It returned one Member of Parliament (MP) to the United Kingdom House of Commons, elected by the first past the post voting system.
The MP, Professor Eoin MacNeill, was also returned for National University of Ireland.
As MacNeill did not take his seat in the United Kingdom House of Commons he could not choose which constituency he would represent and arrange a by-election in the other.
Dowse resigned after being appointed Chief Baron of the Irish Exchequer, causing a by-election.
Hamilton is appointed Treasurer of the Household, prompting a by-election in which he stood unopposed.