of these worthy benefactors to the non-academic geometers of the last century was Mr. Reuben Burrow, who by publishing in 1779 his _Restitution of Apollonius Pergaeus on Inclinations_ gave publicity to a valuable relic which would otherwise have remained buried in the Latin obscurity of Dr. Horsley's more elaborate production. During the greater portion of the time just reviewed, Mr. Jeremiah Ainsworth was resident in the neighbourhood of Manchester, and so early as 1761 was in correspondence with the editors of the _Mathematical Magazine_. He subsequently associated with Mr. George Taylor, a gentleman of kindred habits, then resident in the immediate vicinity, and these worthy veterans of science, as time wore on, collected around them a goodly array of pupils and admirers, and hence may truly be said not only to have laid the foundation of the "Oldham Society," but also to have been the fathers of the Lancashire school of geometers. Such then was the state of affairs in the mathematical world at the period of which we are speaking; all the works just enumerated were attracting the attention of all classes of students by their novelty or elegance; Dr. Hutton and the Rev. Charles Wildbore had the management of the _Diaries_, each vieing with the other in offering inducements for geometrical research; whilst both, in this respect, for a time, had to contend against the successful competition of Reuben Burrow, the talented editor of Carnan's _Diary_: correspondents consequently became numerous and widely extended, each collecting around him his own select circle of ardent inquirers; and thus it was, to use the words of Mr. Harvey, and answer the questions proposed, that inquiries which had hitherto been "locked up in the deep, and to them unapproachable recesses of Plato, Pappus, Apollonius and Euclid * * porisms and loci, sections of ratio and of space, inclinations and tangencies,--subjects confined among the ancients to the very greatest minds, (became) familiar to men whose condition in life was, to say the least, most unpropitious for the successful prosecution of such elevated and profound pursuits." The preceding sketch is respectfully submitted as an attempt to answer the queries of PEN-AND-INK, so far as Lancashire is concerned. It is not improbable that other reasons, equally cogent, or perhaps corrective of several of the preceding, may be advanced by some of your more learned correspondents, whose experience and means of reference are superior to my own. Should any such {60} be induced to offer additions or corrections to what is here attempted, and to extend the inquiry into other localities, your pages will afford a most desirable medium through which to compare _notes_ on a very imperfectly understood but most important subject of inquiry. T. T. WILKINSON. Burnley, Lancashire, June 5. 1850. * * * * * QUERIES ANSWERED, NO. 8.