The amount of information in on-line databases is quite staggering. In just a couple of hours yesterday here's what I managed to dig up about the Gayden family:
From the United States Social Security Death Index on the Rootsweb site:
JOSEPH A GAYDEN, born 08 Dec 1898, died 07 Feb 1992, De Kalb county, Illinois.
EDMUND C GAYDEN, born 15 Apr 190, died 15 Jul 1967, Cook County, Illinois.
Confirmed their births on the FreeBMD site, and that of their elder brother, John:
John Howard Gayden, born December 1896 Qtr, Mile End Old Town, Middlesex.
Joseph Fletcher A Gayden, born March 1899 Qtr, Mile End Old Town, Middlesex.
Edmund Colley Gayden, born June Qtr 1901 Shoreditch, London.
and wrapped it up with a couple more death records from the Illinois State Archives:
Gayden, Samuel Nathaniel, male, white, died 14 February, 1930, Cook County, Chicago.
Gayden, Susanna E., female, white, died 21 March, 1947, Cook County, Maywood Village.
Hmmm, Maywood Village, that's an interesting place.
But no sign of young John, unless this is him in the Commonwealth War Graves Commission database:
Gayden, J., Gunner, died 08/07/1916, age unknown, Royal Garrison Artillery, 152nd Heavy Battery, buried in Warloy-Baillon communal cemetery extension.
Ten years ago I wouldn't have found anything. We've come a very long way in cyberspace.