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ELSIE MAY & ARTHUR ROBERT children of Robert Rutter & Emma Jane Bainbridge of 2 Coningsby Terrace Tarring Rd worthing in 1901
both children died in 1899 ElsieMay age 7 Arthur Robert age 2 both deaths registered @ East Preston Sussex . I am having difficulty finding birth records , I am convinced that they were both born in Worthing /Hove area Robert Rutter & Emma lived in Aldrington Hove in 1895 Daughter lillian was born there but Son Albert Stephen born 1899 in Worthing Emma Jane bainbridge Nee Bacon must have had a terrible year in 1899

????

Births Sep 1897 (>99%)
Baimbridge Arthur Robert Hendon 3a 202

Births Jun 1892 (>99%)
Baimbridge Elsie May E. Preston 2b 358

Marriages Jun 1891 (>99%)
Bacon Emma Jane E. Preston. 2b 643
Bainbridge Robert Ruter P E. Preston 2b 643

This looks like the family but mother's name is Jennie:

1901 England Census
about Albert Stephen Bainbridge Name: Albert Stephen Bainbridge
Age: 1
Estimated Birth Year: abt 1900
Relation: Son
Father's Name: Robert Bainbridge
Mother's Name: Jennie Bainbridge
Gender: Male
Where born: Worthing, Sussex, England

Civil parish: Worthing
Ecclesiastical parish: Holy Trinity
Town: Worthing
County/Island: Sussex
Country: England
Registration district: East Preston
Sub-registration district: Worthing
ED, institution, or vessel: 14
Neighbors: View others on page
Household schedule number: 79
Piece: 959
Folio: 131
Page Number: 12
Household Members: Name Age
Robert Bainbridge 53 , born Newcastle-on-Tyne
Jennie Bainbridge 33 , born Sussex, Worthing
Rose Lilian Bainbridge 5 , born Sussex, Brighton
Albert Stephen Bainbridge 1 , born Worthing

Emma and 2 sons in 1911. Says she's married but no husband with her. She's been married 19 years, 5 children, 3 still living.

1911 England Census
about Albert Bainbridge Name: Albert Bainbridge
Age in 1911: 11
Estimated Birth Year: abt 1900
Relation to Head: Son
Gender: Male
Birth Place: Worthing, Sussex
Civil parish: Worthing
County/Island: Sussex
Country: England
Street Address: 2 Tarring Road Worthing
Occupation: school
Registration district: East Preston
Registration District Number: 84
Sub-registration district: Worthing
ED, institution, or vessel: 12
Household schedule number: 272
Piece: 5331
Household Members: Name Age
Emma J Bainbridge 43
Albert Bainbridge 11
Robert M Bainbridge 7
Ada L Roake Lucas 54
Rose B Smith 44

Ada & Rose are lodgers.

Hi yes you have the right family apparently Robert Rutter almost always called Emma Jane his Jennie Robert was a blacksmith they married june 1891 so going by her death cert Elsie May was probably their first child she died 26th May 1899 aged 7 yrs second child would have been Lillian Rose born 27 May1895 @ 11 Lion Mews Aldrington Hove Sussex birth registered Steyning
Arthur Robert died 3rd August 1899 aged 2 yrs address on death cert is 62 Becket road West Worthing
Albert Stephen my Father was born 17th September 1899 also @62 Becket Road
Robert Matthew born 1904 was born at 2 Coningsby Terrace Tarring Road West Worthing
So far i have not been able to find birth certs for Elsie or Arthur that match date & timeline and am having same prob with Robert Rutter's death cert

But didn't safc post the births of Elsie & Arthur?