VIII. New Series for the QuapRatTuRE of the Contc SEc- 
TrIons, and the ComevTation of LoGaRiTHMSs. 
By Wir11am Watzace, one of the Professors of Ma- 
_ thematics in the Royal Military College at.Great Mar- 
low, and F.R.S. Epix. 
[Read 27th June 1808.]} 
CHE Quadrature of the Genre coasts and the Compu- 
tation of Logarithms, . are problems of confiderable 
importance, not only in the elements of Mathematics, but alfo 
in the higher branches of that fcience. On this account, every 
fuccefsful attempt to fimplify their refolution, as well as any 
new formule which may be found applicable to that purpofe, 
muft always be interefting, and muft in fome meafure contri- 
bute to the improvement of mathematical knowledge. 
; 2, THE object of this Paper, is to give folutions of thefe 
problems, which fhall be at once {imple and elementary, with- 
out employing the fluxional or other equivalent calculus ; and 
it is prefumed, that thofe which follow, will be found to par- 
take fo much of both thefe properties,, that they may even ad- 
/mit of being incorporated with the elements of Geometry and 
Analyfis. Befides, the formule which refult from the invefti- 
eon, are, as far as I know, entirely new, while each is appli- 
Ll 2 cable 
