Still can't work out why William (who should be about 6 years old) isn't on the census
IGI gives 
name: William Lindsay Brown 
gender: Male 
baptism/christening date: 15 Apr 1845 
baptism/christening place: WEMYSS,FIFE,SCOTLAND 
birth date: 11 Jul 1844 
father's name: Henry Brown 
mother's name: Margaret Davidson
1851 Census your William
Piece: SCT1851/459 Place: Wemyss -Fife Enumeration District: 4
Civil Parish: Wemyss Ecclesiastical Parish, Village or Island: Wemyss
Folio: 0 Page: 23 Schedule: 94
Address: East Wemyss
    Surname   First name(s)   Rel   Status   Sex   Age   Occupation   Where      LINDSAY   William   Head   M   M   40   Linen Weaver    Fife - Dysart        
    LINDSAY   Sophia   Wife   M   F   41   -    Fife - Wemyss        
    LINDSAY   Jean   Dau   U   F   19   -    Fife - Wemyss        
    LINDSAY   Jeremiah   Son   U   M   17   Warper    Fife - Wemyss        
    BROWN   William   Nephew   -   M   5   Scholar    Fife - Wemyss  
William Brown married Jessie Lessels (who I think was from Abbotshall
His Headstone inscription in Bennochy Cemetery
133   Erected by Jessie LESSLES in memory of her husband 
William L BROWN died 9.11.1895 age 51
   above Jessie LESSELS died 27.7.1925 age 78
   also James WILSON husband of Jessie BROWN
   died 5.5.1953 age 79
   Wife Jessie Brown died 2.5.1955 age 85
Norrie