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 ex