In 1876 there would not have been anything that could be done for a baby born too early, or with any significant problem. They either survived or they didn't, and the mother and her female supporters just did their best. While medical care existed, there was very little that was available at that time for this problem. According to my mother, who is 90 next month, it was accepted that sometimes babies did not survive when she was a girl.
When I started my midwifery training in 1976, it was quite a big deal if a baby was born at 36 weeks, a real big deal if they were born at 32 weeks, and not very likely to survive with any quality of life if born at 28 weeks. If they did so, they became locally famous for a while. I can recall only one or two from that period where I worked. At that time, the viability age was 28 weeks.
Nowadays, healthy babies born at 36 weeks get the same care and have the same outcomes as babies born at full term. Those born at 32 weeks are expected to do well, as are many born at 28 weeks. It would depend upon whether there were any additional problems apart from being 'undercooked'. The viability age has been reduced to 24 weeks, although babies born at this stage might be expected to have some long-term health problems.
So, to make a stab at answering your question, I would suggest that a baby born more than 4 weeks early in 1876 might not do too well.
I hope that is helpful?