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in water during twelve hours, he found that the latter had absorbed 69 grains, the former only 51. Hence he thinks considerable advantage maybe 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 summcr 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 albumous 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. Tram. 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 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 Logarithm. By Thomas Manning, Esq. Communicated by the Right Hon. Sir Joseph Banks, K.B. P.R.S. Read June 5, 1806. [Phil. Trans. 1806, p. 327.]

If, Mr. Manning observes, there existed as full and extensive lo- garithmic tables as ever will he 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