Cryptic crossword

ACROSS 1. Last course to go south in the Sahara (7)

5. One may spread disease, having aircraft on board (7)

9. Drape pans around to smooth things over (9)

10. Cheating the party by mixing the gin (5)

11. No top-liners show when night sky is clouded over (8)

12. Is of a mind to lament about it (6)

14. Duke, in short: His Grace might fire one (9)

16. Take place of crocus endlessly torn up (5)

17. Steamer that might have to take to the road (5)

19. Tex merely has to reform, but in the utmost way (9)

21. Free of depravity, he being new to it (6)

22. Forecasts it will be a long time for papers to get round it (8) 26. It is set at variance with its flavour (5)

27. The roving about might necessitate a stop until morning (9) 28. Gives soothing drug to steed as necessary (7)

29. Crime that might cause no tears (7) DOWN 1. Takes medicine which does upset the stomach initially (5) 2. Lands as required for such things as are afoot (7)

3. Dismiss one from school in Middlesex Pelham went to (5) 4. Records rugger scores for Bayeux and the like (10)

5. Compare outside pairs with the middle of the fruit (4)

6. Top roof-timber of lodge and pier formed by it (5-4)

7. Very silly of CID to put one out twice (7)

8. At set intervals it’s really rug that makes it (9)

13. How Bert met with ten and an improved living standard (10) 14. Explodes when note turns up among the fruit (9)

15. Speech made in hot situation for American bottom drawer (4-5)

18. I’d saved in the way I’d been counselled to (7)

20. Takes one on to see gang routed (7)

23. From the time that the South turned nice (5)

24. Isn’t a possible form of silken material (5)

25. Defeat of numerous soldiers held up (4)