The Hanoverian design being considered at the same time the original Brunswick came out was an oval bore 1:75'ish twist capable of shooting a standard PRB. The prototype Brunswick had 11 standard square grooves at 1:70'ish and when the change was made to two-groove & belted ball, the twist remained 1:70'ish until it was increased to 40'ish then 30'ish to try getting some kind of accuracy from the belted ball. Forsyth wasn't involved with the Brunswick which was the Brit’s first documented attempt to use a belted ball with the belt running parallel to the bore, the Bubba in charge who selected the belted ball Brunswick was George Lovell.
Belted balls were nothing new at the time the Brit's got around to the Brunswick but the previous styles including those associated with the earlier two-groove barrels oriented the belt perpendicular to the bore opting to key the belt to the rifling thus eliminating the stripping in fast-twists but creating a projectile that still sucked for accuracy. Earlier twin square style groove and the oval-bore (radius groove) rifles used standard PRB’s, not belted balls and performed quite well even at long ranges. One must consider the fact that the Brit's lagged far behind much of the rest of Europe in weapons development and technology right up into the 20th century. Better than a century after the Russian's pretty much perfected the shotgun choke, the Brit's were still insistent that the only way to increase shotgun range was to use a bigger bore and simply throwing a larger payload of pellets in the hopes some will connect. Aside from the odd gun here and there, it also took about as long for the Brit's to finally figure out that one doesn't need 4+ feet of barrel to make an effective weapon just as they refused to accept the value of the superior sighting systems used by others as early as the 16th century. By the time the Brit's were screwing with belted balls in the Brunswick, others in Europe were producing excellent long range accuracy with conical bullets for which the much faster rifling twist rates were required. This boils down to the chicken or egg debate where in the case of the Brit’s, the egg being the belted ball came before the fast-twist chicken because the first belted ball Brunswick rifles were slow-twist and the faster twist rifling didn’t come about until later as they tried to get some kind of acceptable accuracy from the belted balls that others had long since culled as being worthless. That’s not to say fast-twist rifling didn’t exist because we know it did, what the evidence shows is that the British belted balls did not come about as a result of the fast-twist rifling.
According to George in "English Guns and Rifles" the issue Brunswick was always a 2 groove. While adopted in 1836 it was not actually in the hands of the troops until 1839. It was a very poor rifle. Far less accurate than the flintlock rifle it replaced that had slow twist conventional rifling. They were trying to make a more accurate rifle than the Baker, they failed miserably. But the prevailing wisdom of the time was that a faster twist was needed and the belted ball was needed to allow that twist.
This rifling form came about in the British sporting rifles because they were over twisting large bore sporting rifles, 12-8-4 bore, to the point of making them useless with conventional rifling. This is detailed by George.
Samuel Baker's 2 groove rifle (the 2 ounce apparently was a 12 bore that used a 2 ounce conical according to George, he may have been familiar with the actual rifle) was in use in the 1850s and Forsyth was writing in the late 1850s. My reprint of "Sporting Rifle and its Projectiles" was originally published in 1863 just a few years before the self-contained cartridge breech loader began to really replace the ML.
By the 1850s the Brunswick had been mostly or wholly supplanted by the slow twist Rifle Musket in the major militaries of the world making the rifle companies, until that time elite units, obsolete.
But the belted ball lived on in the English sporting rifle.
Fast twists are required for bullets
and elongated projectiles have a better grip on the grooves than the ball since their high inertia will cause the bullet to expand to groove diameter even if a relatively hard alloy. So the fast twists and bullets is apples and oranges to balls or belted balls. The British also experimented with and apparently produced a number of "winged" bullet rifles with mechanically fitted bullets some with 4 "wings" that engaged very deep grooves. Various shapes were tried. While these may have shot better than the belted ball in the hunting rifle of the time they were considered useless. A number of 19th century writers point this out, Greener, Samuel Baker and Forsyth.
Baker had a 4 ounce conical bullet mould made for his 21 pound "3 ounce belted ball " "Devil Stopper" and "...it entirely destroyed is efficacy and brought me to such scrapes that I at length gave up the conical ball as useless." This was was written in the "Field" in 1861. The charge in this belted ball rifle was 12 drams or 330 grains. If George is correct it likely had a twist of 1:30 or even fasters, too fast for conventional rifling to hold a patch with a spherical ball this size and this charge of powder. So the belted ball.
And yes the British knew the belted ball design dated to the 1620s. But its use in England appeared with the fast twists that made the conventional RB unusable. The interesting part is in rifles under 20-16 bore the English staid with the slow twists for the most part. And conventional rifling and balls
Dan