1882.] 



On certain Geometrical Theorems. 



35 



given off from, the thin, exogenous, Xylem zone which encloses the 

 medulla, whilst at the same points the continuity of the Xylem ring 

 is interrupted, as was also the case with the Dadoxylons, by an 

 extension of the medullary cells into the primitive cortex. Sections 

 of the petiolar bases of the leaf-scales of the bud show that these 

 bundles enter each petiole in parallel pairs, subsequently subdividing- 

 and ramifying in the Adiantiform leaf. This curious resemblance 

 between Salisburia and Dadoxylon, accompanied as it is by other 

 resemblances in the structure of the wood, bark, and medulla, suggest 

 * the probability that our British Dadoxylon was a Carboniferous plant 

 of Salisburian type, of which Trigonocarpum may well have been the 

 fruit. If so, the further possibility suggests itself that this plant 

 may have been the ancestral form whence sprang the Baieras of the 

 Oolites, and, through them, the true Salisburias of Cretaceous and of 

 recent times. 



The Society adjourned over Ascension Day to Thursday, May 2-5. 



May 25, 1882. 



THE PRESIDENT in the Chair. 



The Presents received were laid on the table and thanks ordered for 

 them. 



Mr. Bindon Blood Stoney was admitted into the Society. 

 The following Papers were read : — 



I. " On certain Geometrical Theorems. No. 2." By W: H. L. 

 Russell, F.R.S. Received May 10, 1882.' 



(4.) The following is a short method of determining the conic of 

 5 pointic-contact with a given curve. Write the conic 



*y + ftxij=y2 + [LX* + v%+p ...... (1), 



then differentiating four times and writing D for — , we have, re- 



dx 



membering that the four first differential coefficients of the two curves 

 coincide, — 



a D I / + /3D(^)=D i / 2 + 2 /< a^^ (2), 



«D2y+pD*(xy)=-DY + fy (3), 



*DSy+(2B\x2j)=my2 . (4), 



*D^+/3D4(^)=Dy ■ • (5), 



D 2 



