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