sirgknight

If a rim size is 26 X 1&3/8 will any size 26 inch tire fit the rim; i.e. 26 X 1.75? or, do we need to stay with the 1&3/8 size?

juicemouse

As the bicycle has evolved over the years, many different tire size standards have been developed. Almost all of them are incompatible with one another. Sheldon Brown wrote a comprehensive article about all these different standards, and it's here on his website:

https://sheldonbrown.com/tire-sizing.html

In your case, you'll definitely have to stick to fractional designations of tire width instead of decimal designations (i.e. not 26 x 1.75), and may even be restricted to the 26 x 1 3/8 size you have on there now. The way to find this out for sure would be to look for an ISO standard designation on the side of the tire that you have on there right now and match the last number up to your new tire. This is explained in the article I linked to above. Since the title of your post indicates that the bike is "old", the tire on there now might be old too, in which case it might not have any ISO designation. If you tell us the make and preferably the model of the bike, we might be able to tell you what ISO rim size you have, or if you know something about it you might be able to figure it out for yourself from the descriptions of the bikes that normally had certain rim sizes in the ISO chart on the linked-to page above.