Pressure required to give Rotation to Rifled Projectiles. 205 



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 velocity 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 Com- 

 mittee, 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 advantages 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 Ex- 

 plosives, 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 ap- 

 peared, and have led to much discussion 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 argu- 

 ment, which lies in confounding velocity with rate of accelera- 

 tion. 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 parabolic or uniformly increasing twist ; and in this inves- 

 tigation I shall adopt the notation used in my former paper. 



10. Take, then^ as the plane of ccy a plane at right angles to the 

 axis of the gun. If the angle of rifling commence at zero, increa- 

 sing to, say one turn in n calibres, let the plane of xy pass through 

 the commencement of the rifling ; but if the rifling do not com- 



