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.
PEN-AND-INK.
Footnote 1:[(return)]
Although at one period of our life we took great pains to make a collection of the periodicals which, during the last century, were devoted wholly or partially to mathematics, yet we could never even approximate towards completeness. It was not, certainly, from niggardly expenditure. Indeed, it is doubtful whether a complete set exists, or could even be formed now.
See Philosophical Magazine, Sept. 1850.