If you look at the research section of iomfhs.im you will find indexes to births, marriages and burials.
The births show children born to Archibald and Elizabeth Braid:-
Eleanor Emily 1892 - buried 1900
Elizabeth Jane 1897 - buried 1898
Leah Robina - misread as Sarah
Margaret Annie - Anne
Walter 1901
Since Elizabeth died 1901 then William Walter may belong to Eleanor Mary Sheard if he is not Walter 1901.
In the birth index there is an Eleanor May Braid 1904 and an Archibald 1908 who died after 1 day. They may belong to the new marriage but it would limit the scope for a birth in 1903.
The burials show Archibald, the father was buried 1910.
You need to search the birth register to find if William Walter 1903 was another child.
Len Faragher