.i:i;v. 



UUXXERY. 



7a 



The above formula is obtained thus, t - - nearly ; and 1" : t : : 32 : 

 33 1 = the velocity generated or destroyed by gravity in ( I ) time ; 

 therefore, 32 1 : </ : : : r - jjj but t = .'. r = -gJJ* = *&* 



force of resistance. From the results of the experiment*, which 

 though not sufficient to establish a perfectly true theory, enable us to 

 obtain results sufficiently accurate for all practical purposes, it appears 

 that the resistances are in rather a higher ratio than the squares 

 of the diameters of the shot; and, as examples of the amount 

 of the resistance, it may be observed, that a ball weighing 3 Ibs., 

 when moving at the rate of 500 feet per second, was opposed by 

 a force equal to about 35} Ibs. ; and, when moving with the velocity of 

 1700 feet per second, by a force equivalent to the pressure of above 

 154 Ibs. It was found also that there is a gradual increase in the 

 exponent of the resistance as the velocity increases, probably on 

 account of the partial vacuum behind the ball. . When the motions 

 were slowest, the resistance was nearly proportional to the square of 

 the velocity ; and when the shot moved at the rate of 1500 feet per 

 second, that exponent seemed to have attained its maximum, the 

 resistance being then nearly as the 2j power of the velocity, Beyond 

 that rate of motion the exponent of the resistance gradually decreased. 

 In the preceding fornmUc the height h, or that which is due to 



V s 



the initial velocity, is by the theory of forces equal to 5- ; where v 



represents the initial velocity, and g, as before, = 32J feet. To obtain 

 the value of u it must be observed that, from hydrostitical principles, 

 we have 4 r*rp D for the resistance experienced in moving through a 

 fluid by a body which is terminated in front by a hemispherical 

 surface ; where r is the semi-diameter of the sphere, D is the specific 

 gravity of the fluid (air in the present case), and p is a co-efficient 

 which must be determined by experiment. Then the mass of the 

 shot being equal to jr'irD' (where D' is the specific gravity of the 



shot), dividing the former of these terms by the latter we have g-,- 



for the retardative power of the resistance. Hence V"5 becomes 



v ^p 



the terminal, or constant velocity, with which the shot would descend 

 in the air when the resistance of the latter becomes equal to the acce- 

 lerative power of gravity. 



, Now, in the preceding investigations, -g- was made to represent 



A.D/> 



-jj ; therefore, substituting for A its equivalent I s r, and for u its 



4 r jy 

 equivalent J r> T D', we shall get H = g ; which, being compared with 



the above expression for the terminal velocity, is evidently the height 

 due to that velocity, or the space through which a body must descend 

 from rest, m racuo, to acquire that velocity. 



Dr. Hutton, having formed a table exhibiting the resistances expe- 

 rienced by shot when moving with different velocities, determined from 

 it, by simple proportions, the values of the terminal velocities for solid 

 shot weighing from 1 Ib. to 42 Ibs. (Tract 37, art 69.) And in the same 

 Tract (art. 122) he has given a table of terminal velocities for several 

 natures of shells. These last velocities necessarily differ from those of 

 solid shot, because the shells have less weight than solid shot of equal 

 diameters. Assuming therefore that the internal diameter is A of the 

 external diameter of a shell, he estimates the ratio of the weights of 

 the solid and hollow shot to be as 1-42 to 1 ; and, in order to express 

 the terminal velocities of the latter he diminishes those of the former 

 in that ratio. Hence the formula for the terminal velocity of a shell 

 should be 



Syr 



1-42 



3 Dp 



and from the numbers given in the tables it appears that n may be 

 considered as equal to 0-6849. On putting this formula in numbers, 

 r and .7 must be expressed in terms of the same denomination. 



It is easy to conceive that by increasing the charge to a certain 

 amount the velocity will also be increased, and that when the quantity 

 of powder is so great that the ball is driven out of the barrel before 

 >e whole ban tune to act upon it, the velocity must become less. 

 Twere U evidently therefore a certain quantity of powder which will 

 produce the greatest possible velocity ; and this may be determined by 

 making the differential of the expression above found, for the velocity, 

 equal to wsro, the length a of the space occupied by the charge being 

 considered as variable. Dr. Hutton makes the charges for producing 

 the maximum velocity to vary with tho length of the gun : thus the 

 length of the bore being equal to 10, 20, 30, 40, and 50 calibres, the 

 numbers 0-5, 0'84, 1-0, 1-28, and 1'43 will respectively express the 



""*&, Ow P" rde1 ' m term of "> weight of the shot. (Tract 37, 

 art. 189.) 



The service charges, in terms of the weight of the shot, 



For brass and iron guns 

 For brass howitzers . 

 For carronades 



'. 



From experiments which have been carried on at Woolwich, on 

 Button Heath, and in France, the following very brief abstract of the 

 circumstances attending the Sight of projectiles has been drawn up : 



I. Experiments with solid shot fired at point blank. 



II. Ricochet practice in 1821. 



Solid Skat. 



From the result of the experiments it appears that at a range of 

 400 yards, with a weight of powder equal to ,'j of the weight of the 

 shot, about two-thirds of the rounds took effect : at 600 yards, with 

 charges from & to &, from one-half to one-third took effect; and, at 

 800 yards, with charges from ,', to , l , from one-third to two-fifths took 

 effect. It is hence concluded that ricochet batteries should, if possible, 

 be at distances between 400 and 600 yards from the object : at a 

 greater distance much of the ammunition would bo uselessly ex- 

 pended. Also that, with both shot and shells, the best elevation for 

 enfilading a work is from 6 to 9 above the crest of the parapet of the 

 work. 



IIL Practice with a 10-inch 

 mortar, Button Heath, 1811. The 

 elevation = 45' and the weight of 

 the shell =96 Ibs. 



Practice with a French 12-inch 

 mortar, Toulon, 1830. The ele- 

 vation = 45* and .the weight of 

 the shell =162 Ibs. 



