Yorkshire trailed Sussex by only 46 runs with six wickets remaining at stumps on Thursday but heavy rain at Hove prevented their progress on day three.
Visiting first-team coach Jason Gillespie even took to the field in his bare feet to get his own take on the conditions.
Durham, however, managed to add 88 more runs to the 82 they scored against Derbyshire on day two, without loss, and respective contributions of 59 and 50 from Borthwick and Smith boosted the cause as they closed in on a first batting point, reaching lunch on 172 for two.
Middlesex and Nottinghamshire were also thwarted by the morning weather at Lord's but Surrey managed to close to within nine runs of Somerset's total at Taunton despite an early rain delay.
Dominic Sibley (12) and Hashim Amla (nought) were both bowled by Lewis Gregory - but Rory Burns and Vikram Solanki contributed 39 runs.
In Division Two, promotion favourites Lancashire declared on 453 for four at Emirates Old Trafford after Paul Horton reached 156 off 268 balls.
Leicestershire's response got off to an inauspicious start as Oliver Newby took the wickets of Greg Smith (nought) and Angus Robson (nine) before Kyle Hogg had Ned Eckersley caught behind by Alex Davies for just four runs.
The visitors reached 17 for three by lunch to trail Lancashire by 436 runs.
The resumption of Kent's second innings in Canterbury was delayed until 12:40pm but there was enough time for Sam Northeast (nine) and Robert Key (15) to add 24 runs and close to within 145 runs of Essex for no loss before the break.
The wet weather meant there would be no early play at New Road, though, with hosts Worcestershire left trailing Hampshire by 327 runs with eight wickets remaining.
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