EXAMPLE. The obliquity of the plane is 6° 4', the angles of the direction As fquare of the fine DAx 83° 56′=9.99756=19.99512 Is to fine DAZ X 31° 34' 9.71891 The angles of direction, obliquity of the plane, and amplitude being given, to find the amplitude of any given elevation. EXAMPLE. The angle of obliquity KAx is 6° 4', any angle of direction 37° 38', and its amplitude is 7040, any other angle of direction 33° being given, to find the amplitude for that other direction. PROBLEM V. The impetus and obliquity being given, to find the greatest random. EXAMPLE. Let the impetus be 4200, obliquity of the plane 6° 4′, required the greatest random. If to 45° you add half the angle of obliquity, the fum is the direction that carries fartheft up an ascent. If from 45° you subtract half the angle of obliquity, the remainder is the direction which carries farthest on a descent. The greatest distance up an ascent is equal to twice the im petus, wanting the height of the mark above the horizontal plane. And the greatest distance down a defcent is equal to twice the impetus, together with the depreffion of the object below the horizontal line. In actual service, cafes on afcents and defcents are seldom attended to. COMPUTATION OF SHOT. It is customary to pile iron balls and shells in horizontal rows; the piles are denominated according to the figure of their refpective bafes. The bafe is commonly an equilateral triangle, fquare, or rectangle. Triangular and fquare piles, when com plete plate, terminate in a fingle ball, and a rectangular pile in a fingle row. The two first, when complete, form a pyramid, the last a wedge. PROBLEM I. To find the number of balls in a triangular pile, RULE. Put n for the number of balls in a fide of the bafe row, then -nxn+1 × n+2, gives the number of balls in the pile. 6 EXAMPLE. I. Required the number of balls in a triangular pile, a fide of the base tire contains 30 balls. 30=n 930 32=1+2 1860 2790 6)29760 4960 balls in the pile. Ex. 2. How many balls are in a triangular pile, the fide of the bottom-row being 25? Anf. 2925 Anf. 1540. Ex. 3. Required the number of balls in a triangular pile, the fide of the bafe-row being 20. Ex. 4. How many balls are in a triangular pile, the baferow being 10? Anf. 220. How many balls are in a triangular pile, whose base Anf. 20 PROBLEM II. To find the number of balls in a fquare pile RULE. Put n for the number of balls in the fide of the fquare bafe, then nXn+1 × 2n+1 is the number of balls in the pile. EXAMPLE I. How many balls are in a fquare pile of 30 balls to the fide of the bafe-row? 30 n 31=1+1 930 61=2n+1 930 5580 6)56730 9455 balls in the pile. Ex. 2. How many balls are in a pile, the fide of the fquare bafe being 15 balls? Ex. 3. How many balls are in a fquare pile of 13 tires? Anf. 1240. Anf. 819. Ex. 4. How many balls are in a square pile of 12 tires? Anf. 650. Ex. 5. How many balls are in a square pile, whose base-row confifts of 10 balls? PROBLEM III. Anf. 385. To find the number of balls in a pile, whose base is a rectangle or oblong. RULE. Put / for the number of balls in the length, and b for the | breadth, then 34+1—b×6×b+1, will give the number of balls in the oblong pile. 6 EXAMPLE 1. How many balls are in an oblong pile, the length of the bafe courfe is 40 and breadth 20? |