Below is a list of eight interments in the Dalziel Parish cemetery in Motherwell, usually called the Globe cemetery. All 8 are interred in public ground, sometimes called common ground. In other words, they had a pauper's burial. Some had the AR spelling of Millar, while some had the ER spelling, I have transcribed them all here as MILLAR, for consistency. All dates are of interment, you can probably knock off 2 days to get the exact date of death.
They may help fill in some blanks in your family tree.
MATTHEW THOMSON MILLAR. 15 Cowie's Square. Aged 9 months.
Parents - Archibald Millar & Isabella Paterson.
28th December 1876.
JOHN MILLAR. Craigneuk. Aged 8 months.
Parents - Archibald Millar & Isabella Paterson.
24th November 1880.
WILLIAM PATERSON MILLAR. Craigneuk. Aged 8 months.
Parents - Archibald Millar & Isabella Paterson.
26th March 1887.
STILLBORN CHILD MILLAR. 201 Windmillhill Street. (Motherwell).
Parents - John Millar & Isabella Gardner.
27th March 1890.
ALEXANDER MILLAR. Craigneuk. Aged 1 year.
Parents - Archibald Millar & Isabella Paterson.
2nd December 1891.
ARCHIBALD MILLAR, miner. 216 Craigneuk. Aged 63 years. Married.
Parents - James Millar & Ellen Thomson.
25th December 1897.
ALLAN MILLAR. 9 McDonald's Land, Craigneuk. Aged 1 year.
Parents - James Millar & Isabella B. Gardner.
16th October 1900.
MATTHEW THOMSON MILLAR. Burnside's Land, Craigneuk. Aged 13 months.
Parents - James Millar & Isabella Gardner.
19th August 1902.
A "Land" here in Scotland referred to a "land of houses", usually but not always, a tenement building (of various sizes). Mostly they were named after the proprieter, in this case - McDonald and Burnside.