▁of ▁this ▁kind ▁were ▁repeated ▁with ▁sufficient ▁accuracy ▁for ▁confirm ing ▁the ▁Lor ent z - E in stein ▁formula . ▁However , ▁this ▁problem ▁occurred ▁only ▁with ▁this ▁kind ▁of ▁experiment . ▁The ▁investig ations ▁of ▁the ▁fine ▁structure ▁of ▁the ▁hydro gen ▁lines ▁already ▁in ▁ 1 9 1 7 ▁provided ▁a ▁clear ▁confirm ation ▁of ▁the ▁Lor ent z - E in stein ▁formula ▁and ▁the ▁ref ut ation ▁of ▁Abraham ' s ▁theory . ▁ ▁Rel ativ istic ▁momentum ▁and ▁mass ▁ ▁Plan ck ▁( 1 9 0 6 a ) ▁defined ▁the ▁relativ istic ▁momentum ▁and ▁gave ▁the ▁correct ▁values ▁for ▁the ▁longitud inal ▁and ▁trans verse ▁mass ▁by ▁correct ing ▁a ▁slight ▁mistake ▁of ▁the ▁expression ▁given ▁by ▁Ein stein ▁in ▁ 1 9 0 5 . ▁Plan ck ' s ▁expressions ▁were ▁in ▁principle ▁equivalent ▁to ▁those ▁used ▁by ▁Lor ent z ▁in ▁ 1 8 9 9 . ▁Based ▁on ▁the ▁work ▁of ▁Plan ck , ▁the ▁concept ▁of ▁relativ istic ▁mass ▁was ▁developed ▁by ▁Gilbert ▁Newton ▁Lewis ▁and ▁Richard ▁C . ▁Tol man ▁( 1 9 0 8 , ▁ 1 9 0 9 ) ▁by ▁defining ▁mass ▁as ▁the ▁ratio ▁of ▁momentum ▁to ▁velocity . ▁So ▁the ▁older ▁definition ▁of ▁longitud inal ▁and ▁trans verse ▁mass , ▁in ▁which ▁mass ▁was ▁defined ▁as ▁the ▁ratio ▁of ▁force ▁to ▁acceleration , ▁became ▁super fl uous . ▁Finally , ▁Tol man ▁( 1 9 1 2 ) ▁interpreted ▁relativ istic ▁mass ▁simply ▁as ▁the ▁mass