GUNNERY. 



2 X 16 feet 1 inch is the velocity acquir- 

 ed bv the descent of a body in a second of 

 time; the square of which (4 X the square 

 of 16 feet 1 inch) is to the square of the 

 velocity required, as 16 feet 1 inch is to 

 the impetus at the point given; wherefore 

 multiplying 1 that impetus by four times the 

 square of 16 feet 1 inch, and dividing- the 

 product by 16 feet 1 inch, the quotient 

 will be the square of the required veloci- 

 ty : whence this rule. Multiply the im- 

 Eetus by four times 16 feet 1 inch, or 64 

 :et ^, and the square root of the product 

 is the velocity. 



Thus suppose the impetus at the point 

 of projection to be 3,000, and the per- 

 pendicular height of the other point 100; 

 the impetus at that point will be 2,900. 



I Then 2,900 feet multiplied by 641. f ee t 



: gives 186,566 feet, the square of 432 

 nearly, the space which a body would run 



i through in one second, if it moved uni- 



t formly. 



And to determine the impetus or height, 

 from which a body must descend, so as at 

 the end of the descent it may acquire a 

 given velocity, this is the rule : 



Divide the square of the given velocity 

 (expressed in feet run through in a se- 

 cond) by 64^ feet, and the quotient will 

 be the impetus. 



The duration of a projection made per- 

 pendicularly upwards is to that of a pro- 

 jection in any other direction whose im- 

 petus is the same, as the sine complement 

 of the inclination of the plane of projec- 

 tion (which in horizontal projections is ra- 

 dius) is to the sine of the angle contained 

 between the line of direction and that 

 plane. 



Draw out A t (fig. 8,) till it meets m B 

 continued in E, the body will reach the 

 mark B in the same time it would have 

 moved uniformly through the line A E; 

 but the time of its fall through M A the 

 impetus, is to the time of its uniform mo- 

 tion through A E, as twice the impetus is 

 to A E. And therefore the duration of 

 the perpendicular projection being dou- 

 ble the time of its fall, will be to the time 

 of its uniform motion through A E, as 

 four times the impetus is to A E ; or as 

 A E is to E B 5 that is, as A t is to t D ; 

 which is as the sine of the angle t D A (or 

 M A B its complement to a semicircle) is 

 the sine of the angle t A D. 



Hence the time a projection will take to 

 arrive at any point in the curve may be 

 found from the following data, viz. the im- 

 petus, the angle of direction, and the in- 

 clination of the plane of projection, which 

 in this case is the angle the horizon make 

 VOL. VI, 



with a line drawn from the point of pro- 

 jection to that point. 



Hence also, m horizontal cases, the du- 

 rations of projections in different direc- 

 tions with the same impetus are as the 

 sines of the angles of elevation. But in 

 ascents or descents, their durations are as 

 the sines of the angles which the lines of 

 direction make with the inclined plane. 

 Thus, suppose the impetus of any projec- 

 tion were 4,500 feet ; then 16 feet 1 inch: 

 1" : : 4,500 feet : 2r5", the square of the 

 time a body will take to fall perpendicu- 

 larly through 4,500 feet, the square root 

 of which is 16" nearly, and that doubled 

 gives 32", the duration of the projection 

 made perpendicularly upwards Then, 

 to find the duration of a horizontal pro- 

 jection at any elevation, as 20; say R : S. 

 angle 20 : : 32" : duration of a projection 

 at that elevation with the impetus 4,500. 

 Or if with the same impetus a body at 

 the direction of 35 was projected on a 

 plane inclined to the horizon 17, say as 

 sine 73 : sine 18 : : 32" : duration re- 

 quired. 



The tables in the next leaf, at one view, 

 give all the necessary cases, as well for 

 shooting at objects on the plane of the 

 horizon, with proportions for their solu- 

 tions, as for shooting on ascents and de- 

 scents. We shall in this place mention 

 some of* the more important maxims laid 

 down by Mr. Robins, as of use in prac- 

 tice. 1. In any piece of artillery, the 

 greater quantity of powder with which it 

 is charged, the greater will be the veloci- 

 ty of the bullet. 2. If two pieces of the 

 same bore, but of different length*, are 

 fired with the same charge of powder, the 

 longer will impel the bullet with a great- 

 er celerity than the shorter. 3. The ranges 

 of pieces at a given elevation are no just 

 measures of the velocity of the shot : for 

 the same piece fired successively at an in- 

 variable elevation, with the powder, bul- 

 let, and every other circumstance, as near- 

 ly the same as possible, will yet range to 

 very different distances. 5. The greatest 

 part of the uncertainty in the ranges of 

 pieces arises from the resistance of the 

 air. 6. The resistance of the air acts up- 

 on projectiles by opposing their motion, 

 and diminishing celerity; and it also di- 

 verts them from the regular track which, 

 they would otherwise follow. 7. If the 

 same piece of cannon be successively fired 

 at an invariable elevation, but with va- 

 rious charges of powder, the greatest 

 charge being the whole weight of the ball 

 in powder, and the least not less than the 

 fifth part of that weight ; then, if the ele- 

 vation be not lees than eight or ten d- 



M 



