That sounds ASB to me. How'd they be able to develop it that quickly? I know they once had a faulty field pice which could sometimes shoot a large hail of bullets all at once, but the jump from that to even a gatling gun seems a tad much for 1775.1775 - The French develop the very first version of the Machine gun and add it to their army.
I know that it seems ASB. But the fact is that in OTL, the development of the very first version of the machine gun was in 1718.
http://en.wikipedia.org/wiki/Puckle_Gun
I think that this only needs a more interested king.
Mind you, in 1775 it'd've had 57 years to improve upon, if given proper funding and support.TBH, there's a fine line between advancing technology and going a step too far. The Puckle gun might've worked, and indeed it did fire quickly, but how would reloading it have gone? Was it man-portable? Did it jam easily? Was it cheap?