Bicycle with giant chainring

Here is a picture from a recent history of bicycles, called "Bike".

The caption reads: "Bicycle police in Stanford, Connecticut, in about 1910. The large gears on these bicycles suggest that these policemen were serious about chasing down offenders, though it would have taken some effort to work up speed."

This picture prompted me to seek out a bike with similar chainrings, but I have had no luck so far. I bought a mountain bike with what seemed like really tiny chainrings compared to these. The mechanic advised me to try it out before putting on road bike chainrings. I did try it out this summer, and yes, smaller chainrings are good for off road. But compared to these police bikes, even road bike chainrings are small.

Then I remembered another old bike I saw somewhere. I remembered that I have in my library an old Sears Roebuck calendar for Fall, 1900. Here is its illustration of the Acme Prince.

And look at the size of those chainrings! Just like those police bikes. This, by the way, was right at the end of the bike boom, when they could not give bicycles away. Not ten years before, a bike could not be had for less than a hundred dollars. Here is the text of the caption below the above  drawing.

"This handsome up-to-date bicycle is built with a diamond flush joint frame, 22, 24, or 26-Inch as desired. High grade steel connections, heavy nickel plate fork crown, heavy nickel plate drop or upturned handle bar. Well-made 28 inch wheels with good strong rims and swaged steel spokes, equipped with our own high grade season guaranteed Soroco single tube pneumatic tires, high grade, heavy nickel plated barrel hubs, with ball bearings ball retainers, good grade. heavy nickel plate ball bearing and ball retaining pedals, late new style one piece crank hanger. Handsome nickel plated sprockets, the bearings are all made from fine tool steel, are all ball bearing, accurately true to gauge. We use a good quality of chain. Gear 68 to 84 inches, as desired. We furnish a high grade, full padded saddle, finish the wheel in either black, green or maroon as desired, with all usual parts nickel plated, and at our special $14.75 price it comes complete with tool bag, pump, wrench, oiler and repair kit."

Needless to say, you could not get a bag or a pump for $14.75 now, much less a whole bike. You get a hint at the size of the chainring when it says it can have "68 to 84 (gear) inches." By comparison, my Czechoslovakian "Rapido" single speed, coaster brake bike, which I use for short trips about town, has 70 gear inches, which I find is fine for going slow (running the dog) or fairly fast.

My father, growing up in Hamilton in the 1920's, tells the story of how all the bikes in the neighbourhood were single speeds. Somehow, he got a hold of one with an unusually small rear sprocket. He took a long time to get up to speed, but once he did he left his buddies behind. Probably, it had the 84 gear inches mentioned in this catalogue.

There follows in this catalogue the women's version of this bike, also with oversized chainrings, appropriately called the Princess.

Is this as large a chainring as the ones on those police bikes? I do not know. Surely there is a way to calculate it. Maybe some readers will have comments on this question.