271

THKORT AND PRACTICE

TRACT 37 .

such a relocity to those shells, must have contrived somenew kind of large cannon on the occasion. It is said theseshells, after being filled with lead, are bored ; that they sel-dom burst; and when they do, the explosion is inconsider-able.

PROBLEM XVI.

To determine the Circumstances of Ranges at other obliqueElevations.

126. Having shown, in the preceding articles and pro-blems, how, from our theory of the air’s resistance, can befound, first the initial or projectile velocity of shot and shells;2dly, the terminal velocity, or the greatest velocity a ballcan acquire by descending by its own weight in the air; 3dly,the height a ball will ascend to in the air, being projectedvertically with a given velocity, also the time of that ascent;4thly, th e greatest horizontal ranges of given shot, projected ,with a given velocity; as also the particular angle of eleva-tion of the piece, to produce that greatest range. It remainsnow to-fenquire, what laws and regulations can be given re-specting the ranges, and times of flight, of projects made atother angles of elevation.

127. Rules for the general solution of this problem wouldbe best derived from experiments; and these should be madeat all elevations, and with all charges, and with various sizesof balls; observing both the ranges and times of flight, iaevery experiment. Such experiments would give us the re-lations existing, in all cases, among all these four terms, viz,the ranges, the times of flight, the velocities or charges, andthe size of the balls. Numerous and various as our experi-ments are, as before related, and fruitful as they are in usefulconsequences, we have obtained but a small portion of thoseabove alluded to; nor do I know of any proper set of suchexperiments anywhere to be found. Such must thereforestill remain a valuable desideratum. The few that we havebeen able to make, are those collected in arts. 8 and 24 of