VOL. XIX.] PHILOSOPHICAL TRANSACTIONS. 27 



A Proposition of General Use in the Art of Gunnery, showing the Rule oj 

 laying a Mortar to pass, in order to strike any Object above or below the 

 Horizon. By E. Halley. N" 2!6, p. 68. 



It was formerly the opinion of those concerned in artillery, that there was a 

 certain requisite of powder for each gun, and that in mortars, where the distance 

 was to be varied, it must be done by giving a greater or less elevation to the 

 piece. But now our later experience has taught us that the same thing may 

 be more certainly and readily performed, by increasing and diminishing the 

 quantity of powder, whether regard be had to the execution to be done, or to 

 the charge of doing it. For when bombs are discharged with great elevations 

 of the mortar, they fall too perpendicular, and bury themselves too deep in the 

 ground, to do all that damage they might, if they came more oblique, and 

 broke upon or near the surface of the earth ; which is a thing acknowledged by 

 the besieged in all towns, who unpave their streets, to let the bombs bury 

 themselves, and thereby stifle the force of their splinters. A second conveni- 

 ence is, that at the extreme elevation, the gunner is not obliged to be so curi- 

 ous in the direction of his piece, but it will suffice to be within a degree or two 

 of the truth ; whereas in the other method of shooting, he ought to be very 

 exact. But a third, and no less considerable advantage is, in the saving the 

 powder, which in so great and so numerous discharges, as we have lately seen, 

 must needs amount to a considerable value. And for sea mortars, it is scarcely 

 practicable otherwise to use them, where the agitation of the sea con- 

 tinually changes the direction of the mortar, and would render the shot very 

 uncertain, were it not that they are placed about 45 degrees elevation, where 

 several degrees above or under makes very little difference in the effect. 



In N° 179 of these Transactions, I considered and demonstrated all the pro- 

 positions relating to the motion of projectiles, and gave a solution to this pro- 

 blem, viz. to hit an object above or below the horizontal line, with the greatest 

 certainty and least force.* That is, that the horizontal distance of the object 

 being put ^ 6, and the perpendicular height = //, the charge requisite to 

 strike the object with the greatest advantage, was that which with an elevation 

 of 45° would throw the shot on the horizontal line to the distance of 

 y/ b b -\- hh -\- h when the object was above the horizon ; or if it were below 

 it, the charge must be less, so as to reach on the horizon at 45° elevation, at no 

 greater a distance than V' b b -{- h h — h, that is, in the one case, the sum of 

 the hypothenusal distance of the object from the gun, and the perpendicular 



* See p. 270, vol 3, of these Abridgments. 

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