The British Association . 
5°3 
1878.] 
je<51 to laws differing materially from those which it obeys 
at atmospheric pressure. It may also be that some of the 
features accompanying stratification form a magnified image 
of phenomena belonging to disruptive discharges in general ; 
and that consequently, so far from expending among the 
known fadfs of the latter any clue to an explanation of the 
former, we must hope ultimately to find in the former an 
elucidation of what is at present obscure in the latter. A 
prudent philosopher usually avoids hazarding any forecast 
of the practical application of a purely scientific research. 
But it would seem that the configuration of these striae 
might some day prove a very delicate means of estimating 
low pressures, and perhaps also for effedfing some eledfrical 
measurements. Now, it is a curious fadf that almost the 
only small quantities of which we have as yet any adtual 
measurements are the wave-lengths of light ; and that all 
others, excepting so far as they can be deduced from these, 
await further determination. In the meantime, when un- 
able to approach those small quantities individually, the 
method to which we are obliged to have recourse is, as indi- 
cated above, that of averages, whereby, disregarding the 
circumstances of each particular case, we calculate the 
average size, the average velocity, the average direction, &c., 
of a large number of instances. But although this method 
is based upon experience, and leads to results which may 
be accepted as substantially true ; although it may be ap- 
plicable to any finite interval of time, or even any finite 
area of space (that is, for all practical purposes of life), 
there is no evidence to show that it is so when the dimen- 
sions of interval or of area are indefinitely diminished. 
The truth is that the simplicity of Nature which we at 
present grasp is really the result of infinite complexity ; and 
that below the uniformity there underlies a diversity whose 
depths we have not yet probed and whose secret places are 
still beyond our reach. 
The President then proceeded to make special remark on 
some processes peculiar to modern mathematics : he seletfted 
for examination three methods, in respefit of which mathe- 
maticians are often thought to have exceeded all reasonable 
limits of speculation, and to have adopted for unknown 
purposes an unknown tongue, with the view of showing 
that not only in these very cases mathematical science has 
not outstepped its own legitimate range, but that even art 
and literature have unconsciously employed methods similar 
in principle. The three methods in question are— -first, that 
of Imaginary Quantities; secondly, that of Manifold Space ; 
