176 Prof. Sedgwick's Remarks on the President's Address at 



I have had occasion, for another purpose, to consider the 

 question of finding the number of trees with a given number of 

 free branches, bifurcations at least. Thus, Y\g. 



when tlie number of free branches is three, 

 the trees of the form in question are those 

 in the annexed figure, and the number is 

 therefore two. It is not difficult to see 

 that we have in this case (B,. being the 

 numbei' of such trees with r free branches), 



{i-x)-\\-x^)-'^\l-xY\\-xy^* . . 



= 1 + 07 + 2B2.r2 + %2,.Jl^ + ^'Q^x^ + &c. 

 And a like process of development gives — 



1 may mention, in conclusion, that I was led to the consider- 

 ation of the foregoing theory of trees by Professor Sylvester's 

 researches on the change of the independent variables in the dif- 

 ferential calculus. 



2 Stone Buildings. 



January 2, 1856. 



XXIX. Remarks on a passage in the President's Address delivered 

 at the Anniversary Meeting of the Geological Society of London 

 on the 15M of February, 1856. By the Rev. Prof. Sedgwick, 

 M.A., F.R.S. c^c. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



THE remarks which follow might be thought unworthy of 

 publication were they not written in defence of a paper 

 which appeared in your Journal for October and November 

 1854. Mr. Hamilton, in his Anniversary Address, has attacked 

 the conclusions I vindicated in that paper. As, however, he 

 appears neither to have learnt, by a study in the field, what 

 are the great successive physical groups in the older divisions 

 of British palaeozoic rocks, nor to have more than a partial 

 and one-sided knowledge of their history, I should not perhaps 

 have been called upon to notice his statements, so far as they are 

 purely geological, either in the way of praise or blame. But he 

 has at the same time charged me with having irregularly gained 

 possession of that which was the property of the Geological 



