25&

THEORY AND PRACTICE

TRACT 37.

93; We have indeed, in this extensive course of experi-ments, completely ascertained and proved many of the im-portant circumstances relating to military projectiles, thatwere before unknown, or only guessed at. Such as, the na-ture and force of fired gunpowder ; the velocity it will com-municate to given bodies ; the laws of its action in guns ofdifferent lengths, and in charges of different quantities; theeffects of the air’s resistance on projectiles, discharged withgiven velocities; the quantity of that resistance, to everydegree of velocity, and to every magnitude of surface. In-consequence of these, we have deduced the general law ofthe resistance, in formulae or functions of the body’s velocity ;■the motion lost in a given time, or in moving through agiven space of air; the time in passing through a givenspace, or the space passed over in a given time ; the wholealtitude and time of vertical ascent; the terminal or greatestvelocity acquired by descending in the air; with other cu-rious particulars.

9-1. The grand problem of all however still remains, thedetermination of a projectile’s trajectory, when dischargedin the air with any velocity, and in any oblique direction.The solutions of this problem that have been accomplished,or rather attempted, by the eminent authors above mentioned,have amounted to nothing more than partial and barrenspeculations, of no use in real practice, though attemptedby talents of the very first order, and with the aid of all theresources of the modern analysis, and even on the most sim-ple hypothesis of the air’s resistance, viz, that of the squareof the velocity only. Hut when it is considered, that evertthis hypothesis is quite inadmissible, and that there is no suchthing as any one single power of the velocity, by which it ispossible to express the resistance; but that two differentpowers, at least, are absolutely necessary for that purpose,as we have shown in the foregoing problems, founded on somany and such correct experiments; when these circum-stances are considered, it will fully appear that no hope re-mains of the practicability, if even of the possibility, of oh-'