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MR. T. T. WILKINSON ON 



and intimately acquainted with Horrocks and Crabtree, his 

 pursuits would probably be of the same nature as those of his 

 illustrious friends; and although his nephew, Richard Townley, 

 is known to have been an ardent cultivator of science, and to 

 have resided principally at Townley, he, like the former, was 

 probably more engaged with experimental physics and astro- 

 nomy than with pure geometry. My copy of Pappi Math. 

 Coll. a Commandino, (Venetiis, 1589,) however, contains his 

 name and armorial bearings, and consequently must formerly 

 have been in his possession. The probable inference therefore 

 is, that he was not altogether ignorant of the contents of this 

 valuable collection of the fragments of ancient geometrical 

 research ; and it may be mentioned to his honour that he was 

 the Jirsi to discover what is usually known as " Marriottes 

 Law" for the expansion of gases, which Professor Oersted 

 remarks, (Phil. Magazine, August, 1826,) he deduced from 

 some experiments made by his friend Mr. Cavendish. Nor 

 is his name altogether unconnected with geometrical inquiries, 

 for he is well known as the reproposer of the ''Problem of 

 Ilipparchus" relating to the determination of the point from 

 which three objects, not in a straight line, may be seen under 

 given angles, which was solved in all its cases-by Mr. Collins, 

 in the Philosophical Transactions for 1671. 



Although the studies of the Lancashire Mathematicians up 

 to this period did not tend to develope themselves very fully 

 in any specific direction, yet it is evident that an interest in 

 the cultivation of Geometry had gradually been created in 

 different localities, and that the number of its admirers in 

 Manchester and its vicinity was steadily increasing; so much 

 so, indeed, that a Mathematical Society was established here in 

 1718, on principles very nearly similar to that in Spital fields, 

 London, which had been founded by Mr. Joseph Middleton 

 the year before. Mr. James Crossley, of Manchester, the 

 learned President of the Chetham Society, has given an inte- 

 resting account, in Notes and Queries, No. 103, of the first two 

 lectures delivered before the Manchester Society by " the late 



