290 DEVELOPMENT of a cert am 



19. 1 SHALL conclude this appendix with an example of the ap- 

 plication of our formula ; and in the determination of the loga- 

 rithms of/, e", &c. 1 -\-e', T.-\-e", &c. by means of the trigonome- 

 trical tables, I fliall avail myfelf of the remarks which have been 

 made for that purpofe at Art. 15. of the preceding paper. As 

 to the quantities fin 2<p\ fin /\.<p'', &c. it is eafy to fee, from their 

 relation to each other, that their logarithms may be readily de- 

 termined by means of the fame tables. 



Example. It is required to determine the length of an el- 

 liptic arch, when e, the excentricity, =V ^ = .7071068, and <p, 

 the arch of the circumfcribing circle = 70°, the femi-tranfverfe 

 being fuppofed =. i. 



I. Calculation of the logarithms oie', i -f- e', &c. 



Logarithms. 



e =. fin « = fin 45°, o', o", 1.8494850 



e =. tan*-? = fin a = fin 9% 52', 45''.4i. 1.2344486 



l.}-f' = fec^ 0.0687694 



/= tan^'= fin a'= fin o% 25. 40''.7 ~3-^733°°^ 



l + /=fec^' - - - 0.0032320 



f"'=tan^ - - - 5-^444734 



2 



i+e"'=kc'-^ ... - 0.0000060 



Because e'" is nearly equal to one-fourth of the fquare of 



e'", (Art. 7.) it is evident that e'\ i +f-, Sec may be all ne- 



gleded. ^ 



^ 2, Calculation 



