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MINUTES OF PROCEEDINGS OF 
base of the shot is a maximum, and becomes greatly reduced during 
the passage of the shot from its seat to the muzzle of the gun. In my 
former paper I showed, in fact, that in a uniform twist the pressure on 
the studs was a constant fraction of the pressure on the base of the 
shot, the value of the fraction of course depending on the angle of the 
rifling; and as it is evident that the tension of the powder-gases at the 
muzzle is very small when compared with the tension of the same gases 
at the seat of the shot, it follows that in such a system of rifling the 
studs may have scarcely any work to do at the muzzle, while they may 
be severely strained at the commencement of motion. 
6. If, then, the defect of the ordinary or uniform system of rifling 
be that the studs are severely strained at the first instants of motion 
and are insignificantly strained at the instant of quitting the gun, it is 
obvious that it is possible to remove this inequality, and at the same 
time allow the projectile to leave the bore with the same angular velo¬ 
city, by reducing the twist at the seat of the shot, and gradually 
increasing it until it gains the desired angle at the muzzle. In fact, if 
we know the law according to which the pressure of the powder varies 
throughout the bore, it is theoretically possible to devise a system of 
rifling which shall give a uniform pressure on the studs throughout 
the bore. 
7. These reasons doubtless led the late Ordnance Select Committee, to 
whom the application of the increasing twist to the service guns is due, 
to propose its introduction ; and they selected as the simplest form of 
an increasing spiral the curve which, when developed on a plane 
surface, should have the increments of the angle of rifling uniform. 
This curve is, as is well known, a parabola; and as considerable advan¬ 
tages have been claimed for the parabolic system of rifling, I propose 
in this paper to examine and evaluate them. 
I may add that I should not have given the results I now give, 
before the full experiments made by the Committee of Explosives, as 
well as some investigations undertaken by Mr. Abel and myself are 
published, were it not that several groundless assertions concerning the 
Woolwich rifling have recently appeared, and have led to much dis¬ 
cussion and very unnecessary uneasiness. 
8. The argument commonly advanced against an accelerating twist 
is based upon the fact of the shot moving slowest at first, it being 
supposed that while moving slowest the shot will require less force to 
make it rotate; but there is a fallacy in this argument, which lies in 
confounding velocity with rate of acceleration. The shot undoubtedly 
moves slowest at first, but it acquires velocity most rapidly at first, and 
it is the gain of velocity that determines the strain upon the stud. 
9. The first question/then, which I propose is, to determine the 
pressure on the studs of a projectile fired from a gun rifled on a para¬ 
bolic or uniformly increasing twist; and in this investigation I shall 
adopt the notation used in my former paper. 
10. Take, then, as the plane of xy a plane at right angles to the 
axis of the gun. If the angle of rifling commence at zero, increasing 
to, say one turn in n calibres, let the plane of xy pass through the com¬ 
mencement of the rifling; but if the rifling do not commence at zero, 
