Sorry if my reply is a comment and not more concrete info, but I can't help trying to read the human story behind the dates. It's so sad, this desperate attempt to have a son who must have the name Isaac we can read in the two deceased infants and the third child who lived. It must have been this couple's dearest wish.
How tragic the death of a father only a couple of weeks after his son's birth. A young widow with an infant, not easy in Hawick in those days.
Interesting that someone died in Edinburgh but his son back in Hawick. My grandfather Andrew Bowie also lived for a time in his youth in Edinburgh, but returned to live in Hawick as an adult, going back only when he was on his deathbed to pass away in the Edinburgh Royal Infirmary of lung cancer from his forge in Havelock St (Wilton).
The passing on of a name seems to have been SO important in Hawick, the Bowies in my branch are all James or Andrew, with other names creeping in only for rare third sons.
For anyone who is interested: Hawick at the time many of the Isaacs listed didn't make their second birthday seems to have been suffering economic depression. Many were stocking makers and worked in their own homes, now unable with their hand looms to compete with the Leicester and Nottingham mechanised trade. One Bessie Sanderson, 13, commenced work at 7am and finished at 6pm, after which she did seaming work till 9pm. Her youngest colleague was 8 years old.
One Colin Rae, 11, worked from 6 or 7am till 8pm as a winder, two 45-minute breaks to eat.
May Bell, 7, was a winder in her father's stocking shop and for the rest of the day looked after the younger children.
Very few children attended school after 9 years of age.
(from my wonderful book: Hawick in the early sixties, James Edgar, publ. The Hawick Express Office, 1913)