His maternal grandmother , was a mare who was never given a name and was sired by Old D. J. Art Pollard bought Della P from `` Dink '' Parker for $ 1,750 ( $ as of ) in the late 1940s . His second dam , or maternal grandmother , was a mare who was never given a name , sired by Old D. J. Art Pollard purchased Della P from `` Dink '' Parker for $ 1,750 ( approximately $ as of ) in the late 1940s .