[ 4 1 4 ] 
Force are given, and for defining the Catenaria 
and Line of fwifteft Defcent in any Hypothecs of 
Gravity. 
Then the ufual Rules are derived from the inverfe 
Method for computing the Area, the Solid generated 
by it, the Arc of the Curve, and the Surface de- 
ferred by it revolving about a given Axis. The 
meridional Parts in a Sphere, and any Spheroid, are 
determined with the fame Accuracy, and almoft equal 
Facility. The Attradion of a Spheroid at the Equator, 
as well’ as at the Poles, is determined in a more 
general manner than in the Firft Book, or in a Piece 
of the Author’s publiflied at "Paris in 1740. which 
obtained a Part of the Prize propofed by the Royal 
Academy of Sciences for that Year. Several Mecha- 
nical Problems are refolved, concerning the Propor- 
tion the Power ought to bear to the Weight, that the 
Engine may produce the greateft Effed in a given 
Time; and concerning the mod advantageous Por- 
tion of a Plane which moves parallel to itfelf, that a 
Stream of Air or Water may impel it with the greateft 
Force, having regard to the Velocity which the Plane 
may have already acquired. On this Occafion, it is 
fhewn, that the Wind ought to ftrike the Sails of a 
Wind-mill in a greater Angle than that of 54 0 44', 
againft what has been deduced from the fame Prin- 
ciples by a learned Author. The fame Theory is applied 
to the Motion of Ships, abftrading from the Lee-way, 
but having regard to the Velocity of the Ship 5 and 
amongft other Conclufions it appears, that the Velocity 
of a Veffel of one Sail may be greater with a Side-wind, 
than when fhe fails diredly before the Wind ; which, 
perhaps, may be the Cafe of thofe feen by Captain 
\ Dumpier 
