Future weapons based on LAMA small SPOILER.

I would be looking at the next evolution of weapons to be repeating rifles. The Allin breech loader has already been introduced to Safehold. A rifle like the early Spencer with the the Blakeslee Cartridge Box could be the next advance. The rate of fire of the infantry would take a leap, something that RFC seems to like.

I wonder if the Gatling gun in in the Empire's future?

Plenty of threads here which argue against multi barrel, hand cranked machineguns. This is a valid argument when you consider many of the early hand cranked machineguns were the size and weight of field artillery pieces, but also tactically employed as artillery as well. George Armstrong Custer may have had this in mind when he declined the Gatling gun detachment before taking the 7th Cavalry to the Little Bighorn valley...

Many of the arguments against machine guns on Safehold at this time are also based on logistics; the sheer amount of ammunition that will need to be made and transported to the front lines will be a giant issue.

Firepower does not have to be about automatic or semi automatic weapons, the highly trained British Regulars who fought in the opening battles of the Great War could deliver punishing firepower from their bolt action Lee-Enfield rifles through virtue of their long hours of practice (indeed, their forefathers in the Napoleonic Wars could deliver punishing firepower from their muskets for much the same reason), during the opening of the Great War British battalions had only two machineguns each, the aimed accurate firepower of the riflemen was what prevented the British from being brushed aside and swept to the sea.

One of the reasons that the British moved so heavily into machine age warfare during the Great War was the high rate of casualties prevented the long and detailed training of troops on the pre war model, and the Triple Alliance could muster far more manpower than the British on the Western front. The global Empire required the British to divert vast numbers of troops and sailors to man distant outposts. Increasing mechanization (machine guns, poisoned gas, more and more artillery and eventually tanks, "contact patrol" aircraft and most importantly the increasing mechanization of logistics) increased the fighting power of each troop, and the evolution of tactics allowed this fighting power to be used more and more effectively.