Mechanics;

Arch I D is called the Complement of the Arch E I to aQuadrant E D, or 90 Degrees ; and the Arch A K iscalled the Supplement of the Arch E K to a SemicircleEDA, or 180 Degrees.

22. If from the Point I he let fall the PerpendicularI L to the Line or Radius E C,. then is that Line I Lcalled the Sine of the Angle I C E or F C B. In thefame Manner the Line I M is the Sine of the Comple-ment Arch I D, or Angle I C D. But instead of Sine-Complement , we fay, in short, Co-Sine : Thus we faythat IL is the Sine, and I M the Co-Sine , of the AngleICE. The Angle F C B is called the Inclination ot theLine F C to the Line B C ; and the Angle F C D isthe Inclination of the Line F C to the PerpendicularD C : That is, F C is inclined to B C in an Angle of40 Degrees, and to D C in an Angle of 50 Degrees.Hence I L and I M are called the Sines of Inclination re-spectively.

23. Hence, when we say, The Force of a direct Strokeis to that of an oblique one as Radius is to the Sine of In-clination, we only mean, that those Quantities are toeach other as the Radius I C to the Sine I L, or I M,acc rding as the Inclination is 40 or 50 Degrees. Also,when it is said that the centrifugal Force decreases from theEquator towards the Poles , in proportion of Radius to theCo-Sines of the Latitude ; no more is meant than this,that if the Radius C E represent the said Force in theEquator E, and E I be any given Latitude, then, willI M, the Co-Sine of the Latitude, represent the Forcein that Latitude : Or, the Force decreases with theLength of the Line I M, as the Point I moves on fromE to D.

24. In several Books we have Tables of NumbersWhich express the Length of the Sine of every Degreeand Minute of the Quadrant, in suth equal Parts as theRadius C E or C I contains 100000. And firice it isof the greatest Use to know the Proportion of Radiusto the Sine of every Degree, I have here subjoined a't'able thereof, and a Specimen of its Use,

Vol, I,

Q.

Sins

225