President's ADDRESS SECTION' A. 
21 
brought face to face -with any necessary elaborate calculation, in nine 
cases out of ten, his only safe course is to hand over the work to a 
professional calculator. The mathematician in such a case may be 
likened to an architect who plans some noble building, and the calcu- 
lator to the stonemason and bricklayer who know all that is necessary 
about the art of hewing individual stones and putting joint to joint, 
but who have absolutely no conception of and generally no desire to 
conceive the design as a whole. 
When vour uninitiated friends look round your shelves, and 
furtively pick out an odd tome and glance inside, they see their native 
language mixed up with what seems a barbarous tongue. Those 
symbols are so mysterious, not to say ungainly, like many another 
fetish. They may for a moment exercise some fascination, but they 
more probably cause a slight shudder, and the volume is replaced, 
with the remark u how dry.” The reason, of course, is sufficiently 
obvious. The books appear to be dry for exactly the same reason as 
a volume of Shakspeare would appear dry to a child of seven. But 
the unbelief now under consideration is unfortunately not confined 
merely to those who are absolutely without the pale. It ranges 
through a large proportion of the unscientific engineers up to some 
few really scientific though rather narrow-cultured physical investi- 
gators. These men have learnt to know the value of some few 
elementary branches of mathematics as efficient tools for certain 
special operations. But they are so impressed with the undoubted 
truth that of all the many particular problems presented to them 
mathematics can only provide a complete solution of a small number, 
and give useful hints in a few more, that they think the science 
certainly of a little use, but one that they would not sacrifice their 
best powers to. It is useless, in most cases, to tell such as these that 
they really know next to nothing about mathematics, seeing as they 
do but an accidentally straying twig of the main tree. What ! a man 
who can boast that he knows something about the differential calculus, 
yet knows nothing worthy of remark about mathematics ? Un- 
doubtedly, just as the man who can make rhymes may know nothing 
about poetry, or the man who can put marks on a paper, which, without 
being told, you perceive to represent a dog and not a horse, may know 
nothing of art. 
It is probably almost in vain that I have tried already in some 
slight degree to carry home to those who have not experienced it the 
exquisiteness of the pleasure sometimes granted to the pure mathe- 
matician in the exercise of his powers. Perhaps it would be an 
equally easy task to convey to the man born deaf the emotional 
pleasures of music. It is, perhaps, more hopeful to try to hint to 
such as we are now considering some of the fascinations of our science 
that may reasonably be expected to appeal to them. 
hirst, consider the precision of mathematics. Probably no 
engineer, certainly no physicist worthy of the name, but must some- 
times, probably often, have felt the intellectual freedom which appears 
to be gained when all at once some hazily grasped truth reveals itself 
in the new garb of precision. It may be that it is suddenly realised, 
or by some crucial experiment proved, that the data on which the truth 
depends are long familiar fundamental precise ones. It may be again 
that by the like means it is discovered that there is a precise relation 
