1st Son after Father's Father ie. Paternal Grandfather.
2nd Son after Mother's Father ie. Maternal Grandfather.
3rd Son after Father.
4th Son after Father's eldest Brother.
1st Daughter after Mother's Mother ie. Maternal Grandmother.
2nd Daughter after Father's Mother ie. Paternal Grandmother.
3rd Daughter after Mother.
4th Daughter after Mother's Eldest Sister.
The naming pattern seems to be the same for both England and Ireland between 1700 and 1875.
But beware!! You will sometimes find 2 children of the same name, but the eldest child may have died young and then the name was given to another child down the line in the same family with same parents or parent.
Also, don't forget the ones who were named after a relative, but died without being registered.
The naming pattern can be a help but it is not completely reliable.
The name was sometimes used for the middle name of a new born.
Sometimes even if the child's first name was after a relative, the child used his middle name for legal purposes instead of the relative's name.