GUNNERY. 



the King's gunners. To every scholar he 

 administers an oath, not to serve, with- 

 out leave, any other prince or state ; or 

 teach any one the art of gunnery, but 

 such as have taken the said oath. 



GUNNERA, in botany, so named' in 

 honour of J . E. Gunnerus, Bishop of Dront- 

 heim, in Norway, a genus of the Gynan- 

 dria Diandria class and order. Natural 

 order of Urticx, Jussieu. Essential cha- 

 racter : ament with one-flowered scales ; 

 calyx and corolla none ; germ two tooth- 

 ed ; styles two ; seed one. There is but 

 one species, viz. G. Perpensa, marsh ma- 

 rygold- leaved gunnera. Native of the 

 Cape. 



GUNNERY, is the art of determining 

 the course and directing the motion of 

 bodies shot from artillery, or other war- 

 like engines. 



The great importance of this art is the 

 reason it is distinguished from the doc- 

 trine of projectiles in general ; for it is no 

 more than an application of those laws 

 which all bodies observe, when cast into 

 the air, to such as are put in motion by the 

 explosion of guns, or other engines of 

 that sort. And it is the same thing, whe- 

 ther it is treated in the manner of pro- 

 jectiles in general, or of such only as be- 

 long to gunnery ; for from the moment 

 the force is impressed, all distinction with 

 regard to the power which put the body 

 first in motion is lost, and it can only be 

 considered as a simple projectile. See 

 PROJECTILES. 



Prob. I. The impetus of a ball, and the 

 horizontal distance of an object aimed at, 

 with" its perpendicular height or depres- 

 sion, if thrown on ascents or descents, 

 being given, to determine the direction 

 of that ball. 



From the point of projection A (Plate 

 VI. Miscell. fig. 8, 9, 10, 11) draw A m re- 

 presenting the horizontal distance, and 

 B m the perpendicular height of the ob- 

 ject aimed at : bisect A m in H, and A H 

 'in/; on H and / erect H T, / F perpen- 

 dicular to the horizon, and bisecting A B 

 the oblique distance or inclined plane in 

 D, and A D in F. On A raise the impetus 

 A M at right angles with the horizon, and 

 bisect it perpendicularly in c, with the 

 line G G. Let the line A C be normal to 

 the plane of projection A B, and cutting 

 G G in C ; from C as centre, with the ra- 

 dius C A, describe the circle A G M, cut- 

 ting, if possible, the line F S in S, s, points 

 equally distant from G ; lines drawn from 

 A through S, s, will be the tangents or di- 

 rections required. 



Continue A S, A s to T, t ; bisect D T, 

 D t, in V, v j and draw lines from M to 



S, *; then the angle A S F = angle MAS 

 = angle A M s = angle s A F ; and for 

 tlu: same reason angle A * F = angle M As 

 = angle A M S = angle S A F ; where- 

 fore the triangles M A S, S A F, s A F are 

 similar, and A M : A s: : A. s : s F = t v, 

 consequently A T is a tangent of the curve 

 passing through the points A, v, and B; 

 because t v === v D, A D is an ordinate to 

 the diameter T H, and where produced 

 must meet the curve to B. 



In horizontal cases (fig. 10.) v is the 

 highest point of the curve, because the 

 diameter T v H is perpendicular to the 

 horizon. 



When the mark can be hit with two di- 

 rections (the triangles S A M, s A F being 

 similar) the angle which the lowest direct- 

 tion makes with the plane of projection is 

 equal to that which the highest makes 

 with the perpendicular A M, or angle 

 s A F =5 angle SAM. And the angle 

 S A s, comprehended between the lines of 

 direction, is equal to the angle S C G, and 

 is measured by the arch S G. 



When the points S, s coincide with G, 

 or when the directions A S, A 's become 

 A G (fig. 11.) A B will be the greatest 

 distance that can be reached with the same 

 impetus on that plane ; because S F coin- 

 ciding with G^, the tangent of the circle 

 at G, will cut off A , a fourth part of the 

 greatest amplitude on the plane A B. The 

 rectangular triangles m A B, c A C are si- 

 milar, because the angle of obliquity 

 m A B = c A C ; wherefore m A : m B : : 

 one-half impetus : c C, and m A : A B : : 

 A c : A C. 



Horizontal Projections (ibid. fig. 10, 11.) 



When the impetus is greater than half 

 the amplitude, there are two directions, 

 T A H and t A H, for that amplitude ; when 

 equal to it, only one ; and when less, none 

 at all ; and conversely. For in the first 

 case the line F S cuts the circle in two 

 points 9, s, in the second case it only 

 touches it, and in the last it meets not with 

 it at all; and conversely. When there is 

 but one direction for the amplitude A ;n, 

 the angle of elevation is 45 ; and when 

 the angle of elevation is of 45, A m is the 

 greatest amplitude for that impetus, and 

 equal to twice the impetus. The impetus 

 remaining the same, the amplitudes are in 

 proportion to one another as the sines of 

 double the angles of elevation, and con- 

 versely. For drawing s N (fig. 10.) pa- 

 rallel and equal to A F, a fourth part of the 

 amplitude, and supposing lines drawn 

 from s to the points C and M, the angle 

 AC s = 2AMs = 2sAF; therefore 



