If our Queries on this subject be productive of no other result than that
of eliciting the able and judicious analysis subsequently given by MR.
WILKINSON (Vol. ii., p. 57.), they will have been of no ordinary utility.
The silent early progress of any strong, moral, social, or intellectual
phenomenon amongst a large mass of people, is always difficult to trace:
for it is not thought worthy of record at the time, and before it becomes
so distinctly marked as to attract attention, even tradition has for the
most part died away. It then becomes a work of great difficulty, from the
few scattered indications in print (the books themselves being often so
rare[1] that "money will not purchase them"), with perhaps here and there a
stray letter, or a metamorphosed tradition, to offer even a probable
account of the circumstances. It requires not only an intimate knowledge of
the subject-matter which forms the groundwork of the inquiry, both in its
antecedent and cotemporary states, and likewise in its most improved state
at the present time; it also requires an analytical mind of no ordinary
powers, to separate the necessary from the probable; and these again from
the irrelevant and merely collateral.
MR. WILKINSON has shown himself to possess so many of the qualities
_essential_ to the historian of mathematical science, that we trust he will
continue his valuable researches in this direction still further.
It cannot be doubted that MR. WILKINSON has traced with singular acumen the
manner in which the _spirit_ of geometrical research was diffused amongst
the operative classes, and the class immediately above them--the exciseman
and the country schoolmaster. Still it is not to be inferred, that even
these classes did not contain a considerable number of able geometers
anterior to the period embraced in his discussion. The Mathematical Society
of Spitalfields existed more than half a century before the Oldham Society
was formed. The sameness of pursuit, combined with the sameness of
employment, would rather lead us to infer that geometry was _transplanted_
from Spitalfields to Manchester or Oldham. Simpson found his way from the
country to London; and some other Simpson as great as Thomas (though less
favourably looked upon by fortune in furnishing stimulus and opportunity)
might have migrated from London to Oldham. Or, again, some Lancashire
weaver might have adventured to London (a very common case with country
artisans after the expiration of apprenticeship); and, there having
acquired a taste for mathematics, as well as improvement in his mechanical
skill, have returned into the country, and diffused the knowledge and the
tastes he took home with him amongst his fellows. The very name betokens
Jeremiah Ainsworth to have been of a Lancashire family.
But was Ainsworth really the earliest mathematician of his district? Or,
was he merely the first that made any figure in print as a correspondent of
the mathematical periodicals of that day? This question is worthy of MR.
WILKINSON's further inquiry; and probably some light may be thrown upon it
by a careful examination of the _original_ Ladies' and Gentleman's Diaries
of the period. In the reprints of these works, only the names, real or
assumed, of those whose contributions were actually printed, are
inserted--not the list of all correspondents.
Now one would be led to suppose that the study of mathematics was
peculiarly suited to the daily mode of life and occupation of these men.
Their employment was monotonous; their life sedentary; and their minds were
left perfectly free from any _contemplative_ purpose they might choose.
Algebraic investigation required writing: but the weaver's hands being
engaged he could not write. A diagram, on the contrary, might lie before
him, and be carefully studied, whilst his hands and feet 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
_Académie 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 philosophers of the Royal
Society.
These men, from similarity of employment and inevitable contiguity of
position, were brought into intercourse almost of necessity, and the
formation of a little society (such as the "Oldham") the natural
result--the older and more experienced men taking the lead in it. At the
same time, there can be little doubt that the Spitalfields Society was the
pattern after which it was formed; and there can be as little doubt that
one or more of its founders had resided in London, and "wrought" in the
metropolitan workshops. Could the records of the "Mathematical Society of
London" (now in the archives of the Royal Astronomical Society) be
carefully examined, some light might be thrown upon this question. A list
of members attending every weekly meeting, as well as of visitors, was
always kept; and these lists (I have been informed) have been carefully
preserved. No doubt any one interested in the question would, upon
application to the secretary (Professor De Morgan), obtain ready access to
these documents.
The preceding remarks will, in some degree, furnish the elements of an
answer to the inquiry, "_Why_ did geometrical speculation take so much
deeper root amongst the Lancashire weavers, than amongst any other classes
of artisans?" The subject was better adapted to the weaver's mechanical
life than any other that could be named; for even the other favourite
subjects, botany and entomology, required the suspension of their proper
employment at the loom. The formation of the Oldham Society was calculated
to keep alive the aspiration for distinction, as well as to introduce
novices into the arcanium of geometry. There was generous co-operation, and
there was keen competition,--the sure stimulants to eminent success. The
unadulterated love of any intellectual pursuit, apart from the love of fame
or the hope of emolument, is a rare quality in all stages of society. Few
men, however, seem to have realised Basil Montagu's idea of being governed
by "a love of _excellence_ rather than the pride of _excelling_," so
closely as the Lancashire geometers of that period--uncultivated as was the
age in which they lived, rude as was the society in which their lives were
passed, and selfish as the brutal treatment received in those days by
mechanics from their employers, was calculated to render them. They were
surrounded, enveloped, by the worst social and moral influences; yet, so
far as can now be gathered from isolated remarks in the periodicals of the
time, they may be held up as a pattern worthy of the imitation of the
philosophers of our own time in respect to the generosity and strict honour
which marked their intercourse with one another.
Mathematicians seldom grow up solitarily in any locality. When _one_
arises, the absence of all external and social incentives to the study can
only betoken an inherent propensity and constitutional fitness for it. Such
a man is too much in earnest to keep his knowledge to himself, or to wish
to stand alone. He makes disciples,--he aids, encourages, guides them. His
own researches are fully communicated; and this with a prodigality
proportioned to his own great resources. He feels no jealousy of
competition, and is always gratified by seeing others successful. Thus such
bodies of men are created in wonderfully short periods by the magnanimous
labours of one ardent {438} spirit. These are the men that found societies,
schools, sects; wherever one unselfish and earnest man settles down, there
we invariably find a cluster of students of his subject, that often lasts
for ages. Take, for instance, Leeds. There we see that John Ryley created,
at a later period, the Yorkshire school of geometers; comprising amongst
its members such men as Swale, Whitley, Ryley ("Sam"), Gawthorp, Settle,
and John Baines. This, too, was in a district in many respects very
analogous to Lancashire, but especially in the one to which the argument
more immediately relates:--it was a district of weavers, only substituting
wool for cotton, as cotton had in the other case been substituted for the
silk of Spitalfields.
We see nothing like this in the agricultural districts; neither do we in
those districts where the ordinary manufacturing operations themselves
require the employment of the head as well as the hands and feet. With the
exception, indeed, of the schoolmaster, and the exciseman, and the
surveyor, there are comparatively few instances of persons whose employment
was not strictly sedentary having devoted their intellectual energies to
mathematics, independent of early cultivation. To them the subject was more
or less professional, and their devotion to it was to be expected--indeed
far more than has been realised. It is professional now to a larger and
more varied class of men, and of course there is a stronger body of
non-academic mathematicians now than at any former period. At the same time
it may be doubted whether there be even as many really able men devoted to
science purely and for its own sake in this country as there were a century
ago, when science wore a more humble guise.
Combining what is here said with the masterly analysis which MR. WILKINSON
has given of the books which were accessible to these men, it appears that
we shall be able to form a correct view on the subject of the Lancashire
geometers. Of course documentary evidence would be desirable--it would
certainly be interesting too.
To such of your readers as have not seen the mathematical periodicals of
that period, the materials for which were furnished by these men, it may be
sufficient to state that the "NOTES AND QUERIES" is conceived in the exact
spirit of those works. The chief difference, besides the usual
subject-matter, consists in the greater formality and "stiffness" of those
than of this; arising, however, of necessity out of the specific and rigid
character of mathematical research in itself, and the more limited range of
subjects that were open to discussion.
The one great defect of the researches of those men was, that they were
conducted in a manner so desultory, and that the subjects themselves were
often so isolated, that there can seldom be made out more than a few
dislocated fragments of any one subject of inquiry whatever. Special
inquiries are prosecuted with great vigour and acumen; but we look in vain
for system, classification, or general principles. This, however, is not to
be charged to _them_ as a scientific vice, peculiarly:--for, in truth, it
must be confessed to be a vice, not only too common, but almost universal
amongst English geometers; and even in the geometry of the Greeks
themselves, the great object appears to have been "problem-solving" rather
than the deduction and arrangement of scientific truths. The modern French
geometers have, however, broken this spell; and it is not too much too hope
that we shall not be long ere we join them in the development of the
systems they have already opened; and, moreover, add to the list some
independent topics of our own. The chief dangers to which we are in this
case exposed are, classification with incomplete data, and drawing
inferences upon trust. It cannot be denied, at all events, that some of our
French cotemporaries have fallen into both these errors; but the abuse of a
principle is no argument for our not using it, though its existence (or
even possible existence) should be a strong incentive to caution.
These remarks have taken a more general form than it is usual to give in
your pages. As, however, it is probable that many of your readers may feel
an interest in a general statement of a very curious intellectual
phenomenon, I am not without a hope that, though so far removed from the
usual topics discussed in the work, they will not be altogether
unacceptable or useless.