C 333 1 
+7^»+T8pp &c. Whence we have x 
rx'+s+iS- &c - for the Time of 
b\ — 
one Vibratio n- of t he Pendulum ; which,, by 
fubftituting i +^xi for its Equal b } &c. be: 
comes *PA h x 1 * + ^ \ & c - Prom which 
it appears, that the Effect of the Refiftance on the 
Time of Vibration, in fmall Arches, is nearly in 
the duplicate Ratio of thofe Arches. 
Sir Ifaac Newton (from whom it is impoflible 
to difagree without being under fome Apprehen- 
Eons of a Miftake) has, indeed, given a very dif- 
ferent Solution to this Problem (in Princip. ‘Prop . 
27. B. 2.). But as the Conclufion here brought out 
exa&ly agrees with what I have elfewhere given, by 
a different Method, I have great Reafon to believe 
I have no where fallen into an Error. 
The fecond Example I fhall give as an Iiiuftra- 
tion of the foregoing Method is, 
To determine the Apfide Angle ( or the Angle of the 
two Apfes at the Center ) in an Orbit deferibed 
by means of a centripetal Force , which varies 
according to any Pmer of the ‘Diftance . 
■ , ’ , ... . .. . . 
In order to which, let the Velocity Of the Body 
at the higher Apfe be to that whereby it might 
deferibe a Circle at the fame Diftance from the 
Center, in the given Ratio of p to Unity 5 alfo let 
X x that 
