{ ;G)

requisite will be easily had ; for dividing the so sound Semi- Parameter by the

Horizontal Distancegiven b, the Quote into Radius will be the Tangent of the> Elevation sought.

But is a Gcomctrical Construction os this Problem be required ; I think I haveone, that is as easie as any can be expected, which 1 Deduce from the fore-

V-k?? ±pb

* P

going Analytical Salution , vi'z~ - -

r Z b

and ’tis this; Having made the Right Angle L D A, make D A, DF — p, o Tgreatest Range, DG — b, the Horizontal Distance, and D B, D C — h, thePerpendicular Heigbt of die Object ; anddraw G B, and make DE = thereto. F '- 5-174 ‘

Thcn wich the Radius A C, and Center E, Iweep an Arch, which is thething be postiblc, will Intersect the Line A D, in H; and the Line D H,being laid both ways from F, will give the Points K, and L, to which drawthe Unes G L, GK; I sey, the Angles L G D, K G D, are the Elevatiousrequired for Illtting the Oljcll, B. But Note, 1 hat it B, be below theHorizon, its Dcsccnt DC = DB, muli be laid upon A, lo as to have AC—.-to AD -f* DC. Note likewile, That if in Descentt, DH, be greaterthan F D, and so K, fall below D, the Angle K G D, fhall be the Depressionbelow the Horizon.

When I gave the preceding Solution of this Problem, To Hit an Ob- n.ais. {. äj>.jeci above or below the Horizontal Line, with the greatest Certainty and least Force ,i was not aware, that the Elevation there sought did constantly Bificl theAngle between the Perpendicular and the Object, as is Demonstrated from theDifterence and Sum of the Tangent and Secant of any Arch, being alwavsequal to the Tangent and Co-Tangcnt ot the half Complement thereof to aQuadrant. But having difcovered this, I think nothing can be more com-pendious, or bid fairer to compleat the Art of Gunnery , it being as easie toShoot with a JAortar at any Object on demand, as if it were on the Level ;neitber is there need of any Computation, but only simply laying the Gunto-pals, in the middle Line between the Zenith and the Object, and givingJ “ "" XT ‘ any great need of Instruments for this pür-

pote : f or, Jt the Muzste ot the

Bore of the Piece, as it usoally

ie Muzzlc ot the Aiortar be turn’d truly Square to the•, as it usoally is, or ought to be, a piece of Looking-Glals

Piate applied Parallel to the Ma^/s, will, by its Restection, give the truePosition of the Piece ; the Bombardier having no more to do, but to lookPerpendicularly down on the Looking-Glass, alongst a lmall Thread witha Plumbet, and to Raiso or Dcprefs the Elevation of the Picee, till the Ob-ject appear Reflected on the seine Point of the Speculum on which the Plum-bet falis ; for the Angle of Incldence and Refletlion being Equa!, in this caiea Line at -Right Angles to the Speculum, as is the Axis of the Chase of thePiece, will Bisctt the Angle between the Perpendicular and the Object, ac-cording as our Proposition requires.

Vol. I.

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