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Round 4
11 July 1978
| Barry (3) |
½-½ |
Ludgate (2½) |
| Barrington (2) |
1-0 |
Gibson (2) |
| Devenney (2) |
0-1 |
Curtin (2) |
| O'Hare (2) |
0-1 |
Short (2) |
| Wallace (2) |
½-½ |
Littleton (2) |
| Collins (1½) |
½-½ |
Blair (1½) |
| Killane (1½) |
0-1 |
McDaid (1½) |
| Palmer (1½) |
1-0 |
McDonnell (1½) |
| Galligan (1) |
1-0 |
Clarke (1) |
| Griffin (1) |
½-½ |
Carton (1) |
| Bergin (½) |
1-0 |
McCarthy (1) |
| Porter (0) |
1 |
Bye |
Scores after round 4
| Barry | 3½ |
| Barrington | 3 |
| Curtin | 3 |
| Ludgate | 3 |
| Short | 3 |
| Littleton | 2½ |
| McDaid | 2½ |
| Palmer | 2½ |
| Wallace | 2½ |
| Blair | 2 |
| Collins | 2 |
| Devenney | 2 |
| Galligan | 2 |
| Gibson | 2 |
| O'Hare | 2 |
| Bergin | 1½ |
| Carton | 1½ |
| Griffin | 1½ |
| Killane | 1½ |
| McDonnell | 1½ |
| Clarke | 1 |
| McCarthy | 1 |
| Porter | 1 |