In the middle of all Edinburgh's celebrations after finally beating Glasgow and reclaiming the 1872 Cup, there was one nagging doubt.

They have won big games earlier this season and every previous glint of dawn has turned out to be a false one. Was the Glasgow win a blip, or the start of a significant change?

The test comes on Friday when they travel to Galway to face Connacht, the only side to have won at Murrayfield this season. Stevie Scott, the forwards coach, has labelled it an old-fashioned eight-pointer they have to win to keep up the pressure for a place in the top six of the Guinness PRO12 and with it a spot in next season's European Champions Cup.

"I spoke to the forwards when they came back in, and said I was delighted the way they played [against Glasgow]; I was really happy they had managed to perform like that and show real heart and desire.

"I also said we had been here before and we needed to get back on the training field and learn the things we could do better. There were lots of things in the game that weren't great and we need to learn from that, practise this week and take it on to the next game.

"It was great to get the result and win by more than 10 points to get the cup, and we enjoyed the weekend, but now we need to make sure we build on that. It will be very tough in Connacht. It is a tough place to play in the conditions they have - there is never much apart from wind and rain there. They got one over Munster at the weekend so they will be in a good place as well. We can't go beyond our next game."

Just look at this season. Edinburgh opened with a brilliant win over Munster in Limerick, but then lost to Connacht before being thrashed by the Ospreys; they beat Cardiff but then lost to Zebre; they won both their opening European Challenge Cup fixtures against Bordeaux and Lyon but then conceded five tries in losing at Leinster. Every apparent gain has been followed by a reverse.

This week has a slightly different feel to it compared to the previous successes, though. The earlier ones looked more like one-off wins, whereas this time they are coming off a run of success with a double over London Welsh followed by hammering Treviso and even though they lost the away tie against Glasgow, they gave as good as they got for 75 minutes with two mistakes just before half-time the only thing that separated the sides.

As a result, this time there is a run of form to back up their big win. Looking at the way the forwards have come together in recent weeks, even though key players such as Grant Gilchrist, the club's vice-captain, have still to return from injury, Scott can be reasonably happy with the job he has done.

Connacht, however, have been the surprise package of the season, underlining their sudden rise to become genuine contenders in the PRO12 with last week's win over Munster. More important, they are the side currently in sixth spot, the place Edinburgh, currently eighth, are gunning for.

"If you look at getting into that top six, you need to beat the teams around you and the teams below you," Scott pointed out. "If you can get a couple of results against the teams above you that is even better, but these games are important to us and this one is a very important with them getting their win at the weekend. It will be an eight-point swing if you want to look at it like that.

"The game against them at Murrayfield still hurts too. If we had won we would have been unbeaten at home this season. We did not play well at all but also there were a few things that went against us, we should have got a scrum penalty at the end - another day with another referee we might have got it. But the performance was not good enough."