This is not a punt gun as its made for shoulder fire. This is not a market gun as the bore is too small for flock shooting. This is a sporting gun for taking swans one by one in the marshes. Their style is based on what they knew about balistics at the time as well as what they didnt know.
Duck guns for shoulder fire of a little larger bore were used in England in the 18th century. Here is a period write-up comparing and contrasting the duck (waterfowling) gun with the fowling or birding piece.
Duck Guns vs. Fowling Pieces in the 18th Century
...The circumstance of a duck-gun killing at a greater distance than a fowling piece, is not owing to its length, but to its- greater weight and thickness allowing the charge of powder to be doubled, trebled, or even quadrupled, which cannot be done in a fowling piece though strongly reinforced. For a barrel of five or six feet, such as that of a common duck-gun, weighing five or six pounds, and the whole piece twelve or thirteen pounds ; may be fired with a very large charge, without recoiling so much as to hurt the shooter, its weight being sufficient to resist the violent impulse occasioned by the in- crease of the powder. But in a fowling piece of three feet barrel, sufficiently strong to withstand such a charge, and whose weight altogether does not exceed five or six pounds, the recoil would be insupportable. Be- fides, they not only double or treble the powder in a duck-gun, but they put in a much greater quantity of shot than is ever employed in a fowling piece*. * Duck-guns are generally bent a little upwards near the muzzle, which, the gunsmiths say, makes them throw their shot farther than if they were perfectly straight. To obtain, therefore, from a piece of the ordinary length, the fame effects as from a duck-gun, nothing more, perhaps, is necessary than to have the barrel sufficiently strong to admit of the charge being doubled or trebled as required, and the whole piece heavy enough to render the recoil support- able. We may here observe, however, that an increase of the powder above the charge generally used, does not produce a proportional increase of range in the ball or mot: thus a double charge of powder will not throw the, ball or shot to twice the distance, nor a treble charge to three times the distance, the single charge does. This arises from the great resistance given by the air to the motion of the ball or shot, and which is proved to be fourfold if the velocity be doubled, and nine fold when it is trebled by an increase of the powder. So great is the change in opinion of late, with regard to the proper length for gun barrels, that many gunsmiths will now tell us, that short barrels carry farther than long ones ; and the reason they give for this, is, the greater friction of the ball or shot in passing through a long barrel, by which their velocity is retarded and their force diminished. If the barrel be so long that the additional impulse which the ball or shot is continually receiving in its passage, becomes less than the friction between them and the fides of the caliber, then, indeed, the barrel by being shortened will shoot with more force : but as the length of barrel required to produce this effect, is vastly greater than can ever be employed for any purpose, the objection does not Having now, we hope, thrown every light upon this question, that is necessary to determine us in our choice of the length, it will, perhaps, be expected, that we give our opinion, what length of barrel is best calculated for general use. The barrels which we ourselves employ, and which we have found to answer best for every purpose are from 32 to 38 inches; and whether we consult the appearance of the piece, its lightness, or the ease with which it is managed, we believe that a barrel not exceeding the one, or below the other of these numbers, is the most eligible.
An Essay on Shooting, Edie, 1789
