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In the episode, leading criminologist Professor David Wilson is joined by investigative journalist Fiona Walker who travelled to Winchburgh in order to examine the century-old case, recounting the unique way in which the bodies had been preserved and how two eminent pathologists from Edinburgh helped crack the case.
However, as Walker also discovers, the solving of the horrendous case proved controversial when documents surfaced showing the investigation in a less than flattering light; the heart-breaking murders holding one last secret.
Walker tells how it all started one sunny Sunday afternoon in June 1913, when ploughmen Thomas Duncan and James Thompson, walking in Hopetoun Quarry, spotted a dark object in the water there.
Thinking it was a dead sheep soon they poked it with a stick only to realise it was two small bodies tied together with a window cord.
The police were alerted and the bodies taken to Linlithgow police station where the local doctor charged with carrying out a post mortem declared the bodies too badly decomposed to make an autopsy worthwhile.
The Procurator Fiscal disagreed and called in chief police surgeon Harvey Littlejohn and pathologist Sydney Smith.
They discovered both bodies exceptionally well preserved due to the body fat turning into adipocere, also known as corpse wax, a wax-like substance formed where the body's fat turns solid keeping organs intact.
A slow process, the adipocere allowed the examiners to reveal the bodies had been submerged for between 18 months and two years. They could also tell the bodies were those of two young boys, one aged around six, the other about four.
A final clue showing the contents of the boys' stomachs to be the ingredients of Scotch Broth, eaten in the late summer or early autumn of 1911, led to them being identified; that the meal had been eaten about an hour before their death meant they were local to the area and laundry marks on their clothes brought police to a lady who confirmed she had given soup to John and William Higgins on the last day they were seen alive in Winchburgh, in November 1911.
Police arrested their father, widower Patrick Higgins, a man who had previously been imprisoned for neglecting his sons.
Locals who knew him, told how they remembered seeing him walking with his boys towards the quarry. Once there, he tied the brothers together, picked them up and threw them as far as he could into the water.
Having been arrested at his Broxburn home in 1913, Higgins was brought to the High Court in Edinburgh where was tried for the murders, found guilty and, despite a claim of insanity, hanged in October, 1913.
The wasn't the end of the story, however, and in Crime Files, Wilson and Walker discuss the ethics of using stolen body parts as teaching tools for the next generation of doctors after it was discovered Littlejohn and Smith had acquired body parts of the murdered boys for their private anatomical museum.
David Wilson’s Crime Files, BBC Scotland, Sunday, 24 October, 10.30pm