A Chirtmas Eve poser
The basic problem here is that Peter's birth was illegitimate (at 71 South Street in Armadale), and there's no father's name on the birth register entry.
So we don't know if his mother Janet was a wee lass of 15 or an old maid of 40 .......... !!
There's no obvious death register entry for Janet, the mother, but there is the 1912 death of an 18 year old Janet, mother only shown as Janet WARDLAW, housekeeper, - no father's name shown, - the same description as on Peter's 1896 birth register entry, and that of Janet in the 1894 birth register entry in Armadale at 40 South Street, Armadale, - so near certain a sister to Peter, but see later qualification.
There's no appropropriately aged Peter that I can see in the 1901 census, unless he's been adopted into a relative's family, - not necessarily of the WARDLAW surname, - far from uncommon in such situations.
While WARDLAW might appear to be a relatively uncommon surname, as is often the case in such situations, there can be several or even many families within a neighbourhood, complicated in this case by the various possible parishes spreading across the N/NW of West Lothian, the NE of the county of Lanark, and the SE of the county of Stirling ..................
There are only a few Janets of the right age in the 1891 census in W Lothian, all but one of whom are identifiable as members of other WARDLAW families, altho' that's not to say that "a daughter" in such households is a natural daughter, as opposed to an adopted daughter......
But there is a very attractive 1891 census entry where the Janet in question is shown as the granddaughter of the Head, a 62 year old Peter, and this 1891 census entry probably shows a son Robert, - the informant on the 1912 death register entry being Robert WARDLAW, Uncle ....... Murphy's Law cuts in here in that the 1891 image is quite faint, and Robert ain't
that usual a given name in Scotland, - but there is a linked 1883 birth register entry for Robert connecting to this Peter and his wife in the 1891 census.
All speculation of course, and subject to my qualification above in terms of the complication of even unusual surnames not being that straightforward to research when there are several lines in the same small area.
In this case, by exhaustively researching the WARDLAW lines in the parishes of N/NW of West Lothian, the NE of the county of Lanark, and the SE of the county of Stirling , it
might just be possible to approach a near certain conclusion in terms of Janet's parents ....................
David
