Looking through La France Maritime au Temps de Louis XV et Louis XVI: Gravures et dessins des frères Ozanne. Peintures de Joseph Vernet by Alain Boulaire (ISBN 2-911468-75-9), there are many images with barrels. It seems fair to say that there is no one way to transport barrels — they were loaded as people thought convenient, and not always with the head or bilge down.
The first image (p. 60), show a barrel on its head in the stern of a boat.
The second image (p. 68) shows a barrel resting on its bilge on the thwarts. I always prefer to get the center of gravity lower, and I can’t decide if the barrel is in the process of loading or unloading, or they would rather have the easier time of moving it from the thwarts than of lowering it and raising it.
Here (p. 77) the barrel is in the bows of the boat with the bilge of the barrel resting on the stem of the boat.
Another (p. 87) barrel high up on the thwarts.
This image is on the fold of pages 96 and 97. The barrel is half off the edge of the stern.
Lastly (p. 97) is a boat full of barrels, stacked neatly in the bow and stern.
Here is a 33 foot launch specifically designed to carry 150 gallon barrels of water. The scan is from The Boats of Men-of-War by W. E. May, p. 43.
We’ve often wondered if there was a particular way that barrels were always loaded. We’ve tried loading barrels in the bateaux both with the bilge down and with the head down. We’ve also tried with the bilge of the barrel athwart the vessel and with the bilge along the axis of the vessel. As far as convenience of loading empty barrels, having the bilge along the axis of the vessel seems easiest and gets the most barrels in the bateau, but I have no idea if this was the standard method or not.
I was looking through Sailing Vessels in Authentic Early Nineteenth-Century Illustrations (“Sixty Five Plates of Shipping and Craft”) by Edward William Cooke, originally published in 1829 with reprints at various times. I have a Dover Publications book from 1989 (ISBN 0-486-26141-7). On page 16 is a plate which shows a small boat loaded with barrels (see picture). Rather than the barrels all being stacked one way or another, they are all in a jumble, stacked any which way. From this, I conclude that there is no standard method of loading them.