A printer provided with a dampening apparatus, the dampening apparatus comprising: a roller coming into abutment with a plate cylinder; one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder; and a dampening water amount regulating apparatus, and being configured in such a manner that dampening water is transferred from one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder to the roller coming into abutment with the plate cylinder, wherein the dampening water amount regulating apparatus includes a plurality of air supply boxes disposed in a line in an axial direction of the one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder, an air supply pipe that supplies air to any one of the air supply boxes, an air discharge pipe that sucks air from any one of the air supply boxes, and valve mechanisms that increase and decrease an amount of the air for each of the air supply boxes, characterized in that each of the air supply boxes includes an air supply chamber that receives a supply of air, an air discharge chamber that discharges air, an air blowing portion that communicates with the air supply chamber and blows the air to the one of the one or more rollers (5, 7, 8) other than the roller that come into abutment with the plate cylinder and an air blowing passage that communicates with the air discharge chamber and allows the air blown from the air blowing portion to pass along the outer peripheral surface of the one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder, wherein the air supply chamber and the air discharge chamber, of each air supply box, are communicated with their respective counterparts (57, 60) in adjacent air supply boxes, wherein the air blowing portion and the air blowing passage, of each air supply box, are partitioned from their respective counterparts (58, 59), in adjacent air supply boxes, by diaphragms (61, 62). a roller coming into abutment with a plate cylinder; one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder; and a dampening water amount regulating apparatus, and being configured in such a manner that dampening water is transferred from one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder to the roller coming into abutment with the plate cylinder, wherein the dampening water amount regulating apparatus includes a plurality of air supply boxes disposed in a line in an axial direction of the one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder, an air supply pipe that supplies air to any one of the air supply boxes, an air discharge pipe that sucks air from any one of the air supply boxes, and valve mechanisms that increase and decrease an amount of the air for each of the air supply boxes, characterized in that each of the air supply boxes includes an air supply chamber that receives a supply of air, an air discharge chamber that discharges air, an air blowing portion that communicates with the air supply chamber and blows the air to the one of the one or more rollers (5, 7, 8) other than the roller that come into abutment with the plate cylinder and an air blowing passage that communicates with the air discharge chamber and allows the air blown from the air blowing portion to pass along the outer peripheral surface of the one of the one or more rollers (5, 7, 8) other than the roller that comes into abutment with the plate cylinder, wherein the air supply chamber and the air discharge chamber, of each air supply box, are communicated with their respective counterparts (57, 60) in adjacent air supply boxes, wherein the air blowing portion and the air blowing passage, of each air supply box, are partitioned from their respective counterparts (58, 59), in adjacent air supply boxes, by diaphragms (61, 62).