OP PROJECTILES. l8z

it valley; and another be sired with an equal quantity ofpowder of the same quality against the same butt, at thedistance of 675 feet: at the same time let another person, at aplace 5000 or 6000 feet above the former situation, dischargea bullet from a musquet of the same calibre equally charged,and at the same distances as the former one, against a buttequally homogenous and consistent: the penetrations will bemuch deeper from the musquet sired near the butt at thefoot of the mountain, than from that fired near the butt atthe higher situation ; but will be much less at the distance of675 feet, than from the upper one at 675 feet. These effectswere so sensible in the campaigns of 1743, 1744, and 1747,in the Alps, that there were days when the musquets siredat the top of the mountains ranged ^ more than the samemusquets at the bottom : sometimes the mountains wereenveloped in thick clouds, while the vallies beneath wereperfectly clear; at other times the atmosphere in the vallieswas loaded with vapour, while those on the heights enjoyeda cloudless serenity : in short, so great and frequent were thealterations, that the experiments of one day bore no analogyto those of the next.

172. To determine in another manner the law of eachof the unequal movements that constitute the curve of thefourth kind ; let a gun be frequently fired from a horizontalplain P A K, (PI. 6. Fig. 18.) at the foot of a mountainK I H, with the same elevation K A M, and with a chargethat gives a known initial velocity. Fire some rounds fromA, so that the medium of the lines of descent may be from600 to 700 feet: fire again from P, at a greater distancefrom K the foot of the mountain, that the soot falling in I,the lines that express the movements of impulsion and gra-vitation, may be longer : remove the guns still farther fromK, and fire as before; and, having taken the mean result,retire the gun to a still greater distance from the mountain,so that the soot falling on the plane P L, may give thelongest lines of projection and descent possible, under thesecircumstances; always using a second watch to mark thetime of flight of the soot; and, taking every precautionto know whether the slate of the atmosphere remain thesame. From these results two scales applicable to the usesbefore expressed (170) may be constructed. Experimentsconducted in this manner cannot be very erroneous, but,their results are more complicated than the others, (170)

since