He was born at the Shore in Leith on 23 February 1789 the son of Alexander Waddell, a "tide surveyor" (d.1806). It is likely that Alexander studied Navigation and Mathematics at Trinity House in Leith.
In 1806 (aged only 17) he appears in his own right in local street directories as an "inspector of yachts" living at Poplar Lane south of Leith Links. By 1810 he was in the same job but had moved to James Place in Leith.
By 1813 his job title changes to "inspector of cutters and boats" and it is clearer that he is in employment as a Government Customs Official.
By 1820 he is living at Hermitage Hill. He built an observation tower nearby, which may have served as a small observatory. This was called Hermitage Tower.
He appears to be father to both Alexander Waddell (a customs officer in Leith in 1830) and Andrew Waddell FRSE (who inherited his house at Hermitage Hill) and was also an amateur meteorologist.
In 1867 both a James Waddell and Peter Waddell FRSE are living at "Claremont Park" which was how Hermitage Hill was later known. Peter Waddell was also an astronomer and involved himself in lens design.
- Transactions of the Royal Society of Edinburgh 1823 vol.9
- Williamsons Directory 1785
- Edinburgh and Leith Street Directory 1806
- Edinburgh and Leith Post Office Directory 1810
- Buildings of Scotland: Edinburgh, by Gifford, McWilliam and Walker
- Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X. Archived from the original (PDF) on 4 March 2016. Retrieved 5 March 2019.
- Blackwoods Magazine vol 21 -1827- obituaries
- Edinburgh and Leith Post Office Directory 1830
- Edinburgh Philosophical Journal 1820
- Edinburgh and Leith Post Office Directory 1867.
- Practical Holography by Graham Saxby