INCONVERTIBILITY OF BARK INTO ALBURNUM. 



(N) When a is but small, the series given in (G) con- 

 verges but slowly, in which case the following approxi- 

 mation may be used. Since a-\-zz=:t, zz=:t — a, but zzz 



*3 yS /7 /9 y3 *5 *7 i9 



=:«; put 3>:.a—p, and we have, by Emerson's Algebra, 



(P) For example, let a zr '009, then pz= -027, andp"3"r:: 

 •3, and substituting the successive powers of '3, or p^, vire 

 get ^=-3054157, and zzzt— a — -2964157. 



(Q) When n, in (L), consists of a unit and a small frac- 

 tion, we may also approximate to the value of t, by help of 



t t^ t^ t^ 



the two values of z, viz. — , and t 1 > — , &c. ; from 



74 3 5 7 



<* t'*' t^ t^ 1 



which we get 1 , &c. — w— — : call the 



° 3 5 7 9 n 



small fraction, , w; and we have by reversion, <*iz3X 



n 



lu + 5-4 X MJ* 4- 7-86857139 X t«' + 10-33714521 X tc* + 



12-8037915 X iv\ &c. 



II. 



On the Inconvertibility of Bark into Alhurnnm. By Tho- 

 mas Andrew Knight, Esq. F. R. S. In a Letter to Sir 

 Joseph Banks, K. B. P. R.S.* 



My dear Sir, 



JLN a letter which I had the honour to address to you in Matter that 

 the end of last yearf, I endeavoured to prove, that the composes the 

 matter, which composes the bark of trees, previously exists fluid in the^lU 

 in the cells both of their bark and alburnum in a fluid of both bark* 

 state; and that this fluid, even when extra vasated, iscapa-^ ^^^^ 



• Phil. Trans, for 1808, P.I, p. 103. 



f Phil. Trans. 1807 j ora;ournal, vol. XIX, p. 241. 



