An automatic totalisator is a device to add up the bets in a pari-mutuel betting system. The whole of the pot (the stakes on all competitors) is divided pro-rata to the stakes placed on the winning competitor and those tickets are paid out.
Essentially it implements a system of starting price (SP) betting.
In particular it refers to the invention of George Alfred Julius, the English-born, New Zealand educated, Australian inventor, engineer and businessman, a leader of Australian engineering in the first half of the twentieth century.
The term automatic refers to the face that the bets were automatically summed and a ticket issued when a bet was registered on the issuing machines, and it provided a safe and virtually fraud free method of betting, replacing the earlier jam-pot totes, which used either paper transactions or some method of counting bets like steel ball bearings. The machine did not actually calculate the payout.
It is a nice example of the gradually automation of calculation before the computer industry which owed nothing to Julius' invention got going.
The method was widely used in the Australian, New Zealand and American horse-racing industries and for greyhound racing in the UK, though there were other installations in countries as diverse as France, Venezuela and Singapore.