Jay died of lye poisoning when John Martin's sister (Jay's paternal aunt -- John Martin's sister) was babysitting him. (I was told that that it was Amy Martin -- who went on to marry a Hopping.)
Folk lore has it that her hair turned grey soon after that because she felt so bad about Jay's poisoning under her care. (I have my doubts about that part of the story.) Jay's remains were interred with his mother Kitty when they move their remains from Abbyville to Partridge since that is where her mother Sarah Belle Hawkins was buried. Grandma Dorothy said they could only identify her remains by the shoe buckles that her family knew she was buried with.
Update: George Ellis was the grandson of George Garfield Martin (via his daughter Anna Vendetta). He was the family historian, though he died in 2004, his widow (Edith Ellis) has given me a bit more info. Jay's full name was:
William Jay Martin. He went by the name Jay, but also the name "Willie" comes up. His name makes sense as William was John Martin's dad's first name, and Jay was Kittie (Hawkins) Martin's father's middle name.
Likewise, she had his dates as:
(1-6-1875 - 2/23/1876)
Updated (15-May-2015) with a newspaper article:
This is from the Hutchinson News, Thursday March 2, 1876
"From Westminster [that is the township where Abbyville is located and John Martin's homestead was known as the Lone Star.]
A little son of John Martin, Esq., of Westminster, died on Wednesday of last week, under the following circumstances; Mrs. Martin had been sick for about a month and the child which was about a year old had been sent to the residence of Mr. Thos. Hoppings, who is a brother-in-law of the Martins, and Mrs Hoppings was taking care of it. On Tuesday, Mrs Mrs Hoppings was washing. She had a box of concentrated lye setting on the table near. She had just poured the water off of it leaving a little in the box. She went and set down for a while, and suffering with a headache, she leaned her head on the bed. While there the child ___ [cannot read word] got into the box and drank the lye. Medical aid was called at once, but no relief could be given. It died the next day. Rev Mr. Fryrear [cannot read his last name] preached the funeral and the remains were interred at Westminster cemetery on Thursday. While the circumstances cast a gloom over the entire community no blame attaches to Mrs. Hoppings."
NOTE: Mrs Hopping was known as Aunt Amy. Amy (Martin) Hopping (no s on the surname) was John Martin's sister, and the second to the youngest. (John was the youngest.) AMy married Thomas Hopping and was the only other Martin to settle in Kansas.
Note that some years after Kitty died, Kitty and Jay's remains were moved from Abbyville (I assume that is the Westminster cemetery they are talking about) and move them to Partridge. I am guessing Partridge because that is where the Hawkins buried. (Note that Abbyville & Partridge are only 7 miles apart...) The remains were so decomposed, that the only way they were able to identify them were by the shoe buckles that Kitty wore at the time of her death. They had not decayed They buried them together in Partridge.