C^9) 
very uncertain, were it not that they are placed about 
45 Degrees Elevation, where feverai Degrees above or 
under makes very little difference in the Effed. 
In tfumk 179. of thefe Tranfaftions, I confidered and 
demonftrared all the Propofitions relating to the motion 
of Projc&iles, and gave a Soiution to this ProbIem,x^/z. 
To hit an Ohje'5i above cr ielow ths Horizontal Line mth 
the greatejl certainty and leaft force^ as may be feen in 
that Traniaition, /. 16. & 17. That is, thac the Ho* 
rizontal diilance cf the Obj^fr being put — and the 
Perpendicular height =h^ the Charge requlfite to (Irike 
the Otjed with the greateft Advantage, was that which 
with an Elevation or 45° would caft the Shot on the 
Horizontal Line to the diOance of -v/Tr+T^ -j- ^ when 
the Objeft was above the Horizon ; or if it were below 
it, the Charge mufi: be lefler, (b as to reach on the 
Horizon, at 45-° Elevation, no greater a diftance than 
V hh-^-bh — that is, in the one cafe, the Sum cf the 
Hyporhenufal diftance of the Objeft from the Gun and 
the Perpendicular height thereof above the Gun ; and 
in the other cafe, when the Objedi is below the Hori- 
zon, the difference of the fame, per ^j, i. Eucl. And I 
then ftewed how to find the Elevation proper for the 
Gun fo charged, viz. As the Horizontal diftance of the 
Objea-, to the Sum or difference of the Hypothenufal 
diftance and Perpendicular height : : So Radius to the 
Tangent of the Elevation fought. But I was not at that 
time aware that the aforefaid Elevation did conftantly bi- 
feO: the Angle between the Perpendicular and the Objeft, 
as is demonftrated from the Difference and Sum of the 
Tangent and Secant of any Arch being always equal ta 
the Tangent znd Cotangent o( the half Compiement 
thereof to a Quadrant. Having difcovered this, I think 
nothing can be more compendious, or bids fairer to 
compkat the Art of Gunnery, it being as eafie toftoot 
with a Mortar at any Objeft on demand, as if it were 
M nn 
