s to hang a speech upon."

Similar remarks evidently apply to Horrocks and Crabtree (1641); for
although _both_ were natives of Lancashire, and the latter a resident in
the vicinity of Manchester, their early death would prevent the exertion of
any considerable influence; nor does it appear that they ever paid any
attention to the study of the ancient geometry. Richard Towneley, Esq., of
Towneley (1671), is known to have been an ardent cultivator of science, but
his residence was principally in London. It may, however, be mentioned to
his honour, _that he was the first to discover what is usually known as
"Marriotte's Law"_ for the expansion of gases. At a later period
(1728-1763), the name of "John Hampson, of Leigh, in Lancashire," appears
as a correspondent to the _Lady's Diary_; but since he mostly confined his
speculations to subjects relating to the Diophantine Analysis, he cannot be
considered as the originator of the revival in that branch of study now
under consideration. Such being the case, we are led to conclude that the
"Oldham Mathematical Society" was really the great promoter of the study of
the ancient geometry in Lancashire; for during the latter half of the last
century, and almost up to the present date, it has numbered amongst its
members several of the most distinguished geometers of modern times. A
cursory glance at some of the mathematical periodicals of that date will
readily furnish the names of Ainsworth, whose elegant productions in pure
geometry adorn the pages of the _Gentleman's_ and _Burrow's Diaries_;
Taylor, the distinguished tutor of Wolfenden; Fletcher, whose
investigations in the _Gentleman's Diary_ and the _Mathematical Companion_
entitle him to the highest praise; Wolfenden, acknowledged by all as one of
the most profound mathematicians of the last century; Hilton, afterwards
the talented editor of that "work of rare merit" the _Liverpool Student_;
and last, though not least, the distinguished Butterworth, whose elegant
and extensive correspondence occupies so conspicuous a place in the
_Student_, the _Mathematical Repository_, the _Companion_, the _Enquirer_,
the _Leeds Correspondent_, and the _York Courant_. Besides these, we find
the names of Mabbot, Wood, Holt (Mancuniensis), Clarke (Salfordoniiensis),
as then resident at Manchester and in constant communication with, if not
actually members of the society; nor can it be doubted from the evidence of
existing documents that the pr