VOL. XC.] PHILOSOPHICAL TBANSACTIONS. 601 



5 2 +h cc +^ c ' I = S 2a + ?•" + if** 4 



Here likewise, the terms — ±cc and — -jVc 4 maybe added to 0'3465736cc and 

 0*1 793226c 4 , which are = Ice and *nc 4 respectively; the co-efficients of which 

 being denoted by the Roman letters 1 and m, the 3d theorem in the art. before re- 

 ferred to becomes 



— Ice — mc 4 



*$ 



2a 2 



B ~ ~ A **(- + *)* X 1 +aa+ Iacc+ - 



2 ' 2 . 16 



These new forms, to which the theorems are now brought, it is evident are no 

 less convenient, and on examination they will be found no less accurate, than the 



original ones ; and that the common logarithm of -, and consequently the hy- 

 perbolic logarithm of it, is much more easily and expeditiously obtained than the 



1 4- jk/(\ — cc) 



common logarithm of , is too obvious to need a description ; and 



therefore it follows, that a computation by these new formulae will be easier and 

 shorter than by those in the first appendix. Mr. H. besides mentions some other 

 subordinate expedients for facilitating the computations ; he then adds as follows. 



Having now described these short and easy methods of computing the values of 

 a, b, and c, and of deriving the other logarithmic terras from them, and having in- 

 troduced a new and more compendious notation of several of the terms in each of 

 the first 3 theorems, it will be proper next to exhibit those theorems in this im- 

 proved state, and, after that, to give an example or 2 of computing by them. 



1 C "l+e-fcc-gc 4 



= *(« + 9i X I + a + |acc(=b) + j^{ac 4 (=c). 



-| \- h — ice — kc 4 



3c 4 



2a 2 _ 1 f 



3. B = -r- A — 



— Ice — mc 4 



The ingenious author then concludes with an example or two, computed in 

 numbers by these theorems. 



Vh Account of a Peculiarity in the Distribution of the Arteries sent to the Limbs of 

 Slow-moving Animals ; with some other Similar Facts. By Mr. Anthony Carlisle, 

 Surgeon, p. 98. 



The lemur tardigradus, in its injected state, accompanies this paper ; and, for 

 VOL. xviii. 4 H 



