71 
Mr. Binney described to the Section the appearance of cer- 
tain nodules found in the middle ofaseam of coal, in the lower 
part of the Lancashire coalfield, which contain fossil wood 
associated with marine shells. Specimens of the former were 
exhibited to the members, the most perfect of which was that 
of Sagenaria, the old Lepidodendron elegans, in transverse, 
parallel, and tangential sections. The marine shells associated 
with the fossils belong to the genera Aviculopecken, 
Orthoceras, Nautilus, &c. 
Mr. Brothers exhibited a Section of Pearl, Isthmia 
nervosa, infusoria, &c. 
Mr. Whalley exhibited living Diatomacece from Southport. 
PHYSICAL AND MATHEMATICAL SECTION. 
Annual Meeting, March 28th, 1861. 
Mr. E. W. Binney, F.R.S., F.G.S., & c., in the Chair. 
Professor Clifton, of Owens College, was elected a 
member of the Section. 
The following: gentlemen were elected Officers of the 
Section for the ensuing year : — 
President, Mr. Robert Worthington, F.R.A.S. 
, r . t-, • i i fMr. Baxendell, F.R.A.S., 
Vice-Presidents, < _ _ _ 1 ’ 
\Mr. Binney, F.R.S., IcG.S. 
Treasurer, Mr. George Mosley. 
Secretary, Mr. Thomas Heelis, F.R.A.S. 
A Paper was communicated by Mr. Atkinson, from T. T. 
Wilkinson, Esq., F.R.A.S., of Burnley, entitled, “ Geome- 
trical Theorems relating to the Triangle and its Inscribed and 
Escribed Circles.” 
Many curious properties of these two figures have been 
taken notice of by mathematicians, but the following theorems 
Mr. Wilkinson looks upon as new. 
1. Let A B C be any triangle, O 0,0 2 0 3 be the centres 
of its inscribed and escribed circles respectively ; then the 
twelve circles described about the component triangles of the 
complete quadrilaterals O 0 2 0i0 3 , OiO 0 3 0 2 , O 0i0 3 0 2 , will 
pass, four and four, through ABC respectively. 
