239 



in water during twelve hours, he found that the latter had absorbed 

 69 gr,ains, the former only 51. Hence he thinks considerable ad- 

 vantage may be expected from stripping off a portion of the bark 

 from resinous trees, all round their trunks, close to the surface of the 

 ground, in the beginning of the summer preceding the autumn in 

 which they are to be felled. He even thinks it probable, that the 

 timber would be improved by letting them stand a second year ; al- 

 though he admits that some loss would be sustained by the slow 

 growth of the trees in the second summer. 



It may, Mr, Knight says, be suspected, that the increased solidity 

 of the fir- wood above described was confined to the part contiguous 

 to the decorticated space ; but it is well known that taking off a 

 portion of bark round the branch of a fruit-tree, occasions in the 

 succeeding season an increased quantity of blossoms on every part 

 of that branch. This increase probably owes its existence to a stag- 

 nation of the true sap, extending to the extremities of the branch ; 

 and it may therefore be expected that the alburnous matter of the 

 trunk and branches of a resinous tree will be rendered more solid by 

 a similar operation. 



A new Demonstration of the Binomial Theorem, when the Exponent is 

 a positive or negative Fraction. By the Rev. Abram Robertson, 

 A.M. F.R.S. Savilian Professor of Geometry in the University of 

 Oxford. In a Letter to Davies Giddy, Esq. F.R.S. Read June 5, 

 1806. [Phil. Trans. 1806, p. 305.] 



This paper is merely an extension of one formerly communicated 

 to the Society by Mr. Robertson, and printed in the Philosophical 

 Transactions for the year 1795. It is, the author says, so far as re- 

 lates to the raising of integral powers, the same as that paper, and 

 is confessedly new only to the extent mentioned in the title, namely, 

 that the present demonstration is applicable when the exponent is a 

 positive or a negative fraction. The nature of the paper is obviously 

 such, as to render it unsusceptible of abridgement. 



New Method of computing Logarithms. By Thomas Manning, Esq. 

 Communicated by the Right Hon. Sir Joseph Banks, K.B. P.R.S. 

 Read June 5, 1806. [Phil. Trans. 1806,;?. 327.] 



If, Mr. Manning observes, there existed as full and extensive lo- 

 garithmic tables as ever will be wanted, and of whose accuracy we 

 were absolutely certain, and if the evidence for that accuracy could 

 remain unimpaired through all ages, then any new method of com- 

 puting logarithms would be totally superfluous, so far as concerns 

 the formation of tables, and could only be valuable indirectly, and 

 inasmuch as it might show some curious and new views of mathe- 

 matical truth. But the above kind of evidence is necessarily im- 

 paired by the lapse of time, even while the original record remains, 

 and still more when the record must from time to time be renewed 



