The third-wicket pair put on 141 in 45 overs to lead their side from 20-2 in their second innings, 34 runs behind, to a lead of 107 when Kohler-Cadmore was dismissed.
Ballance struck 83 not out, Kohler-Cadmore 69, and Yorkshire had reached 207-3, 153 in front, when rain washed out play from just before tea.
Whether there can still be a positive result remains to be seen, but Kohler-Cadmore is hopeful as Yorkshire pursue a third win in four Championship games.
“I think we’re in a good position,” he said.
“The rain was obviously a frustration, but me and Gary had a nice little partnership there and there’s still enough in the pitch to make sure that we’ll definitely be able to get ten chances (with the ball).
“It’s going to be interesting to see how we play it.
“It’s a funny one because you don’t want to give them too much of a sniff – say we go really hard in the morning and get bowled out with a lead of 200, then they’re well in the game – but we also don’t want to get too many ahead that they just kind of think, ‘Well, we’ll shut up shop from ball one.’”
As Yorkshire set about improving their position on a murky third day, with Hampshire having failed to make the most of a positive situation earlier in the match, there was intrigue off the field as well as interest on it.
Shortly before lunch, it emerged that the England and Wales Cricket board has applied for trademarks for the names of six of the eight franchises for its 100-ball tournament that starts next year – Leeds Superchargers, Birmingham Phoenix, London Spirit (Lord’s), Welsh Fire (Cardiff), Southern Brave (Southampton) and Trent Rockets (Nottingham), with names for the franchises at the Oval and Old Trafford yet to be decided.
The ECB had planned to reveal the team names/brands after the Ashes in September, but, in a development that rather characterised the chaotic nature of PR/marketing for the competition, they contrived to leak out when a trademark expert contacted the London Evening Standard to say that he had seen the various registrations.
Yorkshire were yesterday keeping their part of the bargain by declining to comment on the leaked information, although it is understood that none of the eight planned venues, including Emerald Headingley, has yet to sign a hosting agreement.
“Shambolic” might be too soft a word to describe events which have dogged this concept from the outset, one which an estimated 90 per cent of cricket fans perceive to be about as welcome as a summer cold.
Back to the cricket… the proper stuff, of course, and Yorkshire fared well after resuming on 5-0, still 49 behind.
There were a couple of early setbacks as the opening batsmen each went for nine – Harry Brook and Adam Lyth both caught by Joe Weatherley at second slip off left-arm pace bowler Keith Barker, at which point the mood around Headingley was somewhat gloomy.
But Kohler-Cadmore arrived and whipped Fidel Edwards off his pads to the boundary to get off the mark, off-drive him for another four and then on-drove Barker to the rope at the Emerald Stand end, as if to say: “Don’t worry, Yorkshire supporters, it’s going to be alright.”
Ballance, fresh from the rarity of a first-innings failure, confirmed a growing sense of confidence about the place, batting in a manner that suggested he was in no mood to miss out for a second time.
When play restarts, Ballance will have the opportunity of a fifth century in successive Championship matches dating back to the final game of last season.
Although some seem loath to countenance the prospect of him returning to the Test team, it will be difficult for England to ignore him if keeps playing like this.
Critics harp on about Ballance’s technique – most of them ex-players – but it is not about how you score runs but whether you score them.
This innings was full of trademark nudges, pulls and meaty drives, with only a loud lbw shout from Edwards when Ballance was on 16 interesting the visitors.
Kohler-Cadmore, who played well in the first innings, did so again without going on to the big score that he naturally craves.
The total had reached 161 in the 54th over when he was lbw to Ian Holland having faced 156 deliveries and hit 10 fours.
Jack Leaning helped Ballance add an unbroken 46 inside 12 overs, pulling the leg-spin of Mason Crane to the boundary as the floodlights came on.
At 80-2 in reply to Yorkshire’s first innings 181 when Ajinkya Rahane and then Rilee Rossouw threw their wickets away on day two, Hampshire have wasted a promising platform.
The question now is: can Yorkshire take advantage?