a bromine atom or x u2212 is a methyl sulfate ion and wherein r 4 is a hydrogen atom or a methyl group and wherein r 5 and r 6 is a hydrogen atom or a methyl group n is 1 4 inclusive and m is 1 or 2 the synthetic sizing agent may be any sizing agent that can imparts desired sizing properties preferred sizing agents include alkenyl succinic anhydride asa and alkyl ketene dimer akd and alkeno ketene dimer alkyl isocyanates and alkyl anhydrides the vinyl monomer i may be a quaternary ammonium group containing vinyl monomer produced by quaternizing a dialkylaminoalkyl ester of acrylic acid or methacrylic acid with an alkyl halide or alkyl sulfate specific examples of the vinyl monomer i include quaternized products resulting from dimethylaminoethyl acrylate diethylaminoethyl acrylate dimethylaminoethyl methacrylate diethylaminoethyl methacrylate etc as the quaternizing agent there may be exemplified methyl chloride methyl bromide methyl iodide ethyl bromide etc the vinyl monomer ii includes acrylamide and methacrylamide these monomers are effective in increasing the molecular weight of the resulting polymer due to its high polymerizability they are also effective in improving the water solubility of the produced polymer the vinyl monomer iii may include hydroxymethyl meth acrylate 2 hydroxyethyl meth acrylate hydroxyprolyl meth acrylate and hydroxybutyl meth acrylate the vinyl monomer iiia may include 2 3 dihydroxypropyl meth acrylate and 3 4 dihydroxybutyl meth acrylate the cationic charge of the cationic.