Well, what you have there seems rather self-evident: it is a March-Davis "Admiral".
March-Davis Cycle Mfg. was a fairly regional manufacturer, incorporated in Chicago in 1892 by August R. March and Walter Davis. The company lost most of their manufacturing business located on Canal Street in a large fire in January of the following year, but with insurance money they made a comeback, selling throughout the years of the Great Boom.
As successful as they were for a while, the two principals didn't always see eye-to-eye:
By 1895, March-Davis had joined the National Cycle Board of Trade and promoted their wheels at the first ever Cycle Show in Los Angeles at Hazard's Pavilion. Their booth was notable for the presence of the famous clown Billy Burke (father of Glinda the Good Witch) as an attraction.
(^^Not even kidding - that's Billy Burke.)
In 1896, March Davis moved their manufacturing concern to a factory at the corner of Columbus and Wabansia, with a retail outlet on Washington. Eventually they had outlets as far away as Post Street in San Francisco, and on Broadway in New York, selling the "Admiral" and "March" marques.
Sadly, it seems the weight of these promotions and far-flung stores along with the flagging prices of cycles led to the "bust" of March-Davis in May of 1896.
By 1897 their $100 bikes were selling for under $30 bucks, and it was downhill from there.
The company was reorganized by the courts and struggled on for a while, but the rot had set in, and after about 1899 the once proud March-Davis Cycle Manufacturing Company disappeared without a trace, as far as I know.
And now I've told you probably more than you ever wanted to know about the history of your bike.
It's a sad, familiar story.