How did Griffith experiments show that hereditary factor was involved in the bacterial transformation?

Griffith's experiments, conducted in the 1920s, demonstrated that non-virulent strains of Streptococcus pneumoniae could be transformed into virulent strains when exposed to heat-killed virulent bacteria. He observed that when live non-virulent bacteria were mixed with the heat-killed virulent bacteria, some of the non-virulent bacteria took up the hereditary material from the dead bacteria, becoming virulent themselves. This transformation indicated the presence of a "hereditary factor" that carried the information necessary for virulence, laying the groundwork for the later discovery of DNA as the genetic material.