Most of the children sent to live at the orphanage who died were buried in an unmarked mass grave at St Mary's Cemetery.
Headstones mark the graves of the nuns and staff members buried nearby but no stone or memorial has ever recorded the names of the lost children.
The revelation that up to 400 youngsters - and some adults - are buried there has provoked calls for Scotland's ongoing Child Abuse Inquiry to investigate.
Former First Minister, Jack McConnell, who, on behalf of the Scottish Government, apologised to victims of care home abuse in 2004, said it was shameful they were still waiting for truth and justice. He said: "It is heartbreaking to discover so many children may have been buried in these unmarked graves. After so many years of silence, we must now know the truth of what happened here."
Former residents have accused the nuns and staff who ran the home of beating and neglecting some of the children in their care.
Their allegations formed part of the campaign that inspired the ongoing Scottish Child Abuse Inquiry. The charity that ran Smyllum has already given evidence to the abuse inquiry, claiming earlier this year that abuse allegations were a "mystery" with "no evidence" of mistreatment.
The care given at Smyllum will be scrutinised during the second phase of the inquiry starting in November.
The latest revelations have provoked calls for those sessions to include an attempt to detail the children who died at Smyllum and discover exactly how many are buried in the graveyard at St Mary's.
Relatives of children who died at Smyllum are also calling for an immediate ground investigation at the cemetery using ground-penetrating radar to establish how many bodies are buried there.
The new probe involved scrutiny of thousands of death certificates.
In 2003, burial records given to campaigners by Smyllum bosses suggested 120 children had been buried at St Mary's but relatives believed the figure was too low. The latest figures come after 402 death certificates listing Smyllum as the place of death or normal residence were found in archives.
No details are recorded of the children's lives, apart from their names, date of birth and when they died. Causes of death include accidents and diseases such as tuberculosis, flu and scarlet fever. Some died of malnutrition. The research was carried out by Janet Bishop, of the Association of Scottish Genealogists And Researchers In Archives. She trawled through more than 15,000 official records. Most of the deaths occurred between 1870 and 1930.
It is believed most of the children, without parents or families able to pay for funerals, are buried at St Mary's.
Checks with surrounding cemeteries and local authorities found only two of the 402 laid to rest elsewhere.
11,601 children passed through Smyllum Park between 1864 and 1981, according to evidence given at the Scottish Child Abuse Inquiry.
The Daughters of Charity of St Vincent de Paul declined several requests for interview.
But, in a statement, it said: "We are Core Participants in the Scottish Child Abuse Inquiry and are co-operating fully with that inquiry.
"We remain of the view that this inquiry is the most appropriate forum for such investigations.
"Given the ongoing work of the inquiry we do not wish to provide any interviews.
"We wish to again make clear that, as Daughters of Charity, our values are totally against any form of abuse and thus, we offer our most sincere and heartfelt apology to anyone who suffered any form of abuse whilst in our care."
The Scottish Government said, as Smyllum is part of the inquiry, it would be inappropriate to comment.
- Daily Telegraph