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The pic showing the name is at an angle and is out of focus. It "looks like" Callann" to me, but nothing comes up. I also checked "Callahan" but nothing surfaced. I did discover that Birmingham is not in Alabama, USA, but rather in central England and is well known for its brass foundries that have existed since 1795. I also discovered a name of "Collerin" (1840) in Birmingham, a brass foundry. I can see that as a possible name; same number of letters, same sequence, but not confirmed.
Another item I found was the sliding cover over the front end. It was on a brass microscope made by J.P. Cutts & sons of Sheffield. It was dated 1834.
Please take a more focused picture. Rotate the scope so the name is in line with the picture. Use a pinch of flour, rub into the name, should make it more readable.
Dolland three draw leather covered brass telescope. Run of the mill, lots about, not a high value product, mass produced in the early 1800s
The name Dolland possibly became a generic name for telescopes with an achromatic objective lens, giving the better performance of the telescopes originally patented by Dollond in the 1760s. So Dolland telescopes became cheap copies of the Dollond standard.
This narrative was provided by "The Telescope Collector"
I read the name as Cattanu, personally. The name Cattani comes up occasionally, but never together with the name Fletcher. Many names on the telescopes appear to be opticians, either selling them as an optical instrument or maybe just advertising their business?
Any conection? The family is the Cattaneo family, who seemed to have originated in the Lombardy area of Italy and originally set up (I gather) in Croydon. However there's plenty of evidence of a network of Cattaneo watchmakers and jewellers across England. Henry, Anthony and Joseph operated in York, Ann and Seraphim in Durham, Peter and Pasqual in Croydon and Joseph in Folkestone. In addition there were a couple of companies such as Cattaneo & Co of Briggate Leeds, Cattaneo & Fletcher on Edgbaston Street Birmingham and a third family company (this time of cutlery merchants) named Vipont and Cattaneo based in Leeds and who knows how many others...??