71 



Mr. BiNNEY described to the Section the appearance of cer- 

 tain nodules found in the middle of a seam 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. Wh ALLEY exhibited living DiatomaceiT from Southport. 



PHYSICAL AND MATHEMATICAL SECTION. 

 Annual Meeting, March 28 th, 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. 



Vice-Presidents, jf/' ^"^"^^"i,^;^-^'^-^*' 

 iMr. BiNNEY, F.R.S., F.G.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 O O2O3 be the centres 

 of its inscribed and escribed circles respectively; then the 

 twelve circles described about the component triangles of the 

 complete quadrilaterals O O2O1O3, OiO OsO., O OiOgO., will 

 pass, four and four, through ABC respectively. 



