As Ken explained
Sporting Guns and Gunpowders: Comprising a Selection from Reports of Experiments, and Other Articles Published in The "Field" Newspaper, Relative to Fire Arms and Explosives, Fredrick Toms, 1897
From
The Field Jan. 15, 1896 Vol 91, p. 91
http://books.google.com/books?id=inQCAAAAYAAJ&pg=PA335&lpgA. - Damascus metal is a mechanical mixture of steel and iron.
B. - This mixture is affected in the following way: A number of small thin sheets of iron and steel (alternees), being placed alternately (faggotted or piled), are firmly wired or boxed together (forming the lopin or billet), heated in a furnace, and welded into a solid mass.
C. – The mass is then rolled out into long thin square bars or rods.
D. – The rods are then cut up into convenient pieces.
E. – Each piece is then heated and placed in a machine, in which one end of the piece is fixed, and the piece is rotated from the other end – the result being that the piece is twisted or corkscrewed very finely.
F. – The rods are rolled of various thicknesses, according to the number of rods in the particular barrels to be made. The finer the barrels are required, the smaller is the diameter of the rods, and the greater the number of rods required for a barrel.
G. – Two, three, four, or six rods are then taken, and are heated and welded together at the sides. Thus is made a flat strip, a little more than two, three, four, or six times wider than a single rod.
H. – Damascus barrels are made usually in two (
OR THREE) parts, fore part and back part, the back part being made of thicker metal than the fore part.
I. – This is done to avoid having to roll the strip taper from end to end, and to enable the welder to “jump” the barrel more powerfully than he would be able to “jump” a full length barrel.
J. – The strip is heated and rolled into a ribbon (ribband).
K. – This ribbon is cut into convenient lengths, one length sufficient for a fore part or back part, as the case may be.
L. – The ribbon is then (either with or without being heated) twisted round a round rod (mandrel) in a machine, and thus formed into a spiral tube.
M. – The spiral tube is then heated and welded by “jumping” the edges of the spiral together and hammering round the sides. This process is generally effected thus: an iron rod is inserted into one end of the spiral, and spiral placed in furnace, and when heated sufficiently, the welder withdraws the spiral from the furnace by means of the rod, and places it horizontally under a specially-made trip hammers, and “jumps” it hard vertically on an iron block let into the hearth floor, in order to force the edges of the spiral together. The hammering and “jumping” are repeated alternately as many times as required. The spiral is thus made into a rough tube. The tilt-hammer is not always employed; hand-made barrels being made by a welder and one or two strikers using welding hand-hammers.
N. – The two (
or three) tubes, fore part and back part, are then heated at their joining ends and welded into one, and they then form a finished rough tube.
Aesthetically, the barrels are a bit of a mess with poorly matched tube segments, but that has nothing to do with functionality and you should be proud of your acquisition.
All 6 tube segments appear to be 3 Iron "Oxford" variants; the breech "Horseshoe". The butt weld lines are apparent here
This is a Parker with 3 Iron "Horseshoe" with mismatched segments
More examples here
http://www.picturetrail.com/sfx/album/view/18015717Part of the pattern difference is in the amount of barrel material removed with grinding to the desired thickness.
I would very much like to own your barrels as an example of
SIX English Damascus patterns! 
See
http://www.picturetrail.com/sfx/album/view/18059733
