Joseph Rodgers & Co (not Sons)

[knife7knut]

Looks like a Cake or Bread knife ? likely with a silver handle.
kj

With that saw back I would think it was likely used for frozen foods or possibly to sever the joints on poultry. Hard to tell the size but it looks to have about a 6-7 inch blade.

[kootenay joe]

I cannot make out how 'aggressive' the teeth are. If old i doubt it was for sawing through frozen anything as it would be from before freezers.
I had thought they were of a more scalloped shape as seen in bread knives. Cutting apart joints usually involved saws designed for the purpose.
But you have it in hand so can feel and read the knife better than we can through pictures.
kj

[knife7knut]

Well Roland there were frozen foods before the advent of freezers. It could possibly be used for scaling fish as well. Doesn't look a very robust blade so maybe the frozen food thing is off the table. You are correct;bread knives have a much more scalloped edge to them.The way the word Company is abbreviated indicates it was likely made around 1900 or a bit before.

[kootenay joe]

"there were frozen foods before the advent of freezers"
How so ? Freeze something in the winter and then pack it frozen in a block of ice covered by a few feet of straw in a root cellar, is the only way i can think of. This would not make frozen items common enough that the average household needed a tool to saw through something.
My parents were British. Every Sunday we would share a "joint" ! "Joint" is (was ?) the British word for a piece of meat to be roasted. It would have a bone in it and often a joint as in ham or pork roast, etc. My father was very traditional British, and would carve the joint. He could take apart a joint with a carving knife, never with saw teeth. My point is that sawing through bones was not something done at the table and the o.p. knife is a fancy one, for the table, not for butchering.
kj

[Reavis Ranch]

6 inch blade, pretty sturdy. Handle is hollow; more delicate than the blade.

I would gather a bread knife, or cake knife, from your observations.

[knife7knut]

Check Wikipedia on frozen foods. First developed in 1861 by someone in Australia and developed commercially in the 1880's.

[kootenay joe]

I am surprised to hear this: "frozen foods. First developed in 1861 by someone in Australia and developed commercially in the 1880's"
However household use of a freezer compartment in a fridge goes back to about 1930's. I remember ice boxes which preceded refrigerators.
We are speaking about a 'householder' knife not a commercial use knife.
kj

[Sydres]

Wedding cake knife. Many that I have looked at had the serations.

[kootenay joe]

Wedding Cake knife. That makes sense. I can remember when giving the bride a fancy knife to cut her wedding cake (and then keep) was common practice.
kj