Dunham, Carrigan and Hayden Co. was a premiere hardware store based in San Francisco. I've seen axes, pocketknives, hammers and guns, and now this crosscut saw, marked with their logo. This saw was probably made by another company and carried by D,C &H.
The saw logo reads: "Clean Cut" "This brand is a guarantee of the highest quality" "This saw is hand filed and set" "Patent Ground" "Thin back - Warranted"
Atkins' was Segment Ground. I went back and took another look at those New Zealand Disstons from this (attached) catalog you sent me a few months ago, and sure enough, they're Patent Ground. Maybe one was for crescent ground, the other for straight ground? Patent would then be flat ground, I guess. Disston also had an Imperial Ground, according to Saws that Sing...so maybe they just couldn't agree on what to call it. I don't have the tools to measure the width of the saw at different points, but I'll follow up if I do.