VELOCITY. 



the indices of the velocities 2 and 3 are homogeneal, 

 and therefore the velocity of A is to the velocity of B, 

 a 2 to 3. 



Hence, if the fpace be = s, and the time = /, the velo- 

 city may be exprefled by — ; the fpace being in a ratio of 



the time and the velocity. See Motion. 



Velocity, Circular. See Ciuculau. 



Velocity, Initial, in Gunnery, denotes the velocity with 

 which military projeftiles ifTue from the piece by which they 

 are difcharged. This is now known to be much more con- 

 liderable than was formerly appreliended. For the method 

 of eftimating it, and the refult of a variety of experiments 

 by Mr. Robins, Dr. Hutton, &c. fee Gun, Gunnery, 

 Projectile, and Resistance. 



We Ihall here add, that Mr. Thompfon (Count Rumford) 

 has lately publifiied the refult of a variety of experiments 

 upon gunpowder, and alfo an account of a new method of 

 determining the velocities of all kinds of military projeftiles. 

 From the equality of aftion and re-aftion, it appears, fays 

 Mr. Thompfon, that the momentum of a gun muft be pre- 

 cifely equal to the momentum of its charge ; or that the 

 weight of the gun, multiplied into the velocity of its recoil, 

 is lull equal to the weight of the bullet and of the powder 

 (or the elaftic fluid that is generated from it) multiplied 

 into their refpeftive velocities : for every particle of matter, 

 whether folid or fluid, that iffues out of the mouth of a 

 piece, muft be impelled by the aftion of feme power, which 

 power muft re-aft with equal force againft the bottom of 

 the bore. 



It is eafy to determine the velocity of the recoil in any 

 given cafe, by fufpending the gun in a horizontal pofition by 

 two pendulous rods, and meafuring the arc of its afcent by 

 means of a ribbon, according to the method which Mr. 

 Thompfon has defcribed, and this will give the momentum 

 of the gun, its weight being known, and confequently the 

 momentum of its charge. 



But in order to determine the velocity of the bullet from 

 the recoil, it will be necefljry to find how much the weight 

 and velocity of the elaftic fluid contribute to it. That part 

 of the recoil which arifes from the expanfion of this fluid is 

 always very nearly the fame, whether the powder is fired 

 alone, or whether the charge is made to impel one or more 

 bullets, as Mr. Thompfon has determined by various 

 experiments. 



If, therefore, a gun, fufpended according to the method 

 propofed, is fired with any given charge of powder, but 

 without any bullet or wad, and the recoil is obferved ; and if 

 the fame piece is afterwards fired with the fame quantity of 

 powder, and a bullet of a known weight ; the excefs of the 

 velocity in the latter cafe above that in the former, will be 

 proportional to the velocity of the bullet ; for the difference 

 of thefe velocities, multiplied into the weight of the gun, 

 will be equal to the weight of the bullet multiplied into its 

 velocity. 



Accordingly, if W is put for the weight of the gun ; U, 

 for the velocity of its recoil, when it is fired with any given 

 charge of powder, without any bullet ; V, for the velocity 

 of the recoil when the fame charge is made to impel a bullet ; 

 B, for the weight of the bullet, and v for its velocity ; we 



V — U X W 

 ftiall have v — .- . Let B = 580 grains, W =: 



336,000 grains ; and, therefore, B : W ;; 580 : 336,000; 



;. e. •.: \ : 579.31 nearly, and V — U is found by experi- 

 ment to be equal to 1.8522 ; and, confequently, 11 = 

 1.8522 X 579.31 — 1073 feet in a fecond ; which is very 

 near 1083 feet in a fecond, the mean of the velocities de- 

 termined by the pendulum after the manner of Mr. Robins. 



But the theorem will be rendered more fimple by putting 

 c for the chord of the recoil in EngUfli inches, when the 

 piece is fired with powder only, and C for the chord when 

 a bullet is difcharged by the fame charge ; and then 



V — U X W 

 C — c will be as V — U ; and confequently, as 5 ' 



which meafures the velocity of the bullet, the ratio of W to 

 B remaining the fame. 



Suppofing, therefore, C — c = I inch, and the velocity 

 of the bullet to be computed from that chord ; the velocity 

 in any other cafe, in which C — c is greater or lefs than one 

 inch, will be found by multiplying the difference of tlie 

 chords C andc by the velocity that anfwers to a difference 

 of one inch. Or the velocity of the bullet, exprefled in 

 feet per fecond, may in all cafes be found by multiplying the 

 diff"erence of the chords C and c by 1 18.35 } the weight of 

 the barrel, the length of the fufpending rods, and the weight 

 of the bullet, remaining the fame, whatever be the charge of 

 powder or its ftrength. 



According to this rule, Mr. Thompfon has computed by 

 feveral experiments the velocities of bullets from the recoil, 

 and compared them with the velocities obtained by the pen- 

 dulum. The refult, making the neceffary allowances for 

 the difference in the conchifions arifing from thefe two me- 

 thods, leads Mr. Thompfon to infer, that there is the greateft 

 probabihty that the velocities of bullets may in all cafes be 

 determined by the recoil with great accuracy ; and if this 

 method fucceeds with mufquet-bullets, it may alfo be ap- 

 plied as well to cannon-balls and bomb-fheUs ot the largeft 

 dimenfions : he apprehends alfo, that it will be much pre- 

 ferable to any other method hitherto known, not only as it 

 may be applied indiff'erently to all kinds of military projec- 

 tiles, with little trouble or expence, but alfo becmfe by 

 this method the velocities with which bullets are aftually 

 projefted are determined ; whereas, by the pendulum, their 

 velocities can only be afcertained at fome diftance from the 

 gun, after they have loft a part of their initial velocities by 

 the refiftance of the air through which they are obliged to 

 pafs to arrive at the pendulum. 



Thofe who advert to what has been deUvered under the 

 article Gunnery, will find that, according to Mr. Robins's 

 theory, farther confirmed by Dr. Mutton's experiments, 

 when bullets of the fame diameter, but different weights, 

 are difcharged from the fame piece by the fame quantity of 

 powder, their velocities fliould be in the fubduplicate ratio 

 of their weights. 



But this theory, fays Mr. Thompfon, is founded upon a 

 fuppofition, that the aftion of the elaflic fluid, generated 

 from the gunpowder, is always the fame in every given 

 part of the bore when the charge is the fame, whatever may 

 be the weight of tlie bullet ; and as no allowance is made 

 for the expenditure of force required to put the fluid itfelf 

 in motion,, or for the lofs of it by the vent, he concludes 

 that the theory is defeftive. And from a variety of experi- 

 ments, made with a view of afcertaining this point, he infers, 

 that the ratio of the velocities of bullets to their weights is 

 different from that which Mr. Robiiis's theory fuppofes ; 

 and from other experiments he finds, that the velocities 

 computed, according to the reciprocal fub-triplicate ratio 

 of the weights, agree much better with the conclufions de- 

 duced 



