TRACT 37.

OF GUNNKRV.

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this Tract; and these afford us but very few and imperfectrules, and are chiefly these following. 1st, That the rangeswith the one-pound balls, at an elevation of 15 degrees, arenearly proportional to the times of flight. 2nd, That theranges with the 3-pound balls, at 45° elevation, are nearly asthe times of flight, and also as the projectile velocities. Be-sides these inferences, it does not appear that the experimentsare extensive enough to afford many more useful conclusions.By trials however among many of the numbers in the tablein art. 24, it appears that in most of them, at an elevationbetween 45° and 30°, the time of flight is nearly equal toof the square root of the range; in which respect it nearlyagrees with the similar rule for the time of flight, in the pa-rabolic theory, at the angle (45°) for the greatest range,which time it is well known is equal to £ of the square rootof the said range in feet, and that whether the shot consist ofmaterials very dense or very light. Whence it is probablethat, with the help of a few other ranges at several elevations,some general relations might be evinced between the rangesand the times of flight, with the tangents of the elevations.

But such experiments and enquiries as these, unfortunately,it is no longer in my power either to procure, or by anymeans to promote. We can therefore only endeavour torender, without them, what service we can, to the state andto philosophy, by such means as are in our power.

128. There are some few theoretical principles which itmay be useful to notice here, as first mentioned by professorBobison. Thus, balls of equal density, discharged at thesame elevation, with velocities which are proportional to thesquare-roots of their diameters, will describe similar curves;because then the resistances will be in proportion as the mo-menta or quantities of motion. For, the resistance r, is dVnearly; d being the diameter, and v the velocity. But, vbeing as y d , y will be as d ; consequently rfV will be as d 3 tthat is, r is as d 3 , But the momentum is as the magnitudeor mass, which is as d 3 also, the cube of the diameter. There-fore the resistance is proportional to the momentum, when

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