By Dennis Murray BBC Ireland correspondent

Gerry Adams, the Sinn Fein president is frequently accused of being a member of the IRA's ruling body, the so-called Army Council.

At the same time, he is feted round the world as a peace-maker, as the man who is trying to take the gun out of Irish politics.

According to opinion polls, Gerry Adams is one of the most popular political leaders in the Republic

I saw Mr Adams in the sunshine in County Kerry, working on behalf of the party's candidate in the constituency of Kerry North, Martin Ferris.

I first saw Mr Ferris being led into the anti-terrorist Special Criminal Court in the mid 1980s in handcuffs, having been arrested aboard a trawler called the Marita Anne, which was laden with tonnes of guns, explosives and surveillance equipment.

Mr Ferris was sentenced to a lengthy jail sentence for being caught red-handed running guns. Was this a subject mentioned much on the doorsteps, I enquired?

"No", he said, "not at all. Sure that's history."

Real chance

Mr Ferris has a real chance of becoming a member of the Irish parliament in this general election, as does another party colleague, Sean Crowe, in one of the Dublin constituencies.

Sinn Fein at present has only one seat in that parliament, the Dail, but Gerry Adams and the rest of the party are hoping that when it sits again after the election, there will be three.

Sinn Fein has set its sights on more seats in the Dail

In any other parliament, that would make them a fringe party.

But such are the vagaries of the electoral system in the Republic of Ireland, that three seats might just hand them the balance of power.

The system is the single transferable vote. All the candidates are on the ballot paper, and voters put a number against the name of their choice - 1, 2, 3 - in order of preference.

I'll spare you all the technicalities and bizarre results this can produce, save to say that while, for example, 10% of the vote should equate to 10% of the seats, often it does not.

This is because of the old adage that all politics is local.

Local politics

Nowhere is that more true than Ireland, where there is an out-of-proportion number of independents, who are elected on single issues - the local hospital, television reception, and often to keep someone else out.

Sinn Fein is the only party organising north and south of the border

One member of the largest party, Fianna Fail, who some years ago was involved in a two-weeks after polling day count to decide who had won the last seat in his multi-seat constituency, told me:

"Power corrupts, and absolute power corrupts absolutely. But nothing corrupts as absolutely as the absolute lack of absolute power."

This was a lament about the dependence on independents to prop up minority governments, or the necessity of coalitions and about the absence of single party government - the last one to be elected was in 1997.

Gerry Adams, according to opinion polls, is one of the most popular political leaders in the Republic.

Cross-border campaign

Sinn Fein is one of the few all-Ireland parties organising both north and south of the border, and also appears to be one of the few that is getting political capital from voters for its involvement in the peace process.

Three seats does not sound like much, but the balance of power has rested on something similar - or less - in the past.

Former Eurovision winner Dana is running as an independent

That is because the mainstream parties - including the largest, Prime Minister Bertie Ahern's Fianna Fail, and the largest opposition party, Michael Noonan's Fine Gael - insist that because of the Irish Constitution, Sinn Fein cannot be part of a coalition.

That is because the constitution states that the country can have only one army, that of the state. No party can have its own private army - in this case the IRA.

Mr Ferris argues that if Sinn Fein's support is necessary then come the day, the main parties will come a-calling to horse trade. Sinn Fein also argues that there are no "organic links" between the party and the IRA.

Increasing electoral support might help persuade the un-reconstructable gunmen that the ballot box is more productive than the armalite

Really?

No one is conned by that - but it seems those likely to vote for Sinn Fein don't care that much.

Sinn Fein was, for more than half a century, an abstentionist party - arguing that real republicans should not vote at all with the country partitioned.

It split in 1986 over the issue of taking seats in the Dail. Now, though, it is as sleek a political machine as Ireland has ever seen - and after every vote it can get.

Here's a quirky final thought. There are those who revile Sinn Fein and all it stands for, who are hoping for a decent political result for the party. Why?

Because increasing electoral support might help persuade the un-reconstructable gunmen in the republican movement that the ballot box is, after all, more productive than the armalite.