[ H* 3 
confequently its Fluxion as the Fluxion of the Ray 
itfelf dire&ly, and the Square of the Ray inverfely, its 
Variation would have been dire&ly as the Meafure of 
it, according to Sir Ifaac Newtons Definition, and 
inverfely as the Square of the Ray of Curvature: Ac- 
cording to this Explication, it would have been mea- 
fured by the Angle of Contadt contained by the 
Curve and Circle of Curvature, in the fame manner 
as the Curvature itfelf is meafured by the Angle of 
Contact contained by the Curve and Tangent. The 
Ground of this Remark will better appear from an 
Example : According to Sir Ifaac Newtons Expli- 
cation, the Variation of Curvature is uniform in the 
Logarithmic Spiral, the Fluxion of the Ray of Cur- 
vature in this Figure being always in the fame Ratio 
to the Fluxion of the Curve; and yet while the 
Spiral is produced, though its Curvature decreafes, it 
never vanishes ; which mud appear ftrange to fuch as 
do not attend to the Import of his Definition. It 
is eafy, however, to derive one of thefe Meafures of 
this Variation from the other, and becaufe Sir Ifaac 
Newtons is (generally fpeaking) aligned by more 
Emple Expreffions, the Author has the rather con- 
formed to it in this Treatife, but thought it neceffary 
to give the Caution we have mentioned. 
The greateft Part of this Chapter is imployed in 
treating of ufeful Problems, that have a Dependence 
on the Curvature of Lines. Firfi, the Properties of 
the Cycloid are briefly demonftrated, with the Appli- 
cation of this Dottrine to the Motion of Pendulums, 
by fhewing that when the Motion of the generating 
Circle along the Bafe is uniform, and therefore may 
meafure the Time, the Motion of the Point that 
dc- 
