true in abstract science, I may, perhaps, 
be allowed to point out, in illustration of my argument, 
that in art unreal forms are frequently used for suggesting 
ideas, for conveying a meaning for which no others seem to 
be suitable or adequate. Are not forms unknown to biology, 
situations incompatible with gravitation, positions which 
challenge not merely the stability but even the possibility of 
equilibrium — are not these the very means to which the 
artist often has recourse in order to convey his meaning and 
to fulfil his mission ? Again, if we turn from art to letters, 
truth to nature and to faCt is undoubtedly a characteristic 
of sterling literature ; and yet in the delineation of outward 
nature itself, still more in that of feelings and affections, of 
the secret parts of character and motives of conduct, it fre- 
quently happens that the writer is driven to imagery, to an 
analogy, or even to a paradox, in order to give utterance to 
that of which there is no direCt counterpart in recognised 
speech. 
Passing to the second of the three methods— -viz., that of 
manifold space — Mr. Spottiswoode remarked that our whole 
experience of space is in three dimensions, viz., of that which 
has length, breadth, and thickness : there is, however, another 
aspeCb under which even ordinary space presents to us a four- 
fold, or indeed a manifold, charaCfer. In modern physics space 
is regarded not as a vacuum in which bodies are placed and 
forces have play, but rather as a plenum with which matter 
is co-extensive. And from a physical point of view the pro- 
perties of space are the properties of matter, or of the 
medium which fills it. Similarly, from a mathematical 
point of view, space may be regarded as a locus in quo, as a 
plenum, filled with those elements of geometrical magnitude 
which we take as fundamental. These elements need not 
always be the same. For different purposes different ele- 
