The boat race at Brunswick between the Kate Kenan belonging to Mr. Randolph Spalding, and the John Dufour, belonging to Mr. David Baily, took place on Monday, the distance being one mile. The Kate Kenan came out winner by some fifty yards. The su bet was $1,000 a side, besides several large amounts by others, making altogether as much perhaps as $10,000. The Kate Kenan was rowed by blacks and the John Dufour by whites--each boat having six oars.