Royal Society; 139 
ground, to do all that damage they might, if they came more 
oblique, and broke upon, or near thefurface of the earth j which 
is a thing acknowledged by the befieged in all towns, who unpave 
their flreets, to let the bombs bury themfelves, and thereby they 
ftifle the force of their iplinters. A fecond convenience is, that at the 
extreme elevation, the gunner is not obliged to be fb curious in 
the direftion of his piece, but it will fufiBce to be within a degree 
or two of the truth 5 whereas, in the other method of fhooting, he 
ought to be very cautious. But a third and no lefs confiderabic 
advantage is, in the faving of the king's powder, which in fb great 
and {b numerous difcharges, muft needs amount to a confiderable 
value • and for lea mortars it is fcarcely practicable otherwile to 
life them, where the agitation of the lea continually changes the 
direflion of the mortar, and would render the fhot very uncertain, 
were it not that they are placed about 45° elevation, where leve- 
ral degrees above or under, make very little difference in the 
When Mr. Halley gave the fblution of this problem 5 viz. to 
hit an obje61:, above or below the horizontal line, with the grea- 
teft certainty, and leaft force 5 he was not then aware, that the 
elevation there fought did conftantly bife£l the angle between the 
perpendicular and the obje6l, as is demonftrated from_ the diffe- 
rence and fum of the tangent and fecant of any arch, being always 
equal to the tangent and "co-tangent of the half complement there- 
of, to a quadrant^ but having difcovered this, he thinks nothing 
can be more compendious, or bid fairer to compleat the art of 
gunnery 5 it being as ealy to fhoot with a mortar at any objefi:, 
on demand, as if it were on the level; neither is there need of 
any computation, but only fimply la^^ing the gun in the middle 
line, between the zenith, and the objedt, and giving it its due 
charge 5 nor is there any great need of inftruments for this pur- 
pofe- for if the muzzle be turned truly fquare to the bore of the 
piece, as it ufually is, or ought to be, a piece of looking-glafs 
plate, applied parallel to the muzzle, will, by its reflection, give 
the true pofition of the piece, the bombardeer having no more to 
do, but to look perpendicularly down on the looking-glafs along 
a fmall thread with a plummet, and to raile or deprefs the ele- 
vation of the piece, till the objed appear reflected on the fame 
point of the Speculum^ on which the olummet falls 5 for the angle 
of incidence and reflection being equal, in this cafe a line at right 
angles to the Speculumy as is the axis of the chale of the piece, 
will biffect the angle between the perpendicular and the objeft, 
according as the propofltion requires. 
