Research wide guide / narrow guide.
Trickiest inaccuracy issue on a lathe, or other machine tool with sliding components, is sideways twist. For any given degree of clearance, slop or wear long and thin gives less angle of twist than short and fat. So all other things being equal (they never are tho') a thin guide is a better design than a wide one of the same length.
Lathe guideways are predominantly triangular. Vee ways. Not only long and thin but also favourable when it comes to wear because both sides of the guide and the thing that runs on it should wear together so the running on part (the saddle) theoretically just drops down without increasing clearances leading to more slop. Except that most jobs only use a small amount of the potential travel up and down the bed so wear is uneven with the most used part of the bed wearing more and the saddle wearing to match it. What actually happens starts getting complicated. Typically the other side of the saddle runs on a flat which keeps things stable and can support considerable load. But the flat parts also wear, at different rates too causing the saddle to twist slightly vertically further increasing the variations in shape along the guide. In practice it all works out pretty well until the machine has done lots and lots of work. Lathe guideway bearing areas are large, load per unit area pretty low and speeds modest. If you could lubricate things like the innards of a car engine a lathe, certainly a manual lathe, bed and saddle would last a lifetime or two.
In some ways two Vees are best. Southbend certainly thought so. Nice exercise for the gentle reader to sort out why a twin Vees could be good if you wanted to make a decently accurate machine relatively inexpensively and why its not more common.
Hardinge use the wide guide principle with their flat dovetail edged bed and go to considerable effort to make it work really well. Easy to forget that the original intent was to produce production machinery with relatively inexpensive, easily replaced, sacrificial wear beds. Morphing that into a high class toolroom product does beg the question "Why."
Older English lathes, especially the relatively inexpensive ones, used similar dovetail form beds. Primarily because such are inexpensive to produce on simple machinery. Big disadvantage of such beds is that both top and sides wear. Take up the wear OK by tightening gib strips but after very little wear things pull up tight enough that only the worn part of the bed can be used. Gibs have to be pretty tight or everything shakes under cuts. Vee bed systems can tolerate running relatively loose if need be. on any decent size machine the weight of the saddle helps keep things behaving.
Cross and top slides use wide guide style dovetails because there is pretty much no practical, affordable, alternative for that position.
An alternative is box, square edged ways. Common on big CNC machines as being the most rigid if well engineered. Also used on smaller lathes mostly because of easier and cheaper production. Myford used such for most of their post war production with two rectangular section shears, one at the front of the bed and one at the rear. Produced in both wide guide, running against the front of the front shear and back of the rear one, and narrow guide form with guides on both sides of the front shear. Folk have been arguing the toss about which is best ever since the lathes got enough use to wear.
Clive