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The Romans themselves were a little less... er... hands-on than the Etruscans. One of the 'official' forms of Roman divination was augury. At its core, augury involved observing the sky for signs from the gods. An augur would 'inaugurate' a region in the sky as his templum (a word which could denote any sacred area, not just a physical building). Then he would watch how birds flew across this region (did they fly from left to right? or right to left?), or for bolder signs like lighting (Jupiter clearly had something to say then...)
Unlike other forms of divination, augury was not intended to foretell future events - it was rather used to find out whether the gods approved of some course of action. So for example, before setting off on a military campaign, an augur would have to check with the gods - did they have permission to set out? (Always best to have Jupiter willing.)
Augurs were also consulted before assemblies - if the gods didn't approve, the assembly wouldn't be held. If some sign became apparent during an assembly, the assembly would be adjourned. Even the acts of assemblies could be made null & void, and in fact the college of augurs could even declare an election invalid. This happened in 163 BC, when the father of the Gracchi (at the time a consul and an augur) suddenly 'remembered' that he forgot to take the auspices before crossing the pomerium (the city's sacred boundary) for an assembly. The two new consuls who had been elected in that assembly were forced to resign their office. 'vitio facti abdicarunt' was recorded on the list of magistrates.
Clearly the opportunity for political manipulation was great...