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