The great debate, the endless questions, the historic evidence, the ideas and theories, the dilemma, rake, fleam angle, taper, belly, grip, set, down to the saw bolts has been discussed where ever woodworkers gather and talk saws.
I will be discussing saw sharpening only briefly (if that is possible) as it is covered elsewhere including here. I will talk of set (oh wait I did that part) but I am going to discuss whetting or side joining saws as the final and I believe important step in properly saw sharpening. I will get to hammer straightening a bent blade which I should have done earlier but there is nothing I can do about it now.
A cross cut saw is used to cut across the grain of the wood and are sharpened like knife points to score then shear the fibers of the wood.
A rip or splitting saw is used to cut with the grain and are sharpened like chisel points (or little tiny plow plane blades) to excavate the wood from the groove. Usually with fewer teeth per inch and larger gullets to remove the dross.
Now in order to blur the line a little, here is a RIP/CROSS CUT saw blade in a nineteenth century American pattern bow saw, curly hickory arms, maple handles, white oak stretcher and the walnut and mahogany toggle is inspired by Eric Sloane. The blade is after one illustrated in Salaman.

And while it may be difficult to see the blade is cranked at 90 degrees in the middle of the thin blade. The portion on the right is sharpened rip and the portion on the left is sharpened rip. I use this saw to remove the waste between the pins when finishing my dovetails (tails first, as I gang saw the tails). It is surprisingly easy to use and astounds people when I demonstrate how it works. It cuts (rips) down to the score line, then when the crank (with its tapered transition) is pushed it begins to cut (cross cut) to finish the removal. Attention must be paid to the angles of the pins and sawing is done on the money side (the one that shows).
Tooth count: the general reference for the coarseness of saws is TPI or teeth per inch. Now there are PPI or points per inch and I don’t know why there is a difference, perhaps a saw maker could respond? Rip saws usually have fewer teeth per inch with larger gullets to remove the dreck rapidly as is their want. Cross cut have finer teeth and vary remarkably as do the teeth of rip saws. And here is a general guideline (I avoided the use of the word rule), finer tooth patterns are for thinner boards and coarser tooth patterns are for thicker wood. This helps eliminate the saw dust easily. Fine toothed saws, either rip or cross cut will tend to bind up on thicker boards. Finer teeth produce finer cuts and are more suitable for thin pieces of wood.
Some blades are taper ground with the teeth being the thickest and the back being thinner. This helps reduce binding and allows for little or no set to the blade and still cut and not bind. Some open hand saws are tapered in the same way but also tapered to be thinner at the tip and tapering to thicker at the handle. This of course makes the nicker nib nice and thin and capable of breaking off. (It is easily filed back into the tip of the blade). That nib works just fine, it doesn’t need to be as wide as the teeth, all it needs to do is make that fine nick on the edge of the board to start the cut.
And the reason for the blades being wider at the handle or heel and narrower at the toe? Because you can use the narrow toe to correct any errors in sawing as the narrower tip allows for correction to an arrant saw kerf. Like a narrower blade can make a tighter circle, a narrower part of a blade can do the same thing.
And apparently not all saw were provided straight as many had bellies (breasted) with the teeth being higher in the center. Now I am not talking those floor or veneer saws but open hand saws, cabinet and panel saws (maybe there is a distinction there). And the P.S. Stubbs blade I have, albeit a web blade has a belly. I am not sure it could be called breasted because the entire blade as a belly (convex), the back being slightly concave.
And of course there are those progressive toothed saws, finer at the tip and coarser over the rest of the blade, this is to assist in starting the cut after using the nicker nib.
And there are examples of both cross cut and rip in open and framed. The open saw is lighter in weight but can have a much thicker blade than a framed saw. The frame saw has the advantage of using thin and narrow blades for certain applications like cutting curves, they can also be used to hold thin and wider rip blades for splitting boards with a thin kerf. The disadvantages of framed saws are weight (which isn’t that much of a disadvantage) and most importantly limited cutting because of the frame. At some point, unless ripping off the edge of a board the frame will get in the way.
The advantage of the open saw is that it has no frame (and no back) so it can cut through pieces of wood that could not easily be done with a frame saw. Speaking of back saws, as many of you know I am not a big fan of backed saws, I am down to only one very small brass backed Gent’s Saw that I use for fine work. Larger back saws have always felt awkward in my hands and I never found one I liked, and I have gone through a couple dozen. I think this is another marketing ploy by manufacturers, ‘a thinner saw kerf’, I think less saw, more money. Why would anyone in the nineteenth century worried about the size of the kerf? Ok, marquetry, but that is a different saw.
When I saw dovetails, I use my widest (kerf) unbacked dovetail saw, the more wood I can saw out the less I have to remove with a chisel. If I did finer work, maybe I would want a thinner saw. But my dovetail saws are all used for general purpose ripping of small pieces, I grab the big rip saw to rip the big boards.
Then there are the saws that need to cut both cross cut and rip, like a fine turning saw, compass saw, coping saw, fret saw, &c, how are these sharpened? Half and half, the teeth are filed with the hook of a rip saw and the fleam or side angle of 80 degrees.
Stephen